| line |
stmt |
bran |
cond |
sub |
pod |
time |
code |
|
1
|
|
|
|
|
|
|
#!/usr/bin/perl -s |
|
2
|
|
|
|
|
|
|
## |
|
3
|
|
|
|
|
|
|
## Crypt::Primes -- Provable Prime Number Generator |
|
4
|
|
|
|
|
|
|
## for Cryptographic Applications. |
|
5
|
|
|
|
|
|
|
## |
|
6
|
|
|
|
|
|
|
## Copyright (c) 1998-2000, Vipul Ved Prakash. All rights reserved. |
|
7
|
|
|
|
|
|
|
## This code is free software; you can redistribute it and/or modify |
|
8
|
|
|
|
|
|
|
## it under the same terms as Perl itself. |
|
9
|
|
|
|
|
|
|
## |
|
10
|
|
|
|
|
|
|
## $Id: Primes.pm,v 0.49 2001/06/11 01:04:23 vipul Exp vipul $ |
|
11
|
|
|
|
|
|
|
|
|
12
|
|
|
|
|
|
|
package Crypt::Primes; |
|
13
|
|
|
|
|
|
|
require Exporter; |
|
14
|
3
|
|
|
3
|
|
48392
|
use vars qw($VERSION @EXPORT_OK); |
|
|
3
|
|
|
|
|
8
|
|
|
|
3
|
|
|
|
|
321
|
|
|
15
|
3
|
|
|
3
|
|
14151
|
use Crypt::Random qw( makerandom makerandom_itv ); |
|
|
0
|
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
16
|
|
|
|
|
|
|
use Math::Pari qw( PARI Mod floor sqrt); |
|
17
|
|
|
|
|
|
|
*import = \&Exporter::import; |
|
18
|
|
|
|
|
|
|
|
|
19
|
|
|
|
|
|
|
@EXPORT_OK = qw( maurer trialdiv rsaparams ); |
|
20
|
|
|
|
|
|
|
( $VERSION ) = '$Revision: 0.50 $' =~ /(\d+\.\d+)/; |
|
21
|
|
|
|
|
|
|
|
|
22
|
|
|
|
|
|
|
## list of small primes for trial division. |
|
23
|
|
|
|
|
|
|
|
|
24
|
|
|
|
|
|
|
@PRIMES = qw( |
|
25
|
|
|
|
|
|
|
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 |
|
26
|
|
|
|
|
|
|
103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 |
|
27
|
|
|
|
|
|
|
199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 |
|
28
|
|
|
|
|
|
|
313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 |
|
29
|
|
|
|
|
|
|
433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 |
|
30
|
|
|
|
|
|
|
563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 |
|
31
|
|
|
|
|
|
|
673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 |
|
32
|
|
|
|
|
|
|
811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 |
|
33
|
|
|
|
|
|
|
941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 |
|
34
|
|
|
|
|
|
|
1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 |
|
35
|
|
|
|
|
|
|
1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 |
|
36
|
|
|
|
|
|
|
1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 |
|
37
|
|
|
|
|
|
|
1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 |
|
38
|
|
|
|
|
|
|
1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 |
|
39
|
|
|
|
|
|
|
1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 |
|
40
|
|
|
|
|
|
|
1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 |
|
41
|
|
|
|
|
|
|
1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 |
|
42
|
|
|
|
|
|
|
1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 |
|
43
|
|
|
|
|
|
|
2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 |
|
44
|
|
|
|
|
|
|
2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 |
|
45
|
|
|
|
|
|
|
2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 |
|
46
|
|
|
|
|
|
|
2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 |
|
47
|
|
|
|
|
|
|
2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 |
|
48
|
|
|
|
|
|
|
2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 |
|
49
|
|
|
|
|
|
|
2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 |
|
50
|
|
|
|
|
|
|
2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 |
|
51
|
|
|
|
|
|
|
3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 |
|
52
|
|
|
|
|
|
|
3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 |
|
53
|
|
|
|
|
|
|
3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 |
|
54
|
|
|
|
|
|
|
3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 |
|
55
|
|
|
|
|
|
|
3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 |
|
56
|
|
|
|
|
|
|
3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 |
|
57
|
|
|
|
|
|
|
3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 |
|
58
|
|
|
|
|
|
|
3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 |
|
59
|
|
|
|
|
|
|
4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 |
|
60
|
|
|
|
|
|
|
4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 |
|
61
|
|
|
|
|
|
|
4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 |
|
62
|
|
|
|
|
|
|
4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 |
|
63
|
|
|
|
|
|
|
4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 |
|
64
|
|
|
|
|
|
|
4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 |
|
65
|
|
|
|
|
|
|
4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 |
|
66
|
|
|
|
|
|
|
4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 |
|
67
|
|
|
|
|
|
|
5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 |
|
68
|
|
|
|
|
|
|
5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 |
|
69
|
|
|
|
|
|
|
5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 |
|
70
|
|
|
|
|
|
|
5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 |
|
71
|
|
|
|
|
|
|
5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 |
|
72
|
|
|
|
|
|
|
5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 |
|
73
|
|
|
|
|
|
|
5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 |
|
74
|
|
|
|
|
|
|
5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 |
|
75
|
|
|
|
|
|
|
6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 |
|
76
|
|
|
|
|
|
|
6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 |
|
77
|
|
|
|
|
|
|
6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 |
|
78
|
|
|
|
|
|
|
6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 |
|
79
|
|
|
|
|
|
|
6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 |
|
80
|
|
|
|
|
|
|
6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 |
|
81
|
|
|
|
|
|
|
6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 |
|
82
|
|
|
|
|
|
|
6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 |
|
83
|
|
|
|
|
|
|
7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 |
|
84
|
|
|
|
|
|
|
7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 |
|
85
|
|
|
|
|
|
|
7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 |
|
86
|
|
|
|
|
|
|
7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 |
|
87
|
|
|
|
|
|
|
7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 |
|
88
|
|
|
|
|
|
|
7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919 7927 |
|
89
|
|
|
|
|
|
|
7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 8081 8087 |
|
90
|
|
|
|
|
|
|
8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 8219 8221 |
|
91
|
|
|
|
|
|
|
8231 8233 8237 8243 8263 8269 8273 8287 8291 8293 8297 8311 8317 8329 8353 |
|
92
|
|
|
|
|
|
|
8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 8501 8513 |
|
93
|
|
|
|
|
|
|
8521 8527 8537 8539 8543 8563 8573 8581 8597 8599 8609 8623 8627 8629 8641 |
|
94
|
|
|
|
|
|
|
8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 8741 8747 |
|
95
|
|
|
|
|
|
|
8753 8761 8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 8863 8867 |
|
96
|
|
|
|
|
|
|
8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 9011 9013 |
|
97
|
|
|
|
|
|
|
9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 9157 9161 |
|
98
|
|
|
|
|
|
|
9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257 9277 9281 9283 9293 |
|
99
|
|
|
|
|
|
|
9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 9419 9421 |
|
100
|
|
|
|
|
|
|
9431 9433 9437 9439 9461 9463 9467 9473 9479 9491 9497 9511 9521 9533 9539 |
|
101
|
|
|
|
|
|
|
9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 |
|
102
|
|
|
|
|
|
|
9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 |
|
103
|
|
|
|
|
|
|
9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 |
|
104
|
|
|
|
|
|
|
9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 |
|
105
|
|
|
|
|
|
|
10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 10181 |
|
106
|
|
|
|
|
|
|
10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 |
|
107
|
|
|
|
|
|
|
10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 |
|
108
|
|
|
|
|
|
|
10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 |
|
109
|
|
|
|
|
|
|
10531 10559 10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 |
|
110
|
|
|
|
|
|
|
10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 |
|
111
|
|
|
|
|
|
|
10771 10781 10789 10799 10831 10837 10847 10853 10859 10861 10867 10883 |
|
112
|
|
|
|
|
|
|
10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 |
|
113
|
|
|
|
|
|
|
11003 11027 11047 11057 11059 11069 11071 11083 11087 11093 11113 11117 |
|
114
|
|
|
|
|
|
|
11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 |
|
115
|
|
|
|
|
|
|
11251 11257 11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 |
|
116
|
|
|
|
|
|
|
11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471 |
|
117
|
|
|
|
|
|
|
11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 11587 11593 |
|
118
|
|
|
|
|
|
|
11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 11719 |
|
119
|
|
|
|
|
|
|
11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 |
|
120
|
|
|
|
|
|
|
11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 |
|
121
|
|
|
|
|
|
|
11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 |
|
122
|
|
|
|
|
|
|
12049 12071 12073 12097 12101 12107 12109 12113 12119 12143 12149 12157 |
|
123
|
|
|
|
|
|
|
12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 |
|
124
|
|
|
|
|
|
|
12277 12281 12289 12301 12323 12329 12343 12347 12373 12377 12379 12391 |
|
125
|
|
|
|
|
|
|
12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 |
|
126
|
|
|
|
|
|
|
12497 12503 12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 |
|
127
|
|
|
|
|
|
|
12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689 |
|
128
|
|
|
|
|
|
|
12697 12703 12713 12721 12739 12743 12757 12763 12781 12791 12799 12809 |
|
129
|
|
|
|
|
|
|
12821 12823 12829 12841 12853 12889 12893 12899 12907 12911 12917 12919 |
|
130
|
|
|
|
|
|
|
12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 |
|
131
|
|
|
|
|
|
|
13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 13147 |
|
132
|
|
|
|
|
|
|
13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 |
|
133
|
|
|
|
|
|
|
13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 |
|
134
|
|
|
|
|
|
|
13397 13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 |
|
135
|
|
|
|
|
|
|
13499 13513 13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 |
|
136
|
|
|
|
|
|
|
13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 |
|
137
|
|
|
|
|
|
|
13723 13729 13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 |
|
138
|
|
|
|
|
|
|
13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931 |
|
139
|
|
|
|
|
|
|
13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057 14071 |
|
140
|
|
|
|
|
|
|
14081 14083 14087 14107 14143 14149 14153 14159 14173 14177 14197 14207 |
|
141
|
|
|
|
|
|
|
14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 |
|
142
|
|
|
|
|
|
|
14369 14387 14389 14401 14407 14411 14419 14423 14431 14437 14447 14449 |
|
143
|
|
|
|
|
|
|
14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 |
|
144
|
|
|
|
|
|
|
14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 14683 |
|
145
|
|
|
|
|
|
|
14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 |
|
146
|
|
|
|
|
|
|
14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 |
|
147
|
|
|
|
|
|
|
14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 |
|
148
|
|
|
|
|
|
|
15017 15031 15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 |
|
149
|
|
|
|
|
|
|
15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241 |
|
150
|
|
|
|
|
|
|
15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 |
|
151
|
|
|
|
|
|
|
15331 15349 15359 15361 15373 15377 15383 15391 15401 15413 15427 15439 |
|
152
|
|
|
|
|
|
|
15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 |
|
153
|
|
|
|
|
|
|
15569 15581 15583 15601 15607 15619 15629 15641 15643 15647 15649 15661 |
|
154
|
|
|
|
|
|
|
15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 |
|
155
|
|
|
|
|
|
|
15773 15787 15791 15797 15803 15809 15817 15823 15859 15877 15881 15887 |
|
156
|
|
|
|
|
|
|
15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991 16001 |
|
157
|
|
|
|
|
|
|
16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 16103 |
|
158
|
|
|
|
|
|
|
16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 |
|
159
|
|
|
|
|
|
|
16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 |
|
160
|
|
|
|
|
|
|
16381 16411 16417 16421 16427 16433 16447 16451 16453 16477 16481 16487 |
|
161
|
|
|
|
|
|
|
16493 16519 16529 16547 16553 16561 16567 16573 16603 16607 16619 16631 |
|
162
|
|
|
|
|
|
|
16633 16649 16651 16657 16661 16673 16691 16693 16699 16703 16729 16741 |
|
163
|
|
|
|
|
|
|
16747 16759 16763 16787 16811 16823 16829 16831 16843 16871 16879 16883 |
|
164
|
|
|
|
|
|
|
16889 16901 16903 16921 16927 16931 16937 16943 16963 16979 16981 16987 |
|
165
|
|
|
|
|
|
|
16993 17011 17021 17027 17029 17033 17041 17047 17053 17077 17093 17099 |
|
166
|
|
|
|
|
|
|
17107 17117 17123 17137 17159 17167 17183 17189 17191 17203 17207 17209 |
|
167
|
|
|
|
|
|
|
17231 17239 17257 17291 17293 17299 17317 17321 17327 17333 17341 17351 |
|
168
|
|
|
|
|
|
|
17359 17377 17383 17387 17389 17393 17401 17417 17419 17431 17443 17449 |
|
169
|
|
|
|
|
|
|
17467 17471 17477 17483 17489 17491 17497 17509 17519 17539 17551 17569 |
|
170
|
|
|
|
|
|
|
17573 17579 17581 17597 17599 17609 17623 17627 17657 17659 17669 17681 |
|
171
|
|
|
|
|
|
|
17683 17707 17713 17729 17737 17747 17749 17761 17783 17789 17791 17807 |
|
172
|
|
|
|
|
|
|
17827 17837 17839 17851 17863 17881 17891 17903 17909 17911 17921 17923 |
|
173
|
|
|
|
|
|
|
17929 17939 17957 17959 17971 17977 17981 17987 17989 18013 18041 18043 |
|
174
|
|
|
|
|
|
|
18047 18049 18059 18061 18077 18089 18097 18119 18121 18127 18131 18133 |
|
175
|
|
|
|
|
|
|
18143 18149 18169 18181 18191 18199 18211 18217 18223 18229 18233 18251 |
|
176
|
|
|
|
|
|
|
18253 18257 18269 18287 18289 18301 18307 18311 18313 18329 18341 18353 |
|
177
|
|
|
|
|
|
|
18367 18371 18379 18397 18401 18413 18427 18433 18439 18443 18451 18457 |
|
178
|
|
|
|
|
|
|
18461 18481 18493 18503 18517 18521 18523 18539 18541 18553 18583 18587 |
|
179
|
|
|
|
|
|
|
18593 18617 18637 18661 18671 18679 18691 18701 18713 18719 18731 18743 |
|
180
|
|
|
|
|
|
|
18749 18757 18773 18787 18793 18797 18803 18839 18859 18869 18899 18911 |
|
181
|
|
|
|
|
|
|
18913 18917 18919 18947 18959 18973 18979 19001 19009 19013 19031 19037 |
|
182
|
|
|
|
|
|
|
19051 19069 19073 19079 19081 19087 19121 19139 19141 19157 19163 19181 |
|
183
|
|
|
|
|
|
|
19183 19207 19211 19213 19219 19231 19237 19249 19259 19267 19273 19289 |
|
184
|
|
|
|
|
|
|
19301 19309 19319 19333 19373 19379 19381 19387 19391 19403 19417 19421 |
|
185
|
|
|
|
|
|
|
19423 19427 19429 19433 19441 19447 19457 19463 19469 19471 19477 19483 |
|
186
|
|
|
|
|
|
|
19489 19501 19507 19531 19541 19543 19553 19559 19571 19577 19583 19597 |
|
187
|
|
|
|
|
|
|
19603 19609 19661 19681 19687 19697 19699 19709 19717 19727 19739 19751 |
|
188
|
|
|
|
|
|
|
19753 19759 19763 19777 19793 19801 19813 19819 19841 19843 19853 19861 |
|
189
|
|
|
|
|
|
|
19867 19889 19891 19913 19919 19927 19937 19949 19961 19963 19973 19979 |
|
190
|
|
|
|
|
|
|
19991 19993 19997 20011 20021 20023 20029 20047 20051 20063 20071 20089 |
|
191
|
|
|
|
|
|
|
20101 20107 20113 20117 20123 20129 20143 20147 20149 20161 20173 20177 |
|
192
|
|
|
|
|
|
|
20183 20201 20219 20231 20233 20249 20261 20269 20287 20297 20323 20327 |
|
193
|
|
|
|
|
|
|
20333 20341 20347 20353 20357 20359 20369 20389 20393 20399 20407 20411 |
|
194
|
|
|
|
|
|
|
20431 20441 20443 20477 20479 20483 20507 20509 20521 20533 20543 20549 |
|
195
|
|
|
|
|
|
|
20551 20563 20593 20599 20611 20627 20639 20641 20663 20681 20693 20707 |
|
196
|
|
|
|
|
|
|
20717 20719 20731 20743 20747 20749 20753 20759 20771 20773 20789 20807 |
|
197
|
|
|
|
|
|
|
20809 20849 20857 20873 20879 20887 20897 20899 20903 20921 20929 20939 |
|
198
|
|
|
|
|
|
|
20947 20959 20963 20981 20983 21001 21011 21013 21017 21019 21023 21031 |
|
199
|
|
|
|
|
|
|
21059 21061 21067 21089 21101 21107 21121 21139 21143 21149 21157 21163 |
|
200
|
|
|
|
|
|
|
21169 21179 21187 21191 21193 21211 21221 21227 21247 21269 21277 21283 |
|
201
|
|
|
|
|
|
|
21313 21317 21319 21323 21341 21347 21377 21379 21383 21391 21397 21401 |
|
202
|
|
|
|
|
|
|
21407 21419 21433 21467 21481 21487 21491 21493 21499 21503 21517 21521 |
|
203
|
|
|
|
|
|
|
21523 21529 21557 21559 21563 21569 21577 21587 21589 21599 21601 21611 |
|
204
|
|
|
|
|
|
|
21613 21617 21647 21649 21661 21673 21683 21701 21713 21727 21737 21739 |
|
205
|
|
|
|
|
|
|
21751 21757 21767 21773 21787 21799 21803 21817 21821 21839 21841 21851 |
|
206
|
|
|
|
|
|
|
21859 21863 21871 21881 21893 21911 21929 21937 21943 21961 21977 21991 |
|
207
|
|
|
|
|
|
|
21997 22003 22013 22027 22031 22037 22039 22051 22063 22067 22073 22079 |
|
208
|
|
|
|
|
|
|
22091 22093 22109 22111 22123 22129 22133 22147 22153 22157 22159 22171 |
|
209
|
|
|
|
|
|
|
22189 22193 22229 22247 22259 22271 22273 22277 22279 22283 22291 22303 |
|
210
|
|
|
|
|
|
|
22307 22343 22349 22367 22369 22381 22391 22397 22409 22433 22441 22447 |
|
211
|
|
|
|
|
|
|
22453 22469 22481 22483 22501 22511 22531 22541 22543 22549 22567 22571 |
|
212
|
|
|
|
|
|
|
22573 22613 22619 22621 22637 22639 22643 22651 22669 22679 22691 22697 |
|
213
|
|
|
|
|
|
|
22699 22709 22717 22721 22727 22739 22741 22751 22769 22777 22783 22787 |
|
214
|
|
|
|
|
|
|
22807 22811 22817 22853 22859 22861 22871 22877 22901 22907 22921 22937 |
|
215
|
|
|
|
|
|
|
22943 22961 22963 22973 22993 23003 23011 23017 23021 23027 23029 23039 |
|
216
|
|
|
|
|
|
|
23041 23053 23057 23059 23063 23071 23081 23087 23099 23117 23131 23143 |
|
217
|
|
|
|
|
|
|
23159 23167 23173 23189 23197 23201 23203 23209 23227 23251 23269 23279 |
|
218
|
|
|
|
|
|
|
23291 23293 23297 23311 23321 23327 23333 23339 23357 23369 23371 23399 |
|
219
|
|
|
|
|
|
|
23417 23431 23447 23459 23473 23497 23509 23531 23537 23539 23549 23557 |
|
220
|
|
|
|
|
|
|
23561 23563 23567 23581 23593 23599 23603 23609 23623 23627 23629 23633 |
|
221
|
|
|
|
|
|
|
23663 23669 23671 23677 23687 23689 23719 23741 23743 23747 23753 23761 |
|
222
|
|
|
|
|
|
|
23767 23773 23789 23801 23813 23819 23827 23831 23833 23857 23869 23873 |
|
223
|
|
|
|
|
|
|
23879 23887 23893 23899 23909 23911 23917 23929 23957 23971 23977 23981 |
|
224
|
|
|
|
|
|
|
23993 24001 24007 24019 24023 24029 24043 24049 24061 24071 24077 24083 |
|
225
|
|
|
|
|
|
|
24091 24097 24103 24107 24109 24113 24121 24133 24137 24151 24169 24179 |
|
226
|
|
|
|
|
|
|
24181 24197 24203 24223 24229 24239 24247 24251 24281 24317 24329 24337 |
|
227
|
|
|
|
|
|
|
24359 24371 24373 24379 24391 24407 24413 24419 24421 24439 24443 24469 |
|
228
|
|
|
|
|
|
|
24473 24481 24499 24509 24517 24527 24533 24547 24551 24571 24593 24611 |
|
229
|
|
|
|
|
|
|
24623 24631 24659 24671 24677 24683 24691 24697 24709 24733 24749 24763 |
|
230
|
|
|
|
|
|
|
24767 24781 24793 24799 24809 24821 24841 24847 24851 24859 24877 24889 |
|
231
|
|
|
|
|
|
|
24907 24917 24919 24923 24943 24953 24967 24971 24977 24979 24989 25013 |
|
232
|
|
|
|
|
|
|
25031 25033 25037 25057 25073 25087 25097 25111 25117 25121 25127 25147 |
|
233
|
|
|
|
|
|
|
25153 25163 25169 25171 25183 25189 25219 25229 25237 25243 25247 25253 |
|
234
|
|
|
|
|
|
|
25261 25301 25303 25307 25309 25321 25339 25343 25349 25357 25367 25373 |
|
235
|
|
|
|
|
|
|
25391 25409 25411 25423 25439 25447 25453 25457 25463 25469 25471 25523 |
|
236
|
|
|
|
|
|
|
25537 25541 25561 25577 25579 25583 25589 25601 25603 25609 25621 25633 |
|
237
|
|
|
|
|
|
|
25639 25643 25657 25667 25673 25679 25693 25703 25717 25733 25741 25747 |
|
238
|
|
|
|
|
|
|
25759 25763 25771 25793 25799 25801 25819 25841 25847 25849 25867 25873 |
|
239
|
|
|
|
|
|
|
25889 25903 25913 25919 25931 25933 25939 25943 25951 25969 25981 25997 |
|
240
|
|
|
|
|
|
|
25999 26003 26017 26021 26029 26041 26053 26083 26099 26107 26111 26113 |
|
241
|
|
|
|
|
|
|
26119 26141 26153 26161 26171 26177 26183 26189 26203 26209 26227 26237 |
|
242
|
|
|
|
|
|
|
26249 26251 26261 26263 26267 26293 26297 26309 26317 26321 26339 26347 |
|
243
|
|
|
|
|
|
|
26357 26371 26387 26393 26399 26407 26417 26423 26431 26437 26449 26459 |
|
244
|
|
|
|
|
|
|
26479 26489 26497 26501 26513 26539 26557 26561 26573 26591 26597 26627 |
|
245
|
|
|
|
|
|
|
26633 26641 26647 26669 26681 26683 26687 26693 26699 26701 26711 26713 |
|
246
|
|
|
|
|
|
|
26717 26723 26729 26731 26737 26759 26777 26783 26801 26813 26821 26833 |
|
247
|
|
|
|
|
|
|
26839 26849 26861 26863 26879 26881 26891 26893 26903 26921 26927 26947 |
|
248
|
|
|
|
|
|
|
26951 26953 26959 26981 26987 26993 27011 27017 27031 27043 27059 27061 |
|
249
|
|
|
|
|
|
|
27067 27073 27077 27091 27103 27107 27109 27127 27143 27179 27191 27197 |
|
250
|
|
|
|
|
|
|
27211 27239 27241 27253 27259 27271 27277 27281 27283 27299 27329 27337 |
|
251
|
|
|
|
|
|
|
27361 27367 27397 27407 27409 27427 27431 27437 27449 27457 27479 27481 |
|
252
|
|
|
|
|
|
|
27487 27509 27527 27529 27539 27541 27551 27581 27583 27611 27617 27631 |
|
253
|
|
|
|
|
|
|
27647 27653 27673 27689 27691 27697 27701 27733 27737 27739 27743 27749 |
|
254
|
|
|
|
|
|
|
27751 27763 27767 27773 27779 27791 27793 27799 27803 27809 27817 27823 |
|
255
|
|
|
|
|
|
|
27827 27847 27851 27883 27893 27901 27917 27919 27941 27943 27947 27953 |
|
256
|
|
|
|
|
|
|
27961 27967 27983 27997 28001 28019 28027 28031 28051 28057 28069 28081 |
|
257
|
|
|
|
|
|
|
28087 28097 28099 28109 28111 28123 28151 28163 28181 28183 28201 28211 |
|
258
|
|
|
|
|
|
|
28219 28229 28277 28279 28283 28289 28297 28307 28309 28319 28349 28351 |
|
259
|
|
|
|
|
|
|
28387 28393 28403 28409 28411 28429 28433 28439 28447 28463 28477 28493 |
|
260
|
|
|
|
|
|
|
28499 28513 28517 28537 28541 28547 28549 28559 28571 28573 28579 28591 |
|
261
|
|
|
|
|
|
|
28597 28603 28607 28619 28621 28627 28631 28643 28649 28657 28661 28663 |
|
262
|
|
|
|
|
|
|
28669 28687 28697 28703 28711 28723 28729 28751 28753 28759 28771 28789 |
|
263
|
|
|
|
|
|
|
28793 28807 28813 28817 28837 28843 28859 28867 28871 28879 28901 28909 |
|
264
|
|
|
|
|
|
|
28921 28927 28933 28949 28961 28979 29009 29017 29021 29023 29027 29033 |
|
265
|
|
|
|
|
|
|
29059 29063 29077 29101 29123 29129 29131 29137 29147 29153 29167 29173 |
|
266
|
|
|
|
|
|
|
29179 29191 29201 29207 29209 29221 29231 29243 29251 29269 29287 29297 |
|
267
|
|
|
|
|
|
|
29303 29311 29327 29333 29339 29347 29363 29383 29387 29389 29399 29401 |
|
268
|
|
|
|
|
|
|
29411 29423 29429 29437 29443 29453 29473 29483 29501 29527 29531 29537 |
|
269
|
|
|
|
|
|
|
29567 29569 29573 29581 29587 29599 29611 29629 29633 29641 29663 29669 |
|
270
|
|
|
|
|
|
|
29671 29683 29717 29723 29741 29753 29759 29761 29789 29803 29819 29833 |
|
271
|
|
|
|
|
|
|
29837 29851 29863 29867 29873 29879 29881 29917 29921 29927 29947 29959 |
|
272
|
|
|
|
|
|
|
29983 29989 30011 30013 30029 30047 30059 30071 30089 30091 30097 30103 |
|
273
|
|
|
|
|
|
|
30109 30113 30119 30133 30137 30139 30161 30169 30181 30187 30197 30203 |
|
274
|
|
|
|
|
|
|
30211 30223 30241 30253 30259 30269 30271 30293 30307 30313 30319 30323 |
|
275
|
|
|
|
|
|
|
30341 30347 30367 30389 30391 30403 30427 30431 30449 30467 30469 30491 |
|
276
|
|
|
|
|
|
|
30493 30497 30509 30517 30529 30539 30553 30557 30559 30577 30593 30631 |
|
277
|
|
|
|
|
|
|
30637 30643 30649 30661 30671 30677 30689 30697 30703 30707 30713 30727 |
|
278
|
|
|
|
|
|
|
30757 30763 30773 30781 30803 30809 30817 30829 30839 30841 30851 30853 |
|
279
|
|
|
|
|
|
|
30859 30869 30871 30881 30893 30911 30931 30937 30941 30949 30971 30977 |
|
280
|
|
|
|
|
|
|
30983 31013 31019 31033 31039 31051 31063 31069 31079 31081 31091 31121 |
|
281
|
|
|
|
|
|
|
31123 31139 31147 31151 31153 31159 31177 31181 31183 31189 31193 31219 |
|
282
|
|
|
|
|
|
|
31223 31231 31237 31247 31249 31253 31259 31267 31271 31277 31307 31319 |
|
283
|
|
|
|
|
|
|
31321 31327 31333 31337 31357 31379 31387 31391 31393 31397 31469 31477 |
|
284
|
|
|
|
|
|
|
31481 31489 31511 31513 31517 31531 31541 31543 31547 31567 31573 31583 |
|
285
|
|
|
|
|
|
|
31601 31607 31627 31643 31649 31657 31663 31667 31687 31699 31721 31723 |
|
286
|
|
|
|
|
|
|
31727 31729 31741 31751 31769 31771 31793 31799 31817 31847 31849 31859 |
|
287
|
|
|
|
|
|
|
31873 31883 31891 31907 31957 31963 31973 31981 31991 32003 32009 32027 |
|
288
|
|
|
|
|
|
|
32029 32051 32057 32059 32063 32069 32077 32083 32089 32099 32117 32119 |
|
289
|
|
|
|
|
|
|
32141 32143 32159 32173 32183 32189 32191 32203 32213 32233 32237 32251 |
|
290
|
|
|
|
|
|
|
32257 32261 32297 32299 32303 32309 32321 32323 32327 32341 32353 32359 |
|
291
|
|
|
|
|
|
|
32363 32369 32371 32377 32381 32401 32411 32413 32423 32429 32441 32443 |
|
292
|
|
|
|
|
|
|
32467 32479 32491 32497 32503 32507 32531 32533 32537 32561 32563 32569 |
|
293
|
|
|
|
|
|
|
32573 32579 32587 32603 32609 32611 32621 32633 32647 32653 32687 32693 |
|
294
|
|
|
|
|
|
|
32707 32713 32717 32719 32749 32771 32779 32783 32789 32797 32801 32803 |
|
295
|
|
|
|
|
|
|
32831 32833 32839 32843 32869 32887 32909 32911 32917 32933 32939 32941 |
|
296
|
|
|
|
|
|
|
32957 32969 32971 32983 32987 32993 32999 33013 33023 33029 33037 33049 |
|
297
|
|
|
|
|
|
|
33053 33071 33073 33083 33091 33107 33113 33119 33149 33151 33161 33179 |
|
298
|
|
|
|
|
|
|
33181 33191 33199 33203 33211 33223 33247 33287 33289 33301 33311 33317 |
|
299
|
|
|
|
|
|
|
33329 33331 33343 33347 33349 33353 33359 33377 33391 33403 33409 33413 |
|
300
|
|
|
|
|
|
|
33427 33457 33461 33469 33479 33487 33493 33503 33521 33529 33533 33547 |
|
301
|
|
|
|
|
|
|
33563 33569 33577 33581 33587 33589 33599 33601 33613 33617 33619 33623 |
|
302
|
|
|
|
|
|
|
33629 33637 33641 33647 33679 33703 33713 33721 33739 33749 33751 33757 |
|
303
|
|
|
|
|
|
|
33767 33769 33773 33791 33797 33809 33811 33827 33829 33851 33857 33863 |
|
304
|
|
|
|
|
|
|
33871 33889 33893 33911 33923 33931 33937 33941 33961 33967 33997 34019 |
|
305
|
|
|
|
|
|
|
34031 34033 34039 34057 34061 34123 34127 34129 34141 34147 34157 34159 |
|
306
|
|
|
|
|
|
|
34171 34183 34211 34213 34217 34231 34253 34259 34261 34267 34273 34283 |
|
307
|
|
|
|
|
|
|
34297 34301 34303 34313 34319 34327 34337 34351 34361 34367 34369 34381 |
|
308
|
|
|
|
|
|
|
34403 34421 34429 34439 34457 34469 34471 34483 34487 34499 34501 34511 |
|
309
|
|
|
|
|
|
|
34513 34519 34537 34543 34549 34583 34589 34591 34603 34607 34613 34631 |
|
310
|
|
|
|
|
|
|
34649 34651 34667 34673 34679 34687 34693 34703 34721 34729 34739 34747 |
|
311
|
|
|
|
|
|
|
34757 34759 34763 34781 34807 34819 34841 34843 34847 34849 34871 34877 |
|
312
|
|
|
|
|
|
|
34883 34897 34913 34919 34939 34949 34961 34963 34981 35023 35027 35051 |
|
313
|
|
|
|
|
|
|
35053 35059 35069 35081 35083 35089 35099 35107 35111 35117 35129 35141 |
|
314
|
|
|
|
|
|
|
35149 35153 35159 35171 35201 35221 35227 35251 35257 35267 35279 35281 |
|
315
|
|
|
|
|
|
|
35291 35311 35317 35323 35327 35339 35353 35363 35381 35393 35401 35407 |
|
316
|
|
|
|
|
|
|
35419 35423 35437 35447 35449 35461 35491 35507 35509 35521 35527 35531 |
|
317
|
|
|
|
|
|
|
35533 35537 35543 35569 35573 35591 35593 35597 35603 35617 35671 35677 |
|
318
|
|
|
|
|
|
|
35729 35731 35747 35753 35759 35771 35797 35801 35803 35809 35831 35837 |
|
319
|
|
|
|
|
|
|
35839 35851 35863 35869 35879 35897 35899 35911 35923 35933 35951 35963 |
|
320
|
|
|
|
|
|
|
35969 35977 35983 35993 35999 36007 36011 36013 36017 36037 36061 36067 |
|
321
|
|
|
|
|
|
|
36073 36083 36097 36107 36109 36131 36137 36151 36161 36187 36191 36209 |
|
322
|
|
|
|
|
|
|
36217 36229 36241 36251 36263 36269 36277 36293 36299 36307 36313 36319 |
|
323
|
|
|
|
|
|
|
36341 36343 36353 36373 36383 36389 36433 36451 36457 36467 36469 36473 |
|
324
|
|
|
|
|
|
|
36479 36493 36497 36523 36527 36529 36541 36551 36559 36563 36571 36583 |
|
325
|
|
|
|
|
|
|
36587 36599 36607 36629 36637 36643 36653 36671 36677 36683 36691 36697 |
|
326
|
|
|
|
|
|
|
36709 36713 36721 36739 36749 36761 36767 36779 36781 36787 36791 36793 |
|
327
|
|
|
|
|
|
|
36809 36821 36833 36847 36857 36871 36877 36887 36899 36901 36913 36919 |
|
328
|
|
|
|
|
|
|
36923 36929 36931 36943 36947 36973 36979 36997 37003 37013 37019 37021 |
|
329
|
|
|
|
|
|
|
37039 37049 37057 37061 37087 37097 37117 37123 37139 37159 37171 37181 |
|
330
|
|
|
|
|
|
|
37189 37199 37201 37217 37223 37243 37253 37273 37277 37307 37309 37313 |
|
331
|
|
|
|
|
|
|
37321 37337 37339 37357 37361 37363 37369 37379 37397 37409 37423 37441 |
|
332
|
|
|
|
|
|
|
37447 37463 37483 37489 37493 37501 37507 37511 37517 37529 37537 37547 |
|
333
|
|
|
|
|
|
|
37549 37561 37567 37571 37573 37579 37589 37591 37607 37619 37633 37643 |
|
334
|
|
|
|
|
|
|
37649 37657 37663 37691 37693 37699 37717 37747 37781 37783 37799 37811 |
|
335
|
|
|
|
|
|
|
37813 37831 37847 37853 37861 37871 37879 37889 37897 37907 37951 37957 |
|
336
|
|
|
|
|
|
|
37963 37967 37987 37991 37993 37997 38011 38039 38047 38053 38069 38083 |
|
337
|
|
|
|
|
|
|
38113 38119 38149 38153 38167 38177 38183 38189 38197 38201 38219 38231 |
|
338
|
|
|
|
|
|
|
38237 38239 38261 38273 38281 38287 38299 38303 38317 38321 38327 38329 |
|
339
|
|
|
|
|
|
|
38333 38351 38371 38377 38393 38431 38447 38449 38453 38459 38461 38501 |
|
340
|
|
|
|
|
|
|
38543 38557 38561 38567 38569 38593 38603 38609 38611 38629 38639 38651 |
|
341
|
|
|
|
|
|
|
38653 38669 38671 38677 38693 38699 38707 38711 38713 38723 38729 38737 |
|
342
|
|
|
|
|
|
|
38747 38749 38767 38783 38791 38803 38821 38833 38839 38851 38861 38867 |
|
343
|
|
|
|
|
|
|
38873 38891 38903 38917 38921 38923 38933 38953 38959 38971 38977 38993 |
|
344
|
|
|
|
|
|
|
39019 39023 39041 39043 39047 39079 39089 39097 39103 39107 39113 39119 |
|
345
|
|
|
|
|
|
|
39133 39139 39157 39161 39163 39181 39191 39199 39209 39217 39227 39229 |
|
346
|
|
|
|
|
|
|
39233 39239 39241 39251 39293 39301 39313 39317 39323 39341 39343 39359 |
|
347
|
|
|
|
|
|
|
39367 39371 39373 39383 39397 39409 39419 39439 39443 39451 39461 39499 |
|
348
|
|
|
|
|
|
|
39503 39509 39511 39521 39541 39551 39563 39569 39581 39607 39619 39623 |
|
349
|
|
|
|
|
|
|
39631 39659 39667 39671 39679 39703 39709 39719 39727 39733 39749 39761 |
|
350
|
|
|
|
|
|
|
39769 39779 39791 39799 39821 39827 39829 39839 39841 39847 39857 39863 |
|
351
|
|
|
|
|
|
|
39869 39877 39883 39887 39901 39929 39937 39953 39971 39979 39983 39989 |
|
352
|
|
|
|
|
|
|
40009 40013 40031 40037 40039 40063 40087 40093 40099 40111 40123 40127 |
|
353
|
|
|
|
|
|
|
40129 40151 40153 40163 40169 40177 40189 40193 40213 40231 40237 40241 |
|
354
|
|
|
|
|
|
|
40253 40277 40283 40289 40343 40351 40357 40361 40387 40423 40427 40429 |
|
355
|
|
|
|
|
|
|
40433 40459 40471 40483 40487 40493 40499 40507 40519 40529 40531 40543 |
|
356
|
|
|
|
|
|
|
40559 40577 40583 40591 40597 40609 40627 40637 40639 40693 40697 40699 |
|
357
|
|
|
|
|
|
|
40709 40739 40751 40759 40763 40771 40787 40801 40813 40819 40823 40829 |
|
358
|
|
|
|
|
|
|
40841 40847 40849 40853 40867 40879 40883 40897 40903 40927 40933 40939 |
|
359
|
|
|
|
|
|
|
40949 40961 40973 40993 41011 41017 41023 41039 41047 41051 41057 41077 |
|
360
|
|
|
|
|
|
|
41081 41113 41117 41131 41141 41143 41149 41161 41177 41179 41183 41189 |
|
361
|
|
|
|
|
|
|
41201 41203 41213 41221 41227 41231 41233 41243 41257 41263 41269 41281 |
|
362
|
|
|
|
|
|
|
41299 41333 41341 41351 41357 41381 41387 41389 41399 41411 41413 41443 |
|
363
|
|
|
|
|
|
|
41453 41467 41479 41491 41507 41513 41519 41521 41539 41543 41549 41579 |
|
364
|
|
|
|
|
|
|
41593 41597 41603 41609 41611 41617 41621 41627 41641 41647 41651 41659 |
|
365
|
|
|
|
|
|
|
41669 41681 41687 41719 41729 41737 41759 41761 41771 41777 41801 41809 |
|
366
|
|
|
|
|
|
|
41813 41843 41849 41851 41863 41879 41887 41893 41897 41903 41911 41927 |
|
367
|
|
|
|
|
|
|
41941 41947 41953 41957 41959 41969 41981 41983 41999 42013 42017 42019 |
|
368
|
|
|
|
|
|
|
42023 42043 42061 42071 42073 42083 42089 42101 42131 42139 42157 42169 |
|
369
|
|
|
|
|
|
|
42179 42181 42187 42193 42197 42209 42221 42223 42227 42239 42257 42281 |
|
370
|
|
|
|
|
|
|
42283 42293 42299 42307 42323 42331 42337 42349 42359 42373 42379 42391 |
|
371
|
|
|
|
|
|
|
42397 42403 42407 42409 42433 42437 42443 42451 42457 42461 42463 42467 |
|
372
|
|
|
|
|
|
|
42473 42487 42491 42499 42509 42533 42557 42569 42571 42577 42589 42611 |
|
373
|
|
|
|
|
|
|
42641 42643 42649 42667 42677 42683 42689 42697 42701 42703 42709 42719 |
|
374
|
|
|
|
|
|
|
42727 42737 42743 42751 42767 42773 42787 42793 42797 42821 42829 42839 |
|
375
|
|
|
|
|
|
|
42841 42853 42859 42863 42899 42901 42923 42929 42937 42943 42953 42961 |
|
376
|
|
|
|
|
|
|
42967 42979 42989 43003 43013 43019 43037 43049 43051 43063 43067 43093 |
|
377
|
|
|
|
|
|
|
43103 43117 43133 43151 43159 43177 43189 43201 43207 43223 43237 43261 |
|
378
|
|
|
|
|
|
|
43271 43283 43291 43313 43319 43321 43331 43391 43397 43399 43403 43411 |
|
379
|
|
|
|
|
|
|
43427 43441 43451 43457 43481 43487 43499 43517 43541 43543 43573 43577 |
|
380
|
|
|
|
|
|
|
43579 43591 43597 43607 43609 43613 43627 43633 43649 43651 43661 43669 |
|
381
|
|
|
|
|
|
|
43691 43711 43717 43721 43753 43759 43777 43781 43783 43787 43789 43793 |
|
382
|
|
|
|
|
|
|
43801 43853 43867 43889 43891 43913 43933 43943 43951 43961 43963 43969 |
|
383
|
|
|
|
|
|
|
43973 43987 43991 43997 44017 44021 44027 44029 44041 44053 44059 44071 |
|
384
|
|
|
|
|
|
|
44087 44089 44101 44111 44119 44123 44129 44131 44159 44171 44179 44189 |
|
385
|
|
|
|
|
|
|
44201 44203 44207 44221 44249 44257 44263 44267 44269 44273 44279 44281 |
|
386
|
|
|
|
|
|
|
44293 44351 44357 44371 44381 44383 44389 44417 44449 44453 44483 44491 |
|
387
|
|
|
|
|
|
|
44497 44501 44507 44519 44531 44533 44537 44543 44549 44563 44579 44587 |
|
388
|
|
|
|
|
|
|
44617 44621 44623 44633 44641 44647 44651 44657 44683 44687 44699 44701 |
|
389
|
|
|
|
|
|
|
44711 44729 44741 44753 44771 44773 44777 44789 44797 44809 44819 44839 |
|
390
|
|
|
|
|
|
|
44843 44851 44867 44879 44887 44893 44909 44917 44927 44939 44953 44959 |
|
391
|
|
|
|
|
|
|
44963 44971 44983 44987 45007 45013 45053 45061 45077 45083 45119 45121 |
|
392
|
|
|
|
|
|
|
45127 45131 45137 45139 45161 45179 45181 45191 45197 45233 45247 45259 |
|
393
|
|
|
|
|
|
|
45263 45281 45289 45293 45307 45317 45319 45329 45337 45341 45343 45361 |
|
394
|
|
|
|
|
|
|
45377 45389 45403 45413 45427 45433 45439 45481 45491 45497 45503 45523 |
|
395
|
|
|
|
|
|
|
45533 45541 45553 45557 45569 45587 45589 45599 45613 45631 45641 45659 |
|
396
|
|
|
|
|
|
|
45667 45673 45677 45691 45697 45707 45737 45751 45757 45763 45767 45779 |
|
397
|
|
|
|
|
|
|
45817 45821 45823 45827 45833 45841 45853 45863 45869 45887 45893 45943 |
|
398
|
|
|
|
|
|
|
45949 45953 45959 45971 45979 45989 46021 46027 46049 46051 46061 46073 |
|
399
|
|
|
|
|
|
|
46091 46093 46099 46103 46133 46141 46147 46153 46171 46181 46183 46187 |
|
400
|
|
|
|
|
|
|
46199 46219 46229 46237 46261 46271 46273 46279 46301 46307 46309 46327 |
|
401
|
|
|
|
|
|
|
46337 46349 46351 46381 46399 46411 46439 46441 46447 46451 46457 46471 |
|
402
|
|
|
|
|
|
|
46477 46489 46499 46507 46511 46523 46549 46559 46567 46573 46589 46591 |
|
403
|
|
|
|
|
|
|
46601 46619 46633 46639 46643 46649 46663 46679 46681 46687 46691 46703 |
|
404
|
|
|
|
|
|
|
46723 46727 46747 46751 46757 46769 46771 46807 46811 46817 46819 46829 |
|
405
|
|
|
|
|
|
|
46831 46853 46861 46867 46877 46889 46901 46919 46933 46957 46993 46997 |
|
406
|
|
|
|
|
|
|
47017 47041 47051 47057 47059 47087 47093 47111 47119 47123 47129 47137 |
|
407
|
|
|
|
|
|
|
47143 47147 47149 47161 47189 47207 47221 47237 47251 47269 47279 47287 |
|
408
|
|
|
|
|
|
|
47293 47297 47303 47309 47317 47339 47351 47353 47363 47381 47387 47389 |
|
409
|
|
|
|
|
|
|
47407 47417 47419 47431 47441 47459 47491 47497 47501 47507 47513 47521 |
|
410
|
|
|
|
|
|
|
47527 47533 47543 47563 47569 47581 47591 47599 47609 47623 47629 47639 |
|
411
|
|
|
|
|
|
|
47653 47657 47659 47681 47699 47701 47711 47713 47717 47737 47741 47743 |
|
412
|
|
|
|
|
|
|
47777 47779 47791 47797 47807 47809 47819 47837 47843 47857 47869 47881 |
|
413
|
|
|
|
|
|
|
47903 47911 47917 47933 47939 47947 47951 47963 47969 47977 47981 48017 |
|
414
|
|
|
|
|
|
|
48023 48029 48049 48073 48079 48091 48109 48119 48121 48131 48157 48163 |
|
415
|
|
|
|
|
|
|
48179 48187 48193 48197 48221 48239 48247 48259 48271 48281 48299 48311 |
|
416
|
|
|
|
|
|
|
48313 48337 48341 48353 48371 48383 48397 48407 48409 48413 48437 48449 |
|
417
|
|
|
|
|
|
|
48463 48473 48479 48481 48487 48491 48497 48523 48527 48533 48539 48541 |
|
418
|
|
|
|
|
|
|
48563 48571 48589 48593 48611 48619 48623 48647 48649 48661 48673 48677 |
|
419
|
|
|
|
|
|
|
48679 48731 48733 48751 48757 48761 48767 48779 48781 48787 48799 48809 |
|
420
|
|
|
|
|
|
|
48817 48821 48823 48847 48857 48859 48869 48871 48883 48889 48907 48947 |
|
421
|
|
|
|
|
|
|
48953 48973 48989 48991 49003 49009 49019 49031 49033 49037 49043 49057 |
|
422
|
|
|
|
|
|
|
49069 49081 49103 49109 49117 49121 49123 49139 49157 49169 49171 49177 |
|
423
|
|
|
|
|
|
|
49193 49199 49201 49207 49211 49223 49253 49261 49277 49279 49297 49307 |
|
424
|
|
|
|
|
|
|
49331 49333 49339 49363 49367 49369 49391 49393 49409 49411 49417 49429 |
|
425
|
|
|
|
|
|
|
49433 49451 49459 49463 49477 49481 49499 49523 49529 49531 49537 49547 |
|
426
|
|
|
|
|
|
|
49549 49559 49597 49603 49613 49627 49633 49639 49663 49667 49669 49681 |
|
427
|
|
|
|
|
|
|
49697 49711 49727 49739 49741 49747 49757 49783 49787 49789 49801 49807 |
|
428
|
|
|
|
|
|
|
49811 49823 49831 49843 49853 49871 49877 49891 49919 49921 49927 49937 |
|
429
|
|
|
|
|
|
|
49939 49943 49957 49991 49993 49999 50021 50023 50033 50047 50051 50053 |
|
430
|
|
|
|
|
|
|
50069 50077 50087 50093 50101 50111 50119 50123 50129 50131 50147 50153 |
|
431
|
|
|
|
|
|
|
50159 50177 50207 50221 50227 50231 50261 50263 50273 50287 50291 50311 |
|
432
|
|
|
|
|
|
|
50321 50329 50333 50341 50359 50363 50377 50383 50387 50411 50417 50423 |
|
433
|
|
|
|
|
|
|
50441 50459 50461 50497 50503 50513 50527 50539 50543 50549 50551 50581 |
|
434
|
|
|
|
|
|
|
50587 50591 50593 50599 50627 50647 50651 50671 50683 50707 50723 50741 |
|
435
|
|
|
|
|
|
|
50753 50767 50773 50777 50789 50821 50833 50839 50849 50857 50867 50873 |
|
436
|
|
|
|
|
|
|
50891 50893 50909 50923 50929 50951 50957 50969 50971 50989 50993 51001 |
|
437
|
|
|
|
|
|
|
51031 51043 51047 51059 51061 51071 51109 51131 51133 51137 51151 51157 |
|
438
|
|
|
|
|
|
|
51169 51193 51197 51199 51203 51217 51229 51239 51241 51257 51263 51283 |
|
439
|
|
|
|
|
|
|
51287 51307 51329 51341 51343 51347 51349 51361 51383 51407 51413 51419 |
|
440
|
|
|
|
|
|
|
51421 51427 51431 51437 51439 51449 51461 51473 51479 51481 51487 51503 |
|
441
|
|
|
|
|
|
|
51511 51517 51521 51539 51551 51563 51577 51581 51593 51599 51607 51613 |
|
442
|
|
|
|
|
|
|
51631 51637 51647 51659 51673 51679 51683 51691 51713 51719 51721 51749 |
|
443
|
|
|
|
|
|
|
51767 51769 51787 51797 51803 51817 51827 51829 51839 51853 51859 51869 |
|
444
|
|
|
|
|
|
|
51871 51893 51899 51907 51913 51929 51941 51949 51971 51973 51977 51991 |
|
445
|
|
|
|
|
|
|
52009 52021 52027 52051 52057 52067 52069 52081 52103 52121 52127 52147 |
|
446
|
|
|
|
|
|
|
52153 52163 52177 52181 52183 52189 52201 52223 52237 52249 52253 52259 |
|
447
|
|
|
|
|
|
|
52267 52289 52291 52301 52313 52321 52361 52363 52369 52379 52387 52391 |
|
448
|
|
|
|
|
|
|
52433 52453 52457 52489 52501 52511 52517 52529 52541 52543 52553 52561 |
|
449
|
|
|
|
|
|
|
52567 52571 52579 52583 52609 52627 52631 52639 52667 52673 52691 52697 |
|
450
|
|
|
|
|
|
|
52709 52711 52721 52727 52733 52747 52757 52769 52783 52807 52813 52817 |
|
451
|
|
|
|
|
|
|
52837 52859 52861 52879 52883 52889 52901 52903 52919 52937 52951 52957 |
|
452
|
|
|
|
|
|
|
52963 52967 52973 52981 52999 53003 53017 53047 53051 53069 53077 53087 |
|
453
|
|
|
|
|
|
|
53089 53093 53101 53113 53117 53129 53147 53149 53161 53171 53173 53189 |
|
454
|
|
|
|
|
|
|
53197 53201 53231 53233 53239 53267 53269 53279 53281 53299 53309 53323 |
|
455
|
|
|
|
|
|
|
53327 53353 53359 53377 53381 53401 53407 53411 53419 53437 53441 53453 |
|
456
|
|
|
|
|
|
|
53479 53503 53507 53527 53549 53551 53569 53591 53593 53597 53609 53611 |
|
457
|
|
|
|
|
|
|
53617 53623 53629 53633 53639 53653 53657 53681 53693 53699 53717 53719 |
|
458
|
|
|
|
|
|
|
53731 53759 53773 53777 53783 53791 53813 53819 53831 53849 53857 53861 |
|
459
|
|
|
|
|
|
|
53881 53887 53891 53897 53899 53917 53923 53927 53939 53951 53959 53987 |
|
460
|
|
|
|
|
|
|
53993 54001 54011 54013 54037 54049 54059 54083 54091 54101 54121 54133 |
|
461
|
|
|
|
|
|
|
54139 54151 54163 54167 54181 54193 54217 54251 54269 54277 54287 54293 |
|
462
|
|
|
|
|
|
|
54311 54319 54323 54331 54347 54361 54367 54371 54377 54401 54403 54409 |
|
463
|
|
|
|
|
|
|
54413 54419 54421 54437 54443 54449 54469 54493 54497 54499 54503 54517 |
|
464
|
|
|
|
|
|
|
54521 54539 54541 54547 54559 54563 54577 54581 54583 54601 54617 54623 |
|
465
|
|
|
|
|
|
|
54629 54631 54647 54667 54673 54679 54709 54713 54721 54727 54751 54767 |
|
466
|
|
|
|
|
|
|
54773 54779 54787 54799 54829 54833 54851 54869 54877 54881 54907 54917 |
|
467
|
|
|
|
|
|
|
54919 54941 54949 54959 54973 54979 54983 55001 55009 55021 55049 55051 |
|
468
|
|
|
|
|
|
|
55057 55061 55073 55079 55103 55109 55117 55127 55147 55163 55171 55201 |
|
469
|
|
|
|
|
|
|
55207 55213 55217 55219 55229 55243 55249 55259 55291 55313 55331 55333 |
|
470
|
|
|
|
|
|
|
55337 55339 55343 55351 55373 55381 55399 55411 55439 55441 55457 55469 |
|
471
|
|
|
|
|
|
|
55487 55501 55511 55529 55541 55547 55579 55589 55603 55609 55619 55621 |
|
472
|
|
|
|
|
|
|
55631 55633 55639 55661 55663 55667 55673 55681 55691 55697 55711 55717 |
|
473
|
|
|
|
|
|
|
55721 55733 55763 55787 55793 55799 55807 55813 55817 55819 55823 55829 |
|
474
|
|
|
|
|
|
|
55837 55843 55849 55871 55889 55897 55901 55903 55921 55927 55931 55933 |
|
475
|
|
|
|
|
|
|
55949 55967 55987 55997 56003 56009 56039 56041 56053 56081 56087 56093 |
|
476
|
|
|
|
|
|
|
56099 56101 56113 56123 56131 56149 56167 56171 56179 56197 56207 56209 |
|
477
|
|
|
|
|
|
|
56237 56239 56249 56263 56267 56269 56299 56311 56333 56359 56369 56377 |
|
478
|
|
|
|
|
|
|
56383 56393 56401 56417 56431 56437 56443 56453 56467 56473 56477 56479 |
|
479
|
|
|
|
|
|
|
56489 56501 56503 56509 56519 56527 56531 56533 56543 56569 56591 56597 |
|
480
|
|
|
|
|
|
|
56599 56611 56629 56633 56659 56663 56671 56681 56687 56701 56711 56713 |
|
481
|
|
|
|
|
|
|
56731 56737 56747 56767 56773 56779 56783 56807 56809 56813 56821 56827 |
|
482
|
|
|
|
|
|
|
56843 56857 56873 56891 56893 56897 56909 56911 56921 56923 56929 56941 |
|
483
|
|
|
|
|
|
|
56951 56957 56963 56983 56989 56993 56999 57037 57041 57047 57059 57073 |
|
484
|
|
|
|
|
|
|
57077 57089 57097 57107 57119 57131 57139 57143 57149 57163 57173 57179 |
|
485
|
|
|
|
|
|
|
57191 57193 57203 57221 57223 57241 57251 57259 57269 57271 57283 57287 |
|
486
|
|
|
|
|
|
|
57301 57329 57331 57347 57349 57367 57373 57383 57389 57397 57413 57427 |
|
487
|
|
|
|
|
|
|
57457 57467 57487 57493 57503 57527 57529 57557 57559 57571 57587 57593 |
|
488
|
|
|
|
|
|
|
57601 57637 57641 57649 57653 57667 57679 57689 57697 57709 57713 57719 |
|
489
|
|
|
|
|
|
|
57727 57731 57737 57751 57773 57781 57787 57791 57793 57803 57809 57829 |
|
490
|
|
|
|
|
|
|
57839 57847 57853 57859 57881 57899 57901 57917 57923 57943 57947 57973 |
|
491
|
|
|
|
|
|
|
57977 57991 58013 58027 58031 58043 58049 58057 58061 58067 58073 58099 |
|
492
|
|
|
|
|
|
|
58109 58111 58129 58147 58151 58153 58169 58171 58189 58193 58199 58207 |
|
493
|
|
|
|
|
|
|
58211 58217 58229 58231 58237 58243 58271 58309 58313 58321 58337 58363 |
|
494
|
|
|
|
|
|
|
58367 58369 58379 58391 58393 58403 58411 58417 58427 58439 58441 58451 |
|
495
|
|
|
|
|
|
|
58453 58477 58481 58511 58537 58543 58549 58567 58573 58579 58601 58603 |
|
496
|
|
|
|
|
|
|
58613 58631 58657 58661 58679 58687 58693 58699 58711 58727 58733 58741 |
|
497
|
|
|
|
|
|
|
58757 58763 58771 58787 58789 58831 58889 58897 58901 58907 58909 58913 |
|
498
|
|
|
|
|
|
|
58921 58937 58943 58963 58967 58979 58991 58997 59009 59011 59021 59023 |
|
499
|
|
|
|
|
|
|
59029 59051 59053 59063 59069 59077 59083 59093 59107 59113 59119 59123 |
|
500
|
|
|
|
|
|
|
59141 59149 59159 59167 59183 59197 59207 59209 59219 59221 59233 59239 |
|
501
|
|
|
|
|
|
|
59243 59263 59273 59281 59333 59341 59351 59357 59359 59369 59377 59387 |
|
502
|
|
|
|
|
|
|
59393 59399 59407 59417 59419 59441 59443 59447 59453 59467 59471 59473 |
|
503
|
|
|
|
|
|
|
59497 59509 59513 59539 59557 59561 59567 59581 59611 59617 59621 59627 |
|
504
|
|
|
|
|
|
|
59629 59651 59659 59663 59669 59671 59693 59699 59707 59723 59729 59743 |
|
505
|
|
|
|
|
|
|
59747 59753 59771 59779 59791 59797 59809 59833 59863 59879 59887 59921 |
|
506
|
|
|
|
|
|
|
59929 59951 59957 59971 59981 59999 60013 60017 60029 60037 60041 60077 |
|
507
|
|
|
|
|
|
|
60083 60089 60091 60101 60103 60107 60127 60133 60139 60149 60161 60167 |
|
508
|
|
|
|
|
|
|
60169 60209 60217 60223 60251 60257 60259 60271 60289 60293 60317 60331 |
|
509
|
|
|
|
|
|
|
60337 60343 60353 60373 60383 60397 60413 60427 60443 60449 60457 60493 |
|
510
|
|
|
|
|
|
|
60497 60509 60521 60527 60539 60589 60601 60607 60611 60617 60623 60631 |
|
511
|
|
|
|
|
|
|
60637 60647 60649 60659 60661 60679 60689 60703 60719 60727 60733 60737 |
|
512
|
|
|
|
|
|
|
60757 60761 60763 60773 60779 60793 60811 60821 60859 60869 60887 60889 |
|
513
|
|
|
|
|
|
|
60899 60901 60913 60917 60919 60923 60937 60943 60953 60961 61001 61007 |
|
514
|
|
|
|
|
|
|
61027 61031 61043 61051 61057 61091 61099 61121 61129 61141 61151 61153 |
|
515
|
|
|
|
|
|
|
61169 61211 61223 61231 61253 61261 61283 61291 61297 61331 61333 61339 |
|
516
|
|
|
|
|
|
|
61343 61357 61363 61379 61381 61403 61409 61417 61441 61463 61469 61471 |
|
517
|
|
|
|
|
|
|
61483 61487 61493 61507 61511 61519 61543 61547 61553 61559 61561 61583 |
|
518
|
|
|
|
|
|
|
61603 61609 61613 61627 61631 61637 61643 61651 61657 61667 61673 61681 |
|
519
|
|
|
|
|
|
|
61687 61703 61717 61723 61729 61751 61757 61781 61813 61819 61837 61843 |
|
520
|
|
|
|
|
|
|
61861 61871 61879 61909 61927 61933 61949 61961 61967 61979 61981 61987 |
|
521
|
|
|
|
|
|
|
61991 62003 62011 62017 62039 62047 62053 62057 62071 62081 62099 62119 |
|
522
|
|
|
|
|
|
|
62129 62131 62137 62141 62143 62171 62189 62191 62201 62207 62213 62219 |
|
523
|
|
|
|
|
|
|
62233 62273 62297 62299 62303 62311 62323 62327 62347 62351 62383 62401 |
|
524
|
|
|
|
|
|
|
62417 62423 62459 62467 62473 62477 62483 62497 62501 62507 62533 62539 |
|
525
|
|
|
|
|
|
|
62549 62563 62581 62591 62597 62603 62617 62627 62633 62639 62653 62659 |
|
526
|
|
|
|
|
|
|
62683 62687 62701 62723 62731 62743 62753 62761 62773 62791 62801 62819 |
|
527
|
|
|
|
|
|
|
62827 62851 62861 62869 62873 62897 62903 62921 62927 62929 62939 62969 |
|
528
|
|
|
|
|
|
|
62971 62981 62983 62987 62989 63029 63031 63059 63067 63073 63079 63097 |
|
529
|
|
|
|
|
|
|
63103 63113 63127 63131 63149 63179 63197 63199 63211 63241 63247 63277 |
|
530
|
|
|
|
|
|
|
63281 63299 63311 63313 63317 63331 63337 63347 63353 63361 63367 63377 |
|
531
|
|
|
|
|
|
|
63389 63391 63397 63409 63419 63421 63439 63443 63463 63467 63473 63487 |
|
532
|
|
|
|
|
|
|
63493 63499 63521 63527 63533 63541 63559 63577 63587 63589 63599 63601 |
|
533
|
|
|
|
|
|
|
63607 63611 63617 63629 63647 63649 63659 63667 63671 63689 63691 63697 |
|
534
|
|
|
|
|
|
|
63703 63709 63719 63727 63737 63743 63761 63773 63781 63793 63799 63803 |
|
535
|
|
|
|
|
|
|
63809 63823 63839 63841 63853 63857 63863 63901 63907 63913 63929 63949 |
|
536
|
|
|
|
|
|
|
63977 63997 64007 64013 64019 64033 64037 64063 64067 64081 64091 64109 |
|
537
|
|
|
|
|
|
|
64123 64151 64153 64157 64171 64187 64189 64217 64223 64231 64237 64271 |
|
538
|
|
|
|
|
|
|
64279 64283 64301 64303 64319 64327 64333 64373 64381 64399 64403 64433 |
|
539
|
|
|
|
|
|
|
64439 64451 64453 64483 64489 64499 64513 64553 64567 64577 64579 64591 |
|
540
|
|
|
|
|
|
|
64601 64609 64613 64621 64627 64633 64661 64663 64667 64679 64693 64709 |
|
541
|
|
|
|
|
|
|
64717 64747 64763 64781 64783 64793 64811 64817 64849 64853 64871 64877 |
|
542
|
|
|
|
|
|
|
64879 64891 64901 64919 64921 64927 64937 64951 64969 64997 65003 65011 |
|
543
|
|
|
|
|
|
|
65027 65029 65033 65053 65063 65071 65089 65099 65101 65111 65119 65123 |
|
544
|
|
|
|
|
|
|
65129 65141 65147 65167 65171 65173 65179 65183 65203 65213 65239 65257 |
|
545
|
|
|
|
|
|
|
65267 65269 65287 65293 65309 65323 65327 65353 65357 65371 65381 65393 |
|
546
|
|
|
|
|
|
|
65407 65413 65419 65423 65437 65447 65449 65479 65497 65519 65521 ); |
|
547
|
|
|
|
|
|
|
|
|
548
|
|
|
|
|
|
|
my $l; |
|
549
|
|
|
|
|
|
|
my @used; |
|
550
|
|
|
|
|
|
|
my @gens; |
|
551
|
|
|
|
|
|
|
|
|
552
|
|
|
|
|
|
|
sub rsaparams { |
|
553
|
|
|
|
|
|
|
my (%params) = @_; |
|
554
|
|
|
|
|
|
|
@used = (); |
|
555
|
|
|
|
|
|
|
my %paramsrsa = (%params, (Relprime => 1)); |
|
556
|
|
|
|
|
|
|
my $p = maurer (%paramsrsa); print "\n" if $params{Verbosity}; |
|
557
|
|
|
|
|
|
|
my $q = maurer (%paramsrsa); print "\n" if $params{Verbosity}; |
|
558
|
|
|
|
|
|
|
return { p => $p, q => $q, e => 65537 } |
|
559
|
|
|
|
|
|
|
} |
|
560
|
|
|
|
|
|
|
|
|
561
|
|
|
|
|
|
|
sub maurer { |
|
562
|
|
|
|
|
|
|
|
|
563
|
|
|
|
|
|
|
my ( %params ) = @_; |
|
564
|
|
|
|
|
|
|
|
|
565
|
|
|
|
|
|
|
my $k = $params { Size }; #-- bitsize of the required prime. |
|
566
|
|
|
|
|
|
|
my $v = $params { Verbosity }; #-- process reporting verbosity. |
|
567
|
|
|
|
|
|
|
#-- whether to find intermediate generators. |
|
568
|
|
|
|
|
|
|
my $p0 = 20; #-- generate primes of bitsize less |
|
569
|
|
|
|
|
|
|
#-- than $p0 with nextprime(). |
|
570
|
|
|
|
|
|
|
my $maxfact = 140; #-- bitsize of the biggest number we |
|
571
|
|
|
|
|
|
|
#-- can factor easily. |
|
572
|
|
|
|
|
|
|
$| = 1; |
|
573
|
|
|
|
|
|
|
|
|
574
|
|
|
|
|
|
|
if ( $k <= $p0 ) { |
|
575
|
|
|
|
|
|
|
my $spr = makerandom Size => $k; |
|
576
|
|
|
|
|
|
|
return Math::Pari::nextprime ( $spr ); |
|
577
|
|
|
|
|
|
|
} |
|
578
|
|
|
|
|
|
|
|
|
579
|
|
|
|
|
|
|
my $c_opt = 0.09; my $m = 20; |
|
580
|
|
|
|
|
|
|
my $B = floor ( $c_opt * ( $k ** 2 ) ); |
|
581
|
|
|
|
|
|
|
my $r = PARI ( 2 ** ( ( rand ) - 1 ) ); |
|
582
|
|
|
|
|
|
|
srand ( makerandom ( Size => 32, Strength => 0 ) ); |
|
583
|
|
|
|
|
|
|
|
|
584
|
|
|
|
|
|
|
if ( $k > ( 2 * $m ) ) { |
|
585
|
|
|
|
|
|
|
my $frs = 0; until ( $frs ) { |
|
586
|
|
|
|
|
|
|
$r = 2 ** ( (rand) - 1 ); |
|
587
|
|
|
|
|
|
|
my $rbits = $k-($r*$k); |
|
588
|
|
|
|
|
|
|
$frs = 1 if $rbits > $m; |
|
589
|
|
|
|
|
|
|
$frs = 0 if ($params{Generator} && ($rbits > $maxfact)); |
|
590
|
|
|
|
|
|
|
} |
|
591
|
|
|
|
|
|
|
} else { |
|
592
|
|
|
|
|
|
|
$r = 0.5; |
|
593
|
|
|
|
|
|
|
} |
|
594
|
|
|
|
|
|
|
|
|
595
|
|
|
|
|
|
|
my $q = maurer ( Size => floor ( $r * $k ) + 2, Verbosity => $v, |
|
596
|
|
|
|
|
|
|
Generator => $params{Generator}, Intermediates => $params{Intermediates} ); |
|
597
|
|
|
|
|
|
|
if ($params{Relprime}) { |
|
598
|
|
|
|
|
|
|
while ((grep /$q/, @used)) { |
|
599
|
|
|
|
|
|
|
print "<" if $v == 1; |
|
600
|
|
|
|
|
|
|
$q = maurer ( Size => floor ( $r * $k ) + 2, Verbosity => $v, Relprime => 1, |
|
601
|
|
|
|
|
|
|
Generator => $params{Generator}, Intermediates => $params{Intermediates} ); |
|
602
|
|
|
|
|
|
|
} |
|
603
|
|
|
|
|
|
|
} |
|
604
|
|
|
|
|
|
|
$q = $q->{Prime} if (ref $q eq 'HASH'); |
|
605
|
|
|
|
|
|
|
|
|
606
|
|
|
|
|
|
|
print "B = $B, r = $r, k = $k, q = $q\n" if $v == 2; |
|
607
|
|
|
|
|
|
|
push @used, $q; |
|
608
|
|
|
|
|
|
|
|
|
609
|
|
|
|
|
|
|
my $o1 = PARI ( 2 * $q ); |
|
610
|
|
|
|
|
|
|
my $o2 = PARI '2' ** PARI "@{[$k - 1]}"; |
|
611
|
|
|
|
|
|
|
my $I = floor ( $o2 / $o1 ); |
|
612
|
|
|
|
|
|
|
my $n = PARI (); |
|
613
|
|
|
|
|
|
|
|
|
614
|
|
|
|
|
|
|
while (1) { |
|
615
|
|
|
|
|
|
|
|
|
616
|
|
|
|
|
|
|
my $R = PARI ( makerandom_itv ( Lower => $I + 1, Upper => 2 * $I ) ); |
|
617
|
|
|
|
|
|
|
$n = floor( 2 * $R * $q + 1 ); |
|
618
|
|
|
|
|
|
|
print "n = $n\n" if $v == 2; |
|
619
|
|
|
|
|
|
|
print "." if $v == 1; |
|
620
|
|
|
|
|
|
|
|
|
621
|
|
|
|
|
|
|
my $a = PARI(); |
|
622
|
|
|
|
|
|
|
if ( trialdiv ( $n, $B ) ) { |
|
623
|
|
|
|
|
|
|
BASE: { |
|
624
|
|
|
|
|
|
|
print "(passes trial division)\n" if $v == 2; print "+" if $v == 1; |
|
625
|
|
|
|
|
|
|
$a = makerandom_itv( Lower => 2, Upper=> $n - 2 ); |
|
626
|
|
|
|
|
|
|
$a = makerandom_itv( Lower => 2, Upper=> $R ) if $params{Generator}; |
|
627
|
|
|
|
|
|
|
my $t1 = Mod (2, $n); my $t2 = Mod ($a, $n); |
|
628
|
|
|
|
|
|
|
my $b = $t2 ** ( $n - 1 ); |
|
629
|
|
|
|
|
|
|
if ( ($b == 1) && ( $q > $n ** (1/3.0) ) ) { |
|
630
|
|
|
|
|
|
|
print "$n is prime! a = $a, R = $R\n" if $v == 2; |
|
631
|
|
|
|
|
|
|
print "($k)" if $v == 1; |
|
632
|
|
|
|
|
|
|
my @s; |
|
633
|
|
|
|
|
|
|
if ($params{Generator}) { |
|
634
|
|
|
|
|
|
|
print "computing a generator...\n" if $v == 2; |
|
635
|
|
|
|
|
|
|
print "# " if $v == 1; |
|
636
|
|
|
|
|
|
|
@s = Math::Pari::factor($R) =~ m:[\[\(\;](\d+)(?=,):g; |
|
637
|
|
|
|
|
|
|
push @s, ($q,2); my $p = PARI (1); for (@s) { $p *= $_ }; |
|
638
|
|
|
|
|
|
|
for (@s) { my $b = Mod ($a, $p) ** PARI($p/$_); |
|
639
|
|
|
|
|
|
|
if ($b == 1) { |
|
640
|
|
|
|
|
|
|
print "@!" if $v == 1; |
|
641
|
|
|
|
|
|
|
print "$a is not a generator\n" if $v == 2; |
|
642
|
|
|
|
|
|
|
next BASE; |
|
643
|
|
|
|
|
|
|
} |
|
644
|
|
|
|
|
|
|
} |
|
645
|
|
|
|
|
|
|
} |
|
646
|
|
|
|
|
|
|
my @factors = ( Factors => \@s, R => $R ) if $params{Factors}; |
|
647
|
|
|
|
|
|
|
my @intermediates = ( Intermediates => \@used ) if $params{Intermediates}; |
|
648
|
|
|
|
|
|
|
return { @factors, @intermediates, Prime => $n, Generator => $a } if $params{Generator}; |
|
649
|
|
|
|
|
|
|
return { @factors, @intermediates, Prime => $n } if $params{Factors} or $params{Intermediates}; |
|
650
|
|
|
|
|
|
|
return $n; |
|
651
|
|
|
|
|
|
|
} |
|
652
|
|
|
|
|
|
|
} |
|
653
|
|
|
|
|
|
|
|
|
654
|
|
|
|
|
|
|
} |
|
655
|
|
|
|
|
|
|
|
|
656
|
|
|
|
|
|
|
} |
|
657
|
|
|
|
|
|
|
|
|
658
|
|
|
|
|
|
|
} |
|
659
|
|
|
|
|
|
|
|
|
660
|
|
|
|
|
|
|
|
|
661
|
|
|
|
|
|
|
sub trialdiv { |
|
662
|
|
|
|
|
|
|
|
|
663
|
|
|
|
|
|
|
my ( $n, $limit, $v ) = @_; |
|
664
|
|
|
|
|
|
|
|
|
665
|
|
|
|
|
|
|
my $end = _trialdiv_limit ( $n, $limit ); |
|
666
|
|
|
|
|
|
|
for ( $i=0; $i <= $end; $i++ ) { |
|
667
|
|
|
|
|
|
|
return undef unless Math::Pari::gmod ( $n, $PRIMES[ $i ] ); |
|
668
|
|
|
|
|
|
|
} |
|
669
|
|
|
|
|
|
|
|
|
670
|
|
|
|
|
|
|
return 1; |
|
671
|
|
|
|
|
|
|
|
|
672
|
|
|
|
|
|
|
} |
|
673
|
|
|
|
|
|
|
|
|
674
|
|
|
|
|
|
|
|
|
675
|
|
|
|
|
|
|
sub _trialdiv_limit { |
|
676
|
|
|
|
|
|
|
|
|
677
|
|
|
|
|
|
|
my ($n, $limit) = @_; |
|
678
|
|
|
|
|
|
|
my $start = 0; |
|
679
|
|
|
|
|
|
|
my $mid; |
|
680
|
|
|
|
|
|
|
my $end = $#PRIMES; |
|
681
|
|
|
|
|
|
|
$limit = int(sqrt($n)) unless $limit; |
|
682
|
|
|
|
|
|
|
|
|
683
|
|
|
|
|
|
|
if ( $limit <= $PRIMES[ $end ] ) { |
|
684
|
|
|
|
|
|
|
while ( ( $start + 1 ) != $end ) { |
|
685
|
|
|
|
|
|
|
use integer; |
|
686
|
|
|
|
|
|
|
$mid = int (( $end + $start ) / 2); |
|
687
|
|
|
|
|
|
|
no integer; |
|
688
|
|
|
|
|
|
|
$start = $mid if $limit > $PRIMES[ $mid ]; |
|
689
|
|
|
|
|
|
|
$end = $mid if $limit <= $PRIMES[ $mid ]; |
|
690
|
|
|
|
|
|
|
} |
|
691
|
|
|
|
|
|
|
} |
|
692
|
|
|
|
|
|
|
|
|
693
|
|
|
|
|
|
|
return $end; |
|
694
|
|
|
|
|
|
|
|
|
695
|
|
|
|
|
|
|
} |
|
696
|
|
|
|
|
|
|
|
|
697
|
|
|
|
|
|
|
"True Value"; |
|
698
|
|
|
|
|
|
|
|
|
699
|
|
|
|
|
|
|
|
|
700
|
|
|
|
|
|
|
=head1 NAME |
|
701
|
|
|
|
|
|
|
|
|
702
|
|
|
|
|
|
|
Crypt::Primes - Provable Prime Number Generator suitable for Cryptographic Applications. |
|
703
|
|
|
|
|
|
|
|
|
704
|
|
|
|
|
|
|
=head1 VERSION |
|
705
|
|
|
|
|
|
|
|
|
706
|
|
|
|
|
|
|
$Revision: 0.49 $ |
|
707
|
|
|
|
|
|
|
$Date: 2001/06/11 01:04:23 $ |
|
708
|
|
|
|
|
|
|
|
|
709
|
|
|
|
|
|
|
=head1 SYNOPSIS |
|
710
|
|
|
|
|
|
|
|
|
711
|
|
|
|
|
|
|
# generate a random, provable 512-bit prime. |
|
712
|
|
|
|
|
|
|
|
|
713
|
|
|
|
|
|
|
use Crypt::Primes qw(maurer); |
|
714
|
|
|
|
|
|
|
my $prime = maurer (Size => 512); |
|
715
|
|
|
|
|
|
|
|
|
716
|
|
|
|
|
|
|
# generate a random, provable 2048-bit prime and report |
|
717
|
|
|
|
|
|
|
# progress on console. |
|
718
|
|
|
|
|
|
|
|
|
719
|
|
|
|
|
|
|
my $another_prime = maurer ( |
|
720
|
|
|
|
|
|
|
Size => 2048, |
|
721
|
|
|
|
|
|
|
Verbosity => 1 |
|
722
|
|
|
|
|
|
|
); |
|
723
|
|
|
|
|
|
|
|
|
724
|
|
|
|
|
|
|
|
|
725
|
|
|
|
|
|
|
# generate a random 1024-bit prime and a group |
|
726
|
|
|
|
|
|
|
# generator of Z*(n). |
|
727
|
|
|
|
|
|
|
|
|
728
|
|
|
|
|
|
|
my $hash_ref = maurer ( |
|
729
|
|
|
|
|
|
|
Size => 1024, |
|
730
|
|
|
|
|
|
|
Generator => 1, |
|
731
|
|
|
|
|
|
|
Verbosity => 1 |
|
732
|
|
|
|
|
|
|
); |
|
733
|
|
|
|
|
|
|
|
|
734
|
|
|
|
|
|
|
=head1 WARNING |
|
735
|
|
|
|
|
|
|
|
|
736
|
|
|
|
|
|
|
The codebase is stable, but the API will most definitely change in a future |
|
737
|
|
|
|
|
|
|
release. |
|
738
|
|
|
|
|
|
|
|
|
739
|
|
|
|
|
|
|
=head1 DESCRIPTION |
|
740
|
|
|
|
|
|
|
|
|
741
|
|
|
|
|
|
|
This module implements Ueli Maurer's algorithm for generating large |
|
742
|
|
|
|
|
|
|
I primes and secure parameters for public-key cryptosystems. The |
|
743
|
|
|
|
|
|
|
generated primes are almost uniformly distributed over the set of primes of |
|
744
|
|
|
|
|
|
|
the specified bitsize and expected time for generation is less than the time |
|
745
|
|
|
|
|
|
|
required for generating a pseudo-prime of the same size with Miller-Rabin |
|
746
|
|
|
|
|
|
|
tests. Detailed description and running time analysis of the algorithm can |
|
747
|
|
|
|
|
|
|
be found in Maurer's paper[1]. |
|
748
|
|
|
|
|
|
|
|
|
749
|
|
|
|
|
|
|
Crypt::Primes is a pure perl implementation. It uses Math::Pari for |
|
750
|
|
|
|
|
|
|
multiple precision integer arithmetic and number theoretic functions. |
|
751
|
|
|
|
|
|
|
Random numbers are gathered with Crypt::Random, a perl interface to |
|
752
|
|
|
|
|
|
|
/dev/u?random devices found on most modern Unix operating systems. |
|
753
|
|
|
|
|
|
|
|
|
754
|
|
|
|
|
|
|
=head1 FUNCTIONS |
|
755
|
|
|
|
|
|
|
|
|
756
|
|
|
|
|
|
|
The following functions are availble for import. They must be explicitely |
|
757
|
|
|
|
|
|
|
imported. |
|
758
|
|
|
|
|
|
|
|
|
759
|
|
|
|
|
|
|
=over 4 |
|
760
|
|
|
|
|
|
|
|
|
761
|
|
|
|
|
|
|
=item B |
|
762
|
|
|
|
|
|
|
|
|
763
|
|
|
|
|
|
|
Generates a prime number of the specified bitsize. Takes a hash as |
|
764
|
|
|
|
|
|
|
parameter and returns a Math::Pari object (prime number) or a hash reference |
|
765
|
|
|
|
|
|
|
(prime number and generator) when group generator computation is requested. |
|
766
|
|
|
|
|
|
|
Following hash keys are understood: |
|
767
|
|
|
|
|
|
|
|
|
768
|
|
|
|
|
|
|
=back |
|
769
|
|
|
|
|
|
|
|
|
770
|
|
|
|
|
|
|
=over 0 |
|
771
|
|
|
|
|
|
|
|
|
772
|
|
|
|
|
|
|
=item B |
|
773
|
|
|
|
|
|
|
|
|
774
|
|
|
|
|
|
|
Bitsize of the required prime number. |
|
775
|
|
|
|
|
|
|
|
|
776
|
|
|
|
|
|
|
=item B |
|
777
|
|
|
|
|
|
|
|
|
778
|
|
|
|
|
|
|
Level of verbosity of progress reporting. Report is printed on STDOUT. |
|
779
|
|
|
|
|
|
|
Level of 1 indicates normal, terse reporting. Level of 2 prints lots of |
|
780
|
|
|
|
|
|
|
intermediate computations, useful for debugging. |
|
781
|
|
|
|
|
|
|
|
|
782
|
|
|
|
|
|
|
=item B |
|
783
|
|
|
|
|
|
|
|
|
784
|
|
|
|
|
|
|
When Generator key is set to a non-zero value, a group generator of Z*(n) is |
|
785
|
|
|
|
|
|
|
computed. Group generators are required key material in public-key |
|
786
|
|
|
|
|
|
|
cryptosystems like Elgamal and Diffie-Hellman that are based on |
|
787
|
|
|
|
|
|
|
intractability of the discrete logarithm problem. When this option is |
|
788
|
|
|
|
|
|
|
present, maurer() returns a hash reference that contains two keys, Prime and |
|
789
|
|
|
|
|
|
|
Generator. |
|
790
|
|
|
|
|
|
|
|
|
791
|
|
|
|
|
|
|
=item B |
|
792
|
|
|
|
|
|
|
|
|
793
|
|
|
|
|
|
|
When set to 1, maurer() stores intermediate primes in a class array, and |
|
794
|
|
|
|
|
|
|
ensures they are not used during construction of primes in the future calls |
|
795
|
|
|
|
|
|
|
to maurer() with Reprime => 1. This is used by rsaparams(). |
|
796
|
|
|
|
|
|
|
|
|
797
|
|
|
|
|
|
|
=item B |
|
798
|
|
|
|
|
|
|
|
|
799
|
|
|
|
|
|
|
When set to 1, maurer() returns a hash reference that contains |
|
800
|
|
|
|
|
|
|
(corresponding to the key 'Intermediates') a reference to an array of |
|
801
|
|
|
|
|
|
|
intermediate primes generated. |
|
802
|
|
|
|
|
|
|
|
|
803
|
|
|
|
|
|
|
=item B |
|
804
|
|
|
|
|
|
|
|
|
805
|
|
|
|
|
|
|
When set to 1, maurer() returns a hash reference that contains |
|
806
|
|
|
|
|
|
|
(corresponding to the key 'Factors') a reference to an array of |
|
807
|
|
|
|
|
|
|
factors of p-1 where p is the prime generated, and also (corresponding |
|
808
|
|
|
|
|
|
|
to the key 'R') a divisor of p. |
|
809
|
|
|
|
|
|
|
|
|
810
|
|
|
|
|
|
|
=back |
|
811
|
|
|
|
|
|
|
|
|
812
|
|
|
|
|
|
|
=over 4 |
|
813
|
|
|
|
|
|
|
|
|
814
|
|
|
|
|
|
|
=item B |
|
815
|
|
|
|
|
|
|
|
|
816
|
|
|
|
|
|
|
Generates two primes (p,q) and public exponent (e) of a RSA key pair. The |
|
817
|
|
|
|
|
|
|
key pair generated with this method is resistant to iterative encryption |
|
818
|
|
|
|
|
|
|
attack. See Appendix 2 of |
|
819
|
|
|
|
|
|
|
[1] for more information. |
|
820
|
|
|
|
|
|
|
|
|
821
|
|
|
|
|
|
|
rsaparams() takes the same arguments as maurer() with the exception of |
|
822
|
|
|
|
|
|
|
`Generator' and `Relprime'. Size specifies the common bitsize of p an q. |
|
823
|
|
|
|
|
|
|
Returns a hash reference with keys p, q and e. |
|
824
|
|
|
|
|
|
|
|
|
825
|
|
|
|
|
|
|
=item B |
|
826
|
|
|
|
|
|
|
|
|
827
|
|
|
|
|
|
|
Performs trial division on $n to ensure it's not divisible by any prime |
|
828
|
|
|
|
|
|
|
smaller than or equal to $limit. The module maintains a lookup table of |
|
829
|
|
|
|
|
|
|
primes (from 2 to 65521) for this purpose. If $limit is not provided, a |
|
830
|
|
|
|
|
|
|
suitable value is computed automatically. trialdiv() is used by maurer() to |
|
831
|
|
|
|
|
|
|
weed out composite random numbers before performing computationally |
|
832
|
|
|
|
|
|
|
intensive modular exponentiation tests. It is, however, documented should |
|
833
|
|
|
|
|
|
|
you need to use it directly. |
|
834
|
|
|
|
|
|
|
|
|
835
|
|
|
|
|
|
|
=back |
|
836
|
|
|
|
|
|
|
|
|
837
|
|
|
|
|
|
|
=head1 IMPLEMENTATION NOTE |
|
838
|
|
|
|
|
|
|
|
|
839
|
|
|
|
|
|
|
This module implements a modified FastPrime, as described in [1], to |
|
840
|
|
|
|
|
|
|
facilitate group generator computation. (Refer to [1] and [2] for |
|
841
|
|
|
|
|
|
|
description and pseudo-code of FastPrime). The modification involves |
|
842
|
|
|
|
|
|
|
introduction of an additional constraint on relative size r of q. While |
|
843
|
|
|
|
|
|
|
computing r, we ensure k * r is always greater than maxfact, where maxfact |
|
844
|
|
|
|
|
|
|
is the bitsize of the largest number we can factor easily. This value |
|
845
|
|
|
|
|
|
|
defaults to 140 bits. As a result, R is always smaller than maxfact, which |
|
846
|
|
|
|
|
|
|
allows us to get a complete factorization of 2Rq and use it to find a |
|
847
|
|
|
|
|
|
|
generator of the cyclic group Z*(2Rq). |
|
848
|
|
|
|
|
|
|
|
|
849
|
|
|
|
|
|
|
=head1 RUNNING TIME |
|
850
|
|
|
|
|
|
|
|
|
851
|
|
|
|
|
|
|
Crypt::Primes generates 512-bit primes in 7 seconds (on average), and |
|
852
|
|
|
|
|
|
|
1024-bit primes in 37 seconds (on average), on my PII 300 Mhz notebook. |
|
853
|
|
|
|
|
|
|
There are no computational limits by design; primes upto 8192-bits were |
|
854
|
|
|
|
|
|
|
generated to stress test the code. For detailed runtime analysis see [1]. |
|
855
|
|
|
|
|
|
|
|
|
856
|
|
|
|
|
|
|
=head1 SEE ALSO |
|
857
|
|
|
|
|
|
|
|
|
858
|
|
|
|
|
|
|
largeprimes(1), Crypt::Random(3), Math::Pari(3) |
|
859
|
|
|
|
|
|
|
|
|
860
|
|
|
|
|
|
|
=head1 BIBLIOGRAPHY |
|
861
|
|
|
|
|
|
|
|
|
862
|
|
|
|
|
|
|
=over 4 |
|
863
|
|
|
|
|
|
|
|
|
864
|
|
|
|
|
|
|
=item 1 Fast Generation of Prime Numbers and Secure Public-Key Cryptographic |
|
865
|
|
|
|
|
|
|
Parameters, Ueli Maurer (1994). |
|
866
|
|
|
|
|
|
|
|
|
867
|
|
|
|
|
|
|
=item 2 Corrections to Fast Generation of Prime Numbers and Secure Public-Key |
|
868
|
|
|
|
|
|
|
Cryptographic Parameters, Ueli Maurer (1996). |
|
869
|
|
|
|
|
|
|
|
|
870
|
|
|
|
|
|
|
=item 3 Handbook of Applied Cryptography by Menezes, Paul C. van Oorschot |
|
871
|
|
|
|
|
|
|
and Scott Vanstone (1997). |
|
872
|
|
|
|
|
|
|
|
|
873
|
|
|
|
|
|
|
=item Documents 1 & 2 can be found under docs/ of the source distribution. |
|
874
|
|
|
|
|
|
|
|
|
875
|
|
|
|
|
|
|
=back |
|
876
|
|
|
|
|
|
|
|
|
877
|
|
|
|
|
|
|
=head1 AUTHOR |
|
878
|
|
|
|
|
|
|
|
|
879
|
|
|
|
|
|
|
Vipul Ved Prakash, Email@vipul.netE |
|
880
|
|
|
|
|
|
|
|
|
881
|
|
|
|
|
|
|
=cut |
|
882
|
|
|
|
|
|
|
|
|
883
|
|
|
|
|
|
|
=head1 LICENSE |
|
884
|
|
|
|
|
|
|
|
|
885
|
|
|
|
|
|
|
Copyright (c) 1998-2001, Vipul Ved Prakash. All rights reserved. This code |
|
886
|
|
|
|
|
|
|
is free software; you can redistribute it and/or modify it under the same |
|
887
|
|
|
|
|
|
|
terms as Perl itself. |
|
888
|
|
|
|
|
|
|
|
|
889
|
|
|
|
|
|
|
=head1 TODO |
|
890
|
|
|
|
|
|
|
|
|
891
|
|
|
|
|
|
|
Maurer's algorithm generates primes of progressively larger bitsize using |
|
892
|
|
|
|
|
|
|
a recursive construction method. The algorithm enters recursion with a |
|
893
|
|
|
|
|
|
|
prime number and bitsize of the next prime to be generated. (Bitsizes of |
|
894
|
|
|
|
|
|
|
the intermediate primes are computed using a probability distribution that |
|
895
|
|
|
|
|
|
|
ensures generated primes are sufficiently random.) This recursion can be |
|
896
|
|
|
|
|
|
|
distributed over multiple machines, participating in a competitive |
|
897
|
|
|
|
|
|
|
computation model, to achieve close to best running time of the algorithm. |
|
898
|
|
|
|
|
|
|
Support for this will be implemented some day, possibly when the next |
|
899
|
|
|
|
|
|
|
version of Penguin hits CPAN. |
|
900
|
|
|
|
|
|
|
|
|
901
|
|
|
|
|
|
|
|