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#!/usr/bin/perl |
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=begin metadata |
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5
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Name: factor |
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6
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Description: factor a number |
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7
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Author: Peter John Acklam, pjacklam@gmail.com |
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License: perl |
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=end metadata |
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=cut |
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package PerlPowerTools::factor; |
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1
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256119
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use strict; |
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1
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1
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1
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4430
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17
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$|++; |
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my $VERSION = '1.003'; |
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# This implementation uses a wheel factorization of order 6, which has basis |
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22
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# primes (2, 3, 5, 7, 11, and 13). The wheel starts at 17, i.e., the first |
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23
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# prime after the basis primes. The circumference of the wheel is 30030, which |
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24
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# is equal to the product of the basis primes and equal to the sum of the gaps |
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# between each spoke in the wheel (see @gaps below). The first round through |
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# the wheel would normally start at 17, the next at 17 + 30030, the next at 17 |
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# + 2*30030 etc. For extra speed, we replace the first round through the wheel |
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28
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# by checking primes only, which requires us to cache all primes smaller than |
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29
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# 17 + 30030. |
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30
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31
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# This is the first prime after the basis primes. |
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32
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33
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my $pinit = 17; |
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34
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35
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# The circumference of the wheel. |
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37
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my $circ = 30030; |
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39
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# All primes smaller than $pinit + $circ. |
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40
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41
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my @primes = qw( 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 |
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42
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83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 |
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43
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191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 |
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44
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293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 |
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45
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419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 |
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46
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541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 |
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47
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653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 |
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48
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787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 |
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49
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919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 |
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50
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1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 |
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51
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1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 |
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52
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1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 |
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53
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1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 |
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54
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1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 |
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55
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1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 |
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56
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1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 |
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57
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1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 |
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58
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1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 |
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59
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2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 |
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60
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2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 |
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61
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2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 |
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62
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2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 |
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63
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2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 |
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64
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2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 |
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65
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2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 |
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66
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2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 |
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67
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2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 |
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68
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3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 |
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69
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3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 |
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70
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3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 |
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71
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3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 |
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72
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3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 |
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73
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3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 |
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74
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3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 |
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75
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3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 |
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76
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4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 |
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77
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4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 |
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78
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4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 |
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79
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4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 |
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80
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4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 |
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81
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4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 |
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82
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4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 |
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83
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5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 |
|
84
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5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 |
|
85
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5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 |
|
86
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5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 |
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87
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5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 |
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88
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5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 |
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89
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5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 |
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90
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5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 |
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91
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6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 |
|
92
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6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 |
|
93
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6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 |
|
94
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6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 |
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95
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6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 |
|
96
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6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 |
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97
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6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 |
|
98
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6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 |
|
99
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7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 |
|
100
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7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 |
|
101
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7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 |
|
102
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7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 |
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103
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7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 |
|
104
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7759 7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 |
|
105
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7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 |
|
106
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8081 8087 8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 |
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107
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8219 8221 8231 8233 8237 8243 8263 8269 8273 8287 8291 8293 8297 8311 8317 |
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108
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8329 8353 8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 |
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109
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8501 8513 8521 8527 8537 8539 8543 8563 8573 8581 8597 8599 8609 8623 8627 |
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110
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8629 8641 8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 |
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111
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8741 8747 8753 8761 8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 |
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112
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8863 8867 8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 |
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113
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9011 9013 9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 |
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114
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9157 9161 9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257 9277 9281 |
|
115
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9283 9293 9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 |
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116
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9419 9421 9431 9433 9437 9439 9461 9463 9467 9473 9479 9491 9497 9511 9521 |
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117
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9533 9539 9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 |
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118
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9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 |
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119
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9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 |
|
120
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9931 9941 9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 |
|
121
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10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 |
|
122
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10181 10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 |
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123
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10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 10429 |
|
124
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10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 |
|
125
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10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 10657 10663 10667 |
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126
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10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 |
|
127
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10831 10837 10847 10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 |
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128
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10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057 11059 11069 |
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129
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11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 |
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130
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11177 11197 11213 11239 11243 11251 11257 11261 11273 11279 11287 11299 11311 |
|
131
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11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 |
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132
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11447 11467 11471 11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 |
|
133
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11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 |
|
134
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11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 |
|
135
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11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 11941 |
|
136
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11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 |
|
137
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12073 12097 12101 12107 12109 12113 12119 12143 12149 12157 12161 12163 12197 |
|
138
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12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301 |
|
139
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12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 |
|
140
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12437 12451 12457 12473 12479 12487 12491 12497 12503 12511 12517 12527 12539 |
|
141
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12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 |
|
142
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12647 12653 12659 12671 12689 12697 12703 12713 12721 12739 12743 12757 12763 |
|
143
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12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 |
|
144
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12911 12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 |
|
145
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13007 13009 13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 |
|
146
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13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 |
|
147
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13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 13397 |
|
148
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13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 |
|
149
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13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 |
|
150
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13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729 13751 13757 |
|
151
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13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 |
|
152
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13883 13901 13903 13907 13913 13921 13931 13933 13963 13967 13997 13999 14009 |
|
153
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14011 14029 14033 14051 14057 14071 14081 14083 14087 14107 14143 14149 14153 |
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154
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|
|
|
|
14159 14173 14177 14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 |
|
155
|
|
|
|
|
|
|
14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423 14431 |
|
156
|
|
|
|
|
|
|
14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 |
|
157
|
|
|
|
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|
|
14557 14561 14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 |
|
158
|
|
|
|
|
|
|
14683 14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 |
|
159
|
|
|
|
|
|
|
14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 14887 |
|
160
|
|
|
|
|
|
|
14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031 |
|
161
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|
|
|
|
|
|
15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 |
|
162
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|
|
|
|
|
|
15161 15173 15187 15193 15199 15217 15227 15233 15241 15259 15263 15269 15271 |
|
163
|
|
|
|
|
|
|
15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359 15361 15373 |
|
164
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|
|
|
|
|
|
15377 15383 15391 15401 15413 15427 15439 15443 15451 15461 15467 15473 15493 |
|
165
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|
|
|
|
|
|
15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 |
|
166
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|
|
|
|
|
|
15641 15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 |
|
167
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|
|
|
|
|
|
15739 15749 15761 15767 15773 15787 15791 15797 15803 15809 15817 15823 15859 |
|
168
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|
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|
|
|
|
15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 |
|
169
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|
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|
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|
|
15991 16001 16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 |
|
170
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|
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|
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|
|
16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 |
|
171
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|
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|
16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 |
|
172
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|
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|
16411 16417 16421 16427 16433 16447 16451 16453 16477 16481 16487 16493 16519 |
|
173
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|
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|
|
16529 16547 16553 16561 16567 16573 16603 16607 16619 16631 16633 16649 16651 |
|
174
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|
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|
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|
|
16657 16661 16673 16691 16693 16699 16703 16729 16741 16747 16759 16763 16787 |
|
175
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|
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|
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|
|
16811 16823 16829 16831 16843 16871 16879 16883 16889 16901 16903 16921 16927 |
|
176
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|
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|
|
16931 16937 16943 16963 16979 16981 16987 16993 17011 17021 17027 17029 17033 |
|
177
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|
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|
17041 17047 17053 17077 17093 17099 17107 17117 17123 17137 17159 17167 17183 |
|
178
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|
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|
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|
17189 17191 17203 17207 17209 17231 17239 17257 17291 17293 17299 17317 17321 |
|
179
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|
17327 17333 17341 17351 17359 17377 17383 17387 17389 17393 17401 17417 17419 |
|
180
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|
17431 17443 17449 17467 17471 17477 17483 17489 17491 17497 17509 17519 17539 |
|
181
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|
17551 17569 17573 17579 17581 17597 17599 17609 17623 17627 17657 17659 17669 |
|
182
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|
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|
|
17681 17683 17707 17713 17729 17737 17747 17749 17761 17783 17789 17791 17807 |
|
183
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|
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|
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|
|
17827 17837 17839 17851 17863 17881 17891 17903 17909 17911 17921 17923 17929 |
|
184
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|
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|
|
17939 17957 17959 17971 17977 17981 17987 17989 18013 18041 18043 18047 18049 |
|
185
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|
|
18059 18061 18077 18089 18097 18119 18121 18127 18131 18133 18143 18149 18169 |
|
186
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|
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|
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|
18181 18191 18199 18211 18217 18223 18229 18233 18251 18253 18257 18269 18287 |
|
187
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|
18289 18301 18307 18311 18313 18329 18341 18353 18367 18371 18379 18397 18401 |
|
188
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|
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|
|
18413 18427 18433 18439 18443 18451 18457 18461 18481 18493 18503 18517 18521 |
|
189
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|
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|
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|
|
18523 18539 18541 18553 18583 18587 18593 18617 18637 18661 18671 18679 18691 |
|
190
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|
|
|
|
|
|
18701 18713 18719 18731 18743 18749 18757 18773 18787 18793 18797 18803 18839 |
|
191
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|
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|
|
18859 18869 18899 18911 18913 18917 18919 18947 18959 18973 18979 19001 19009 |
|
192
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|
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|
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|
|
19013 19031 19037 19051 19069 19073 19079 19081 19087 19121 19139 19141 19157 |
|
193
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|
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|
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|
|
19163 19181 19183 19207 19211 19213 19219 19231 19237 19249 19259 19267 19273 |
|
194
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|
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|
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|
|
19289 19301 19309 19319 19333 19373 19379 19381 19387 19391 19403 19417 19421 |
|
195
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|
|
|
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|
|
19423 19427 19429 19433 19441 19447 19457 19463 19469 19471 19477 19483 19489 |
|
196
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|
|
19501 19507 19531 19541 19543 19553 19559 19571 19577 19583 19597 19603 19609 |
|
197
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|
19661 19681 19687 19697 19699 19709 19717 19727 19739 19751 19753 19759 19763 |
|
198
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|
19777 19793 19801 19813 19819 19841 19843 19853 19861 19867 19889 19891 19913 |
|
199
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|
19919 19927 19937 19949 19961 19963 19973 19979 19991 19993 19997 20011 20021 |
|
200
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|
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|
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|
|
20023 20029 20047 20051 20063 20071 20089 20101 20107 20113 20117 20123 20129 |
|
201
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|
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|
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|
|
20143 20147 20149 20161 20173 20177 20183 20201 20219 20231 20233 20249 20261 |
|
202
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|
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|
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|
|
20269 20287 20297 20323 20327 20333 20341 20347 20353 20357 20359 20369 20389 |
|
203
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|
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|
20393 20399 20407 20411 20431 20441 20443 20477 20479 20483 20507 20509 20521 |
|
204
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|
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|
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|
|
20533 20543 20549 20551 20563 20593 20599 20611 20627 20639 20641 20663 20681 |
|
205
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|
|
|
|
|
|
20693 20707 20717 20719 20731 20743 20747 20749 20753 20759 20771 20773 20789 |
|
206
|
|
|
|
|
|
|
20807 20809 20849 20857 20873 20879 20887 20897 20899 20903 20921 20929 20939 |
|
207
|
|
|
|
|
|
|
20947 20959 20963 20981 20983 21001 21011 21013 21017 21019 21023 21031 21059 |
|
208
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|
|
|
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|
|
21061 21067 21089 21101 21107 21121 21139 21143 21149 21157 21163 21169 21179 |
|
209
|
|
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|
|
21187 21191 21193 21211 21221 21227 21247 21269 21277 21283 21313 21317 21319 |
|
210
|
|
|
|
|
|
|
21323 21341 21347 21377 21379 21383 21391 21397 21401 21407 21419 21433 21467 |
|
211
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|
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|
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|
|
21481 21487 21491 21493 21499 21503 21517 21521 21523 21529 21557 21559 21563 |
|
212
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|
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|
|
21569 21577 21587 21589 21599 21601 21611 21613 21617 21647 21649 21661 21673 |
|
213
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|
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|
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|
|
21683 21701 21713 21727 21737 21739 21751 21757 21767 21773 21787 21799 21803 |
|
214
|
|
|
|
|
|
|
21817 21821 21839 21841 21851 21859 21863 21871 21881 21893 21911 21929 21937 |
|
215
|
|
|
|
|
|
|
21943 21961 21977 21991 21997 22003 22013 22027 22031 22037 22039 22051 22063 |
|
216
|
|
|
|
|
|
|
22067 22073 22079 22091 22093 22109 22111 22123 22129 22133 22147 22153 22157 |
|
217
|
|
|
|
|
|
|
22159 22171 22189 22193 22229 22247 22259 22271 22273 22277 22279 22283 22291 |
|
218
|
|
|
|
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|
|
22303 22307 22343 22349 22367 22369 22381 22391 22397 22409 22433 22441 22447 |
|
219
|
|
|
|
|
|
|
22453 22469 22481 22483 22501 22511 22531 22541 22543 22549 22567 22571 22573 |
|
220
|
|
|
|
|
|
|
22613 22619 22621 22637 22639 22643 22651 22669 22679 22691 22697 22699 22709 |
|
221
|
|
|
|
|
|
|
22717 22721 22727 22739 22741 22751 22769 22777 22783 22787 22807 22811 22817 |
|
222
|
|
|
|
|
|
|
22853 22859 22861 22871 22877 22901 22907 22921 22937 22943 22961 22963 22973 |
|
223
|
|
|
|
|
|
|
22993 23003 23011 23017 23021 23027 23029 23039 23041 23053 23057 23059 23063 |
|
224
|
|
|
|
|
|
|
23071 23081 23087 23099 23117 23131 23143 23159 23167 23173 23189 23197 23201 |
|
225
|
|
|
|
|
|
|
23203 23209 23227 23251 23269 23279 23291 23293 23297 23311 23321 23327 23333 |
|
226
|
|
|
|
|
|
|
23339 23357 23369 23371 23399 23417 23431 23447 23459 23473 23497 23509 23531 |
|
227
|
|
|
|
|
|
|
23537 23539 23549 23557 23561 23563 23567 23581 23593 23599 23603 23609 23623 |
|
228
|
|
|
|
|
|
|
23627 23629 23633 23663 23669 23671 23677 23687 23689 23719 23741 23743 23747 |
|
229
|
|
|
|
|
|
|
23753 23761 23767 23773 23789 23801 23813 23819 23827 23831 23833 23857 23869 |
|
230
|
|
|
|
|
|
|
23873 23879 23887 23893 23899 23909 23911 23917 23929 23957 23971 23977 23981 |
|
231
|
|
|
|
|
|
|
23993 24001 24007 24019 24023 24029 24043 24049 24061 24071 24077 24083 24091 |
|
232
|
|
|
|
|
|
|
24097 24103 24107 24109 24113 24121 24133 24137 24151 24169 24179 24181 24197 |
|
233
|
|
|
|
|
|
|
24203 24223 24229 24239 24247 24251 24281 24317 24329 24337 24359 24371 24373 |
|
234
|
|
|
|
|
|
|
24379 24391 24407 24413 24419 24421 24439 24443 24469 24473 24481 24499 24509 |
|
235
|
|
|
|
|
|
|
24517 24527 24533 24547 24551 24571 24593 24611 24623 24631 24659 24671 24677 |
|
236
|
|
|
|
|
|
|
24683 24691 24697 24709 24733 24749 24763 24767 24781 24793 24799 24809 24821 |
|
237
|
|
|
|
|
|
|
24841 24847 24851 24859 24877 24889 24907 24917 24919 24923 24943 24953 24967 |
|
238
|
|
|
|
|
|
|
24971 24977 24979 24989 25013 25031 25033 25037 25057 25073 25087 25097 25111 |
|
239
|
|
|
|
|
|
|
25117 25121 25127 25147 25153 25163 25169 25171 25183 25189 25219 25229 25237 |
|
240
|
|
|
|
|
|
|
25243 25247 25253 25261 25301 25303 25307 25309 25321 25339 25343 25349 25357 |
|
241
|
|
|
|
|
|
|
25367 25373 25391 25409 25411 25423 25439 25447 25453 25457 25463 25469 25471 |
|
242
|
|
|
|
|
|
|
25523 25537 25541 25561 25577 25579 25583 25589 25601 25603 25609 25621 25633 |
|
243
|
|
|
|
|
|
|
25639 25643 25657 25667 25673 25679 25693 25703 25717 25733 25741 25747 25759 |
|
244
|
|
|
|
|
|
|
25763 25771 25793 25799 25801 25819 25841 25847 25849 25867 25873 25889 25903 |
|
245
|
|
|
|
|
|
|
25913 25919 25931 25933 25939 25943 25951 25969 25981 25997 25999 26003 26017 |
|
246
|
|
|
|
|
|
|
26021 26029 26041 26053 26083 26099 26107 26111 26113 26119 26141 26153 26161 |
|
247
|
|
|
|
|
|
|
26171 26177 26183 26189 26203 26209 26227 26237 26249 26251 26261 26263 26267 |
|
248
|
|
|
|
|
|
|
26293 26297 26309 26317 26321 26339 26347 26357 26371 26387 26393 26399 26407 |
|
249
|
|
|
|
|
|
|
26417 26423 26431 26437 26449 26459 26479 26489 26497 26501 26513 26539 26557 |
|
250
|
|
|
|
|
|
|
26561 26573 26591 26597 26627 26633 26641 26647 26669 26681 26683 26687 26693 |
|
251
|
|
|
|
|
|
|
26699 26701 26711 26713 26717 26723 26729 26731 26737 26759 26777 26783 26801 |
|
252
|
|
|
|
|
|
|
26813 26821 26833 26839 26849 26861 26863 26879 26881 26891 26893 26903 26921 |
|
253
|
|
|
|
|
|
|
26927 26947 26951 26953 26959 26981 26987 26993 27011 27017 27031 27043 27059 |
|
254
|
|
|
|
|
|
|
27061 27067 27073 27077 27091 27103 27107 27109 27127 27143 27179 27191 27197 |
|
255
|
|
|
|
|
|
|
27211 27239 27241 27253 27259 27271 27277 27281 27283 27299 27329 27337 27361 |
|
256
|
|
|
|
|
|
|
27367 27397 27407 27409 27427 27431 27437 27449 27457 27479 27481 27487 27509 |
|
257
|
|
|
|
|
|
|
27527 27529 27539 27541 27551 27581 27583 27611 27617 27631 27647 27653 27673 |
|
258
|
|
|
|
|
|
|
27689 27691 27697 27701 27733 27737 27739 27743 27749 27751 27763 27767 27773 |
|
259
|
|
|
|
|
|
|
27779 27791 27793 27799 27803 27809 27817 27823 27827 27847 27851 27883 27893 |
|
260
|
|
|
|
|
|
|
27901 27917 27919 27941 27943 27947 27953 27961 27967 27983 27997 28001 28019 |
|
261
|
|
|
|
|
|
|
28027 28031 28051 28057 28069 28081 28087 28097 28099 28109 28111 28123 28151 |
|
262
|
|
|
|
|
|
|
28163 28181 28183 28201 28211 28219 28229 28277 28279 28283 28289 28297 28307 |
|
263
|
|
|
|
|
|
|
28309 28319 28349 28351 28387 28393 28403 28409 28411 28429 28433 28439 28447 |
|
264
|
|
|
|
|
|
|
28463 28477 28493 28499 28513 28517 28537 28541 28547 28549 28559 28571 28573 |
|
265
|
|
|
|
|
|
|
28579 28591 28597 28603 28607 28619 28621 28627 28631 28643 28649 28657 28661 |
|
266
|
|
|
|
|
|
|
28663 28669 28687 28697 28703 28711 28723 28729 28751 28753 28759 28771 28789 |
|
267
|
|
|
|
|
|
|
28793 28807 28813 28817 28837 28843 28859 28867 28871 28879 28901 28909 28921 |
|
268
|
|
|
|
|
|
|
28927 28933 28949 28961 28979 29009 29017 29021 29023 29027 29033 29059 29063 |
|
269
|
|
|
|
|
|
|
29077 29101 29123 29129 29131 29137 29147 29153 29167 29173 29179 29191 29201 |
|
270
|
|
|
|
|
|
|
29207 29209 29221 29231 29243 29251 29269 29287 29297 29303 29311 29327 29333 |
|
271
|
|
|
|
|
|
|
29339 29347 29363 29383 29387 29389 29399 29401 29411 29423 29429 29437 29443 |
|
272
|
|
|
|
|
|
|
29453 29473 29483 29501 29527 29531 29537 29567 29569 29573 29581 29587 29599 |
|
273
|
|
|
|
|
|
|
29611 29629 29633 29641 29663 29669 29671 29683 29717 29723 29741 29753 29759 |
|
274
|
|
|
|
|
|
|
29761 29789 29803 29819 29833 29837 29851 29863 29867 29873 29879 29881 29917 |
|
275
|
|
|
|
|
|
|
29921 29927 29947 29959 29983 29989 30011 30013 30029 ); |
|
276
|
|
|
|
|
|
|
|
|
277
|
|
|
|
|
|
|
# An array of gaps between each spoke in the wheel. The largest gap is 18. |
|
278
|
|
|
|
|
|
|
|
|
279
|
|
|
|
|
|
|
my @gaps = qw( 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2 4 2 4 14 4 6 2 10 2 6 6 |
|
280
|
|
|
|
|
|
|
4 6 6 2 10 2 4 2 12 12 4 2 4 6 2 10 6 6 6 2 6 4 2 6 4 14 4 2 4 6 8 6 10 2 4 6 |
|
281
|
|
|
|
|
|
|
2 6 6 6 4 6 2 6 4 8 10 2 10 2 4 2 4 6 8 4 2 4 12 8 4 2 6 4 6 12 2 4 2 12 6 4 |
|
282
|
|
|
|
|
|
|
6 6 6 2 6 10 2 4 6 2 6 6 4 2 10 2 10 2 4 6 6 2 6 6 4 6 8 6 4 2 6 4 6 8 4 2 6 |
|
283
|
|
|
|
|
|
|
4 8 6 4 8 4 6 8 10 2 10 2 6 4 2 4 2 10 2 10 2 4 2 4 14 4 2 4 6 6 2 6 4 8 10 8 |
|
284
|
|
|
|
|
|
|
4 2 4 6 8 6 4 6 6 6 2 6 6 4 2 4 6 2 10 2 4 2 10 2 10 2 6 4 8 6 4 2 4 6 6 8 4 |
|
285
|
|
|
|
|
|
|
2 6 10 8 4 2 6 4 8 10 6 2 4 8 6 6 4 2 4 6 2 6 4 6 2 10 12 2 4 2 4 6 2 6 4 2 4 |
|
286
|
|
|
|
|
|
|
12 2 6 6 10 6 8 4 2 4 2 4 8 6 12 4 6 2 12 4 2 4 6 8 4 2 4 2 12 10 2 4 2 4 6 2 |
|
287
|
|
|
|
|
|
|
10 2 4 6 8 6 4 2 6 4 6 8 4 6 2 4 8 6 4 6 2 4 6 2 6 6 4 6 6 8 6 4 2 10 2 10 2 |
|
288
|
|
|
|
|
|
|
4 2 10 2 6 4 2 10 6 2 6 4 2 6 4 6 8 6 4 2 12 10 6 2 4 6 2 12 4 2 4 8 6 4 2 4 |
|
289
|
|
|
|
|
|
|
2 10 2 10 6 2 4 6 2 6 4 2 10 6 2 6 4 12 6 8 6 4 2 4 8 6 4 6 2 4 6 8 6 6 4 6 2 |
|
290
|
|
|
|
|
|
|
6 4 2 4 2 10 12 2 4 12 2 6 4 2 4 6 6 2 12 6 4 18 2 4 2 4 8 6 4 6 2 4 8 6 6 4 |
|
291
|
|
|
|
|
|
|
2 4 6 2 6 4 2 4 12 2 12 6 4 6 2 6 4 6 6 6 2 6 4 2 6 4 6 8 4 2 4 2 4 14 4 6 2 |
|
292
|
|
|
|
|
|
|
10 2 6 6 4 2 10 2 10 2 4 14 10 2 4 2 4 6 2 6 10 6 6 2 10 2 6 4 6 8 4 2 4 6 8 |
|
293
|
|
|
|
|
|
|
6 10 2 4 6 2 6 6 4 2 4 6 2 6 4 2 6 10 2 10 6 2 4 6 8 4 2 4 12 2 6 4 2 6 4 6 |
|
294
|
|
|
|
|
|
|
12 2 4 2 4 8 6 4 6 2 10 2 6 10 6 6 2 6 4 2 4 2 10 2 12 4 6 6 2 12 4 6 6 2 6 4 |
|
295
|
|
|
|
|
|
|
2 6 4 14 4 2 6 4 8 6 4 6 2 4 6 8 6 6 10 2 6 4 6 2 10 2 10 2 4 2 4 8 6 4 2 4 6 |
|
296
|
|
|
|
|
|
|
6 8 4 8 4 6 8 4 2 4 2 12 6 4 6 6 6 2 6 6 4 2 4 6 2 6 6 4 2 10 2 10 2 6 4 6 2 |
|
297
|
|
|
|
|
|
|
6 4 2 4 6 14 4 2 6 10 8 4 2 4 2 4 8 10 8 4 8 6 10 2 4 6 2 6 4 6 2 10 2 10 2 4 |
|
298
|
|
|
|
|
|
|
2 4 6 8 4 2 4 6 6 2 6 6 6 10 8 4 2 4 6 8 6 4 8 4 6 2 6 6 4 2 4 6 12 2 4 2 10 |
|
299
|
|
|
|
|
|
|
2 10 2 4 2 4 8 10 2 4 6 8 6 4 2 6 4 6 8 4 8 4 8 6 4 6 2 4 6 2 6 6 4 6 6 2 6 6 |
|
300
|
|
|
|
|
|
|
4 2 10 12 2 4 2 4 6 2 6 4 2 16 2 6 4 2 10 6 8 4 2 4 2 12 6 10 2 4 6 2 12 4 2 |
|
301
|
|
|
|
|
|
|
4 8 6 4 2 4 2 12 10 6 2 4 6 2 6 4 2 4 6 6 2 6 4 2 10 6 8 10 2 4 8 6 4 6 2 4 6 |
|
302
|
|
|
|
|
|
|
2 6 6 6 4 6 8 4 2 4 2 10 12 2 4 2 10 2 6 4 2 4 6 6 2 10 2 6 4 14 6 4 2 4 8 10 |
|
303
|
|
|
|
|
|
|
6 2 4 6 2 6 6 4 2 4 8 6 4 2 4 12 2 12 4 2 4 6 2 6 4 2 10 6 2 6 4 8 4 6 8 4 2 |
|
304
|
|
|
|
|
|
|
4 2 4 14 4 6 2 10 8 6 4 2 4 6 2 10 2 4 2 12 10 2 4 6 6 2 6 4 6 6 6 2 6 6 6 4 |
|
305
|
|
|
|
|
|
|
6 12 2 4 6 8 6 10 2 4 8 6 6 4 2 4 6 2 6 4 2 6 10 2 10 2 6 4 6 8 4 6 12 2 6 4 |
|
306
|
|
|
|
|
|
|
2 6 4 6 12 2 4 2 4 14 4 6 2 4 6 2 6 10 2 10 2 6 4 2 4 12 2 10 2 4 6 6 2 6 6 4 |
|
307
|
|
|
|
|
|
|
6 6 2 10 2 6 4 6 8 4 2 6 4 8 6 4 6 2 4 6 8 6 4 2 10 2 6 4 2 6 10 2 10 6 2 4 8 |
|
308
|
|
|
|
|
|
|
6 4 2 4 6 6 2 6 4 8 4 6 8 4 2 4 2 4 8 6 4 6 12 2 6 6 4 6 6 2 6 4 2 4 2 10 2 |
|
309
|
|
|
|
|
|
|
12 6 4 6 2 10 2 4 6 6 8 4 2 6 18 4 2 4 2 4 8 10 6 2 4 8 6 6 6 4 6 2 6 4 6 2 |
|
310
|
|
|
|
|
|
|
10 2 10 2 4 2 4 6 2 6 4 2 4 6 6 8 6 6 4 6 8 4 2 4 2 12 6 4 12 6 2 6 6 4 2 4 6 |
|
311
|
|
|
|
|
|
|
8 6 4 2 10 2 10 2 4 2 4 6 2 10 2 4 6 8 6 4 2 6 4 6 8 4 6 2 4 8 6 4 8 4 6 2 6 |
|
312
|
|
|
|
|
|
|
10 6 6 2 6 6 4 2 10 2 10 2 4 2 4 6 8 4 2 10 6 2 6 4 2 6 10 8 4 2 4 14 6 4 6 2 |
|
313
|
|
|
|
|
|
|
4 6 2 12 4 2 4 8 10 2 4 2 10 2 10 6 2 4 8 6 4 2 4 6 6 2 6 4 2 10 6 8 6 6 4 8 |
|
314
|
|
|
|
|
|
|
6 4 6 2 4 6 2 6 6 6 4 6 2 6 4 2 4 2 10 12 2 4 2 10 2 6 4 2 4 12 2 10 2 10 14 |
|
315
|
|
|
|
|
|
|
4 2 4 2 4 8 6 10 2 4 6 2 12 4 2 4 6 2 6 4 2 4 14 12 4 2 4 6 2 6 4 2 4 6 6 2 6 |
|
316
|
|
|
|
|
|
|
4 2 6 4 6 8 4 6 2 4 14 4 6 2 10 2 6 6 4 2 4 6 12 2 4 2 12 10 2 4 2 10 2 6 4 6 |
|
317
|
|
|
|
|
|
|
6 6 2 6 4 2 6 4 6 8 6 4 6 8 16 2 4 6 2 6 6 4 2 4 8 6 4 2 6 10 2 10 2 4 2 4 6 |
|
318
|
|
|
|
|
|
|
8 4 2 16 2 6 4 8 4 6 12 2 4 2 4 8 6 4 6 2 4 6 8 10 2 4 6 2 6 4 2 4 2 10 2 10 |
|
319
|
|
|
|
|
|
|
2 4 6 6 2 6 6 4 6 6 2 6 6 6 4 6 12 2 6 4 8 6 4 6 2 4 14 6 4 2 10 2 6 4 2 4 2 |
|
320
|
|
|
|
|
|
|
10 2 10 2 6 4 8 6 4 6 6 6 2 6 4 8 4 6 8 4 2 4 2 4 14 4 6 6 6 2 6 6 4 2 10 2 6 |
|
321
|
|
|
|
|
|
|
4 2 4 12 2 10 2 6 4 6 2 6 6 4 6 6 12 2 6 10 8 4 2 4 2 4 8 10 6 2 4 8 6 6 4 2 |
|
322
|
|
|
|
|
|
|
4 6 2 6 4 8 10 2 10 6 2 4 6 2 6 4 2 4 6 6 2 6 6 6 4 6 8 4 2 4 2 4 8 6 4 8 10 |
|
323
|
|
|
|
|
|
|
2 6 6 4 6 6 8 4 2 4 2 10 2 12 4 2 4 6 2 10 2 4 6 8 6 4 2 6 4 14 4 6 2 4 8 6 4 |
|
324
|
|
|
|
|
|
|
6 2 4 6 2 6 6 10 6 2 6 10 2 10 2 10 2 4 2 4 6 2 6 4 2 10 6 8 4 2 6 4 6 8 4 2 |
|
325
|
|
|
|
|
|
|
4 2 12 6 4 6 6 6 2 12 4 2 4 8 6 6 4 2 10 2 10 6 2 4 6 2 6 4 2 4 6 8 6 4 2 10 |
|
326
|
|
|
|
|
|
|
6 8 6 4 2 4 8 6 4 8 4 6 2 6 12 4 6 2 6 4 2 4 2 10 12 2 4 2 10 8 4 2 4 6 6 2 |
|
327
|
|
|
|
|
|
|
10 2 6 18 4 2 4 6 8 6 4 6 2 4 6 2 6 6 4 2 4 6 2 10 2 4 12 2 12 4 2 4 8 6 4 2 |
|
328
|
|
|
|
|
|
|
4 6 6 2 6 4 2 6 4 6 8 4 2 6 4 14 4 6 2 10 2 6 6 4 2 4 6 2 10 2 4 2 22 2 4 2 4 |
|
329
|
|
|
|
|
|
|
6 2 6 4 6 12 2 6 4 2 10 6 8 4 2 4 6 8 6 10 2 4 6 2 12 4 2 4 6 2 6 4 2 6 12 10 |
|
330
|
|
|
|
|
|
|
2 4 2 4 6 8 4 2 4 12 2 6 4 2 6 4 6 12 6 2 4 8 6 4 6 2 4 6 2 6 10 2 4 6 8 4 2 |
|
331
|
|
|
|
|
|
|
4 2 10 2 10 2 4 12 2 6 6 4 6 6 2 6 4 2 6 4 6 8 6 6 4 8 10 6 2 4 6 8 6 4 2 12 |
|
332
|
|
|
|
|
|
|
6 4 2 4 2 10 2 10 2 4 2 4 8 6 4 2 10 6 2 6 4 8 4 6 8 4 2 4 2 4 8 6 4 6 6 6 8 |
|
333
|
|
|
|
|
|
|
6 4 2 4 6 2 6 4 2 4 2 10 2 10 2 10 6 2 6 4 2 4 6 6 8 6 6 10 12 2 4 2 4 8 10 6 |
|
334
|
|
|
|
|
|
|
2 4 8 6 6 4 2 4 6 2 6 4 6 2 10 2 10 2 6 4 6 2 6 4 6 6 6 2 6 6 6 4 6 8 4 2 4 2 |
|
335
|
|
|
|
|
|
|
4 14 4 8 4 6 2 6 6 4 2 10 8 4 2 4 12 2 10 2 4 2 4 6 2 12 4 6 8 10 2 6 4 6 8 4 |
|
336
|
|
|
|
|
|
|
6 2 4 8 6 4 6 2 4 6 2 6 6 4 6 6 2 6 6 6 10 2 10 6 2 4 6 2 6 4 2 10 6 2 6 4 2 |
|
337
|
|
|
|
|
|
|
6 4 6 8 4 2 4 2 12 6 4 6 2 10 2 12 4 6 8 6 4 2 4 2 10 2 16 2 4 6 2 10 2 4 6 6 |
|
338
|
|
|
|
|
|
|
2 6 4 2 10 14 6 4 2 4 8 6 4 6 2 4 6 2 6 6 6 4 6 2 6 4 6 2 10 12 2 4 2 10 2 6 |
|
339
|
|
|
|
|
|
|
4 2 4 6 6 12 2 6 4 14 4 2 4 2 12 6 4 6 6 6 2 6 6 4 2 4 6 2 6 6 4 12 2 12 4 2 |
|
340
|
|
|
|
|
|
|
4 6 2 6 4 2 4 6 8 6 4 2 6 4 6 8 4 2 4 2 4 14 4 8 10 2 6 10 2 4 6 2 10 2 4 2 |
|
341
|
|
|
|
|
|
|
12 10 2 4 2 4 6 8 4 6 6 6 2 6 4 2 6 10 8 4 2 4 6 8 6 10 2 4 6 2 6 6 4 2 4 6 2 |
|
342
|
|
|
|
|
|
|
10 2 6 10 2 10 2 4 2 4 14 4 2 4 12 2 6 4 2 6 4 6 12 2 6 4 8 6 4 6 2 4 6 2 6 |
|
343
|
|
|
|
|
|
|
10 2 4 6 2 6 4 2 4 2 10 12 2 4 6 6 2 6 6 4 12 2 6 4 2 10 6 8 4 2 6 4 8 6 10 2 |
|
344
|
|
|
|
|
|
|
4 6 14 4 2 10 2 6 4 2 4 2 12 10 2 4 2 4 8 6 4 2 4 6 6 2 6 4 8 4 6 8 4 6 2 4 8 |
|
345
|
|
|
|
|
|
|
6 4 6 6 6 2 6 6 4 2 4 6 8 4 2 4 2 10 2 10 2 6 10 2 6 4 2 4 6 6 8 4 2 6 10 8 6 |
|
346
|
|
|
|
|
|
|
4 2 4 8 10 6 2 4 8 6 6 4 2 4 8 6 4 6 2 10 2 10 2 4 2 4 6 2 6 4 2 10 6 2 6 12 |
|
347
|
|
|
|
|
|
|
4 6 8 4 2 4 2 4 8 6 4 8 4 6 8 6 4 2 4 6 8 4 2 4 2 10 2 10 2 4 6 6 2 10 2 4 6 |
|
348
|
|
|
|
|
|
|
8 6 6 6 4 6 12 6 2 4 8 6 4 6 2 4 8 6 6 4 6 6 2 6 6 4 2 10 2 10 2 6 4 6 2 6 4 |
|
349
|
|
|
|
|
|
|
12 6 2 6 4 2 6 4 6 8 4 2 4 2 18 4 6 2 4 6 2 12 4 2 12 6 4 2 4 12 2 10 6 2 4 6 |
|
350
|
|
|
|
|
|
|
2 6 6 4 6 6 2 10 2 10 6 8 6 4 2 4 8 6 4 6 2 4 6 2 6 6 6 4 6 2 6 4 2 6 10 12 6 |
|
351
|
|
|
|
|
|
|
2 10 2 6 4 2 4 6 6 2 10 2 6 4 14 4 2 4 2 4 8 6 4 6 2 10 2 6 6 4 6 6 2 6 4 2 4 |
|
352
|
|
|
|
|
|
|
12 2 12 4 2 4 6 2 10 2 4 6 6 2 6 4 2 6 4 14 4 2 4 2 4 14 4 6 2 10 2 6 6 6 4 6 |
|
353
|
|
|
|
|
|
|
2 10 6 2 12 10 2 4 2 4 6 2 6 4 6 6 6 8 4 2 6 4 6 8 4 2 4 14 6 10 6 6 2 6 6 4 |
|
354
|
|
|
|
|
|
|
2 4 6 2 6 6 6 10 2 10 2 4 2 4 6 8 4 2 4 14 6 4 2 6 4 6 12 2 4 2 4 8 6 4 8 4 6 |
|
355
|
|
|
|
|
|
|
2 6 10 2 4 6 2 6 4 2 4 2 10 2 10 2 4 6 6 8 6 4 6 6 2 6 4 2 6 10 8 4 2 10 8 6 |
|
356
|
|
|
|
|
|
|
4 6 2 4 6 8 6 4 2 10 2 10 2 4 2 10 2 10 2 4 2 4 8 6 4 2 4 6 6 2 6 4 8 4 6 8 4 |
|
357
|
|
|
|
|
|
|
2 6 4 8 6 4 6 6 6 2 6 6 4 2 4 6 2 6 4 2 4 2 10 12 2 6 4 6 2 6 4 2 4 12 8 4 2 |
|
358
|
|
|
|
|
|
|
16 8 4 2 4 2 4 8 16 2 4 8 12 4 2 4 6 2 6 4 6 2 12 10 2 4 2 4 6 2 6 4 2 4 6 6 |
|
359
|
|
|
|
|
|
|
2 6 6 6 4 6 8 4 6 2 4 8 6 4 8 4 6 2 6 6 4 2 4 6 8 4 2 4 2 10 2 10 2 4 2 10 2 |
|
360
|
|
|
|
|
|
|
10 2 4 6 8 6 4 2 6 4 6 8 10 2 4 8 10 6 2 4 6 2 6 6 4 6 8 6 6 4 2 10 2 10 2 4 |
|
361
|
|
|
|
|
|
|
2 4 6 2 6 4 2 10 6 2 6 4 8 4 6 8 4 2 4 2 12 6 4 6 2 4 6 14 4 2 4 8 6 4 2 4 2 |
|
362
|
|
|
|
|
|
|
10 2 10 6 6 6 2 6 4 2 4 6 6 2 6 6 10 6 14 4 2 4 8 6 4 6 2 4 8 6 6 6 4 6 2 6 4 |
|
363
|
|
|
|
|
|
|
2 4 2 10 12 2 6 10 2 6 4 6 6 6 2 10 2 6 4 14 4 2 4 2 4 14 4 6 2 4 6 2 6 6 4 2 |
|
364
|
|
|
|
|
|
|
10 2 6 4 2 4 12 2 12 4 2 4 6 2 6 6 4 6 6 2 10 2 6 4 6 8 4 2 4 2 4 14 4 6 2 10 |
|
365
|
|
|
|
|
|
|
2 6 6 4 2 4 6 2 10 2 6 12 10 6 2 4 6 2 6 4 6 6 6 2 6 4 2 6 4 6 8 4 2 4 6 8 6 |
|
366
|
|
|
|
|
|
|
10 2 10 2 6 6 4 6 6 2 6 4 2 6 10 2 12 4 2 4 6 12 2 4 12 2 6 4 2 6 4 18 2 4 2 |
|
367
|
|
|
|
|
|
|
4 8 6 4 6 2 4 6 2 6 12 4 6 2 6 4 6 2 10 2 10 2 4 6 6 2 6 6 4 6 6 8 4 2 6 4 6 |
|
368
|
|
|
|
|
|
|
8 4 2 6 12 6 4 6 6 6 8 6 4 2 10 2 6 6 4 2 10 2 10 2 4 2 4 8 6 4 2 4 6 8 6 4 8 |
|
369
|
|
|
|
|
|
|
4 6 8 4 2 4 2 4 8 6 4 12 6 2 6 10 2 4 6 2 6 4 2 4 2 10 2 10 2 6 4 6 8 4 2 4 6 |
|
370
|
|
|
|
|
|
|
6 8 4 2 6 10 8 4 2 4 6 8 10 6 2 4 8 6 6 4 2 4 6 2 10 6 2 10 2 10 2 4 2 4 8 6 |
|
371
|
|
|
|
|
|
|
4 2 4 6 6 2 6 6 6 4 6 8 4 2 6 4 8 6 4 8 4 6 2 6 6 4 2 4 6 8 4 2 4 2 10 12 2 4 |
|
372
|
|
|
|
|
|
|
2 4 6 2 10 2 4 14 6 4 2 10 6 8 4 6 2 4 8 6 10 2 4 6 2 12 4 6 6 2 6 6 4 2 12 |
|
373
|
|
|
|
|
|
|
10 2 4 2 4 6 2 6 4 2 10 6 2 6 4 2 6 4 6 8 4 6 2 12 6 4 6 2 4 6 2 12 4 2 4 14 |
|
374
|
|
|
|
|
|
|
4 2 4 2 10 2 10 6 2 10 2 6 4 2 4 6 6 2 6 4 2 10 6 8 6 4 2 4 8 10 6 2 4 6 2 6 |
|
375
|
|
|
|
|
|
|
6 6 4 8 6 4 2 4 2 10 12 2 4 2 10 2 6 4 2 10 6 2 10 8 4 14 4 2 4 2 4 8 6 4 6 2 |
|
376
|
|
|
|
|
|
|
4 6 8 6 4 2 4 6 2 6 4 2 4 12 2 12 4 6 6 2 6 4 2 4 6 6 2 6 6 6 4 6 12 2 4 2 4 |
|
377
|
|
|
|
|
|
|
14 4 6 2 12 6 6 4 2 4 6 2 10 2 4 2 12 10 2 6 4 6 2 6 4 6 6 6 2 6 4 2 6 4 6 8 |
|
378
|
|
|
|
|
|
|
4 2 4 6 14 10 2 4 6 2 6 6 4 2 10 2 6 4 2 16 2 10 2 4 2 4 6 8 6 4 12 2 10 2 6 |
|
379
|
|
|
|
|
|
|
4 6 12 2 4 2 4 8 6 4 6 2 4 6 2 6 10 2 4 6 2 6 4 2 6 10 2 10 6 6 6 2 6 6 4 6 6 |
|
380
|
|
|
|
|
|
|
2 6 4 2 6 4 6 8 4 2 6 4 8 6 4 6 2 10 8 6 4 12 2 6 4 2 4 2 10 2 12 4 2 4 8 10 |
|
381
|
|
|
|
|
|
|
2 4 6 6 2 6 4 8 4 14 4 2 4 2 4 8 6 4 6 6 6 2 6 6 6 4 6 2 6 4 6 2 10 2 10 2 6 |
|
382
|
|
|
|
|
|
|
4 6 2 6 4 2 4 6 6 8 4 2 6 10 8 4 2 4 2 12 10 6 6 8 6 6 4 2 4 6 2 6 10 2 10 2 |
|
383
|
|
|
|
|
|
|
10 2 4 2 4 6 2 6 4 2 4 6 8 6 6 6 4 6 8 4 2 4 2 4 8 6 4 8 4 6 2 6 10 2 4 6 8 4 |
|
384
|
|
|
|
|
|
|
2 4 2 10 2 10 2 4 2 4 6 12 2 4 6 8 6 4 2 6 10 8 4 6 6 8 6 4 6 2 4 6 2 6 6 4 6 |
|
385
|
|
|
|
|
|
|
6 2 12 4 2 10 2 10 2 4 2 4 8 6 4 2 10 6 2 6 4 2 6 4 6 8 4 2 6 12 6 4 6 2 4 6 |
|
386
|
|
|
|
|
|
|
2 12 4 2 4 8 6 4 2 4 2 10 12 6 2 4 6 2 6 4 2 4 12 2 6 4 2 10 6 8 6 4 2 4 8 6 |
|
387
|
|
|
|
|
|
|
10 2 4 6 2 12 6 4 6 2 6 4 2 4 2 22 2 4 2 10 2 6 4 2 4 6 6 2 10 2 6 4 14 4 6 2 |
|
388
|
|
|
|
|
|
|
4 8 6 4 6 2 4 6 2 6 6 4 2 4 6 8 4 2 4 12 2 12 4 2 10 2 6 4 2 4 6 6 2 6 4 2 6 |
|
389
|
|
|
|
|
|
|
4 6 8 6 4 2 4 18 6 2 10 2 6 6 4 2 4 8 10 2 4 2 12 10 2 4 2 4 6 2 6 4 12 6 2 6 |
|
390
|
|
|
|
|
|
|
4 8 4 6 8 4 2 4 6 8 6 10 2 4 6 8 6 4 2 4 6 2 6 4 2 6 10 2 10 2 4 6 6 8 4 2 4 |
|
391
|
|
|
|
|
|
|
12 2 6 6 6 4 6 12 2 4 2 4 8 6 4 6 2 4 8 6 10 2 4 6 2 6 4 2 4 2 10 2 10 2 10 6 |
|
392
|
|
|
|
|
|
|
2 6 10 6 6 2 6 4 2 6 4 6 8 4 2 6 4 14 4 6 2 4 6 8 6 4 2 10 2 6 4 2 4 12 2 10 |
|
393
|
|
|
|
|
|
|
2 4 2 4 8 6 6 4 6 6 2 10 8 4 6 8 4 2 4 2 4 8 6 4 6 6 6 2 6 6 4 2 4 6 2 6 4 2 |
|
394
|
|
|
|
|
|
|
6 10 2 10 8 4 6 2 6 4 2 4 6 6 8 4 2 6 10 8 4 2 4 2 4 8 10 6 2 12 6 6 4 6 6 2 |
|
395
|
|
|
|
|
|
|
6 4 6 2 10 2 12 4 2 4 6 2 10 2 4 6 6 2 6 6 6 4 14 4 2 4 2 4 8 6 4 8 4 6 2 6 6 |
|
396
|
|
|
|
|
|
|
6 4 6 8 4 6 2 10 2 10 2 4 2 4 6 2 10 2 4 6 14 4 2 6 4 6 8 4 6 2 12 6 4 6 6 6 |
|
397
|
|
|
|
|
|
|
2 6 6 4 6 6 2 6 6 4 2 10 2 10 2 4 2 4 6 2 6 4 2 10 8 6 4 2 6 4 6 8 4 2 4 2 12 |
|
398
|
|
|
|
|
|
|
6 4 8 4 6 2 16 2 4 8 6 4 2 4 2 10 2 10 6 2 4 6 8 4 2 4 6 6 2 6 4 2 16 8 6 4 6 |
|
399
|
|
|
|
|
|
|
8 6 4 6 2 4 6 2 6 6 6 4 6 2 10 2 4 2 10 12 2 4 2 12 6 4 2 4 6 6 2 10 2 6 4 14 |
|
400
|
|
|
|
|
|
|
4 2 6 4 8 6 4 6 2 4 6 2 6 6 4 2 4 6 2 6 4 2 4 12 14 4 2 4 6 2 6 4 2 4 12 2 6 |
|
401
|
|
|
|
|
|
|
4 2 10 6 8 4 2 4 2 4 14 10 2 10 2 12 4 2 4 6 2 10 2 4 2 12 10 2 4 2 4 6 2 6 4 |
|
402
|
|
|
|
|
|
|
6 6 6 2 6 4 2 6 4 6 8 4 6 6 8 6 10 2 4 6 2 6 6 4 2 4 6 8 4 2 6 10 2 10 2 4 2 |
|
403
|
|
|
|
|
|
|
10 8 4 2 4 12 2 6 4 2 6 4 6 14 4 2 4 8 10 6 2 4 6 2 6 10 2 4 8 6 4 2 4 2 10 2 |
|
404
|
|
|
|
|
|
|
10 2 4 6 6 2 6 6 10 6 2 6 4 8 4 6 8 4 2 6 4 8 6 4 6 2 4 6 8 6 4 2 10 2 6 4 2 |
|
405
|
|
|
|
|
|
|
4 2 10 2 10 2 4 6 8 6 4 2 4 6 6 2 6 12 4 6 12 2 4 2 4 8 6 4 6 6 8 6 6 4 2 4 6 |
|
406
|
|
|
|
|
|
|
2 6 4 2 4 2 10 2 10 2 6 4 6 2 6 4 6 6 6 8 4 2 6 10 8 4 2 4 2 4 18 6 2 4 8 6 6 |
|
407
|
|
|
|
|
|
|
4 2 10 2 6 4 6 12 2 10 2 4 2 4 6 2 6 6 4 6 6 2 12 6 4 6 8 4 2 4 2 4 8 6 4 8 4 |
|
408
|
|
|
|
|
|
|
6 2 6 6 4 2 4 6 8 4 2 6 10 2 10 6 2 4 6 2 10 2 4 6 8 6 4 2 6 4 6 8 4 6 2 4 8 |
|
409
|
|
|
|
|
|
|
6 4 6 2 10 2 6 6 4 6 6 2 6 6 4 2 10 2 12 4 2 4 6 2 10 2 10 6 2 6 4 2 6 4 14 4 |
|
410
|
|
|
|
|
|
|
2 4 2 12 6 4 6 2 4 6 2 12 6 4 8 6 4 6 2 10 2 10 6 2 4 6 2 6 4 2 4 6 6 8 4 2 |
|
411
|
|
|
|
|
|
|
10 6 8 6 4 2 12 6 4 6 6 6 2 6 6 6 4 6 2 6 6 4 2 10 12 2 4 2 10 2 6 4 2 4 6 8 |
|
412
|
|
|
|
|
|
|
10 2 6 4 14 4 2 4 2 4 8 6 4 8 4 6 2 6 10 2 4 6 2 6 4 2 4 12 2 12 4 2 4 6 8 4 |
|
413
|
|
|
|
|
|
|
2 4 6 6 2 6 4 2 6 10 8 4 2 4 6 14 4 6 2 10 2 6 6 4 2 4 6 2 10 2 4 2 12 10 2 4 |
|
414
|
|
|
|
|
|
|
2 4 8 6 4 6 6 6 2 6 4 2 6 4 6 8 4 2 10 8 6 10 2 4 6 2 6 6 4 2 4 6 2 6 4 2 6 |
|
415
|
|
|
|
|
|
|
10 12 2 4 2 4 6 8 4 2 4 12 2 6 4 2 10 6 12 2 4 2 4 8 6 10 2 4 6 2 16 2 4 6 2 |
|
416
|
|
|
|
|
|
|
6 4 2 4 2 12 10 2 4 6 6 2 6 6 4 6 6 2 6 4 2 6 4 6 8 4 8 4 8 6 4 6 2 4 6 8 6 4 |
|
417
|
|
|
|
|
|
|
2 10 8 4 2 4 2 10 2 10 2 4 2 12 6 4 2 4 6 6 2 6 4 8 4 6 8 6 4 2 4 8 10 6 6 6 |
|
418
|
|
|
|
|
|
|
2 6 6 4 2 4 8 6 4 2 4 2 10 2 10 2 6 4 6 2 6 4 2 10 6 8 4 8 10 8 4 2 4 2 4 8 |
|
419
|
|
|
|
|
|
|
10 6 2 4 14 6 4 2 4 6 2 6 4 6 2 10 2 10 2 4 6 6 2 6 4 2 4 6 6 2 6 6 6 4 6 12 |
|
420
|
|
|
|
|
|
|
2 4 2 4 8 6 4 8 4 8 6 6 4 2 4 6 8 4 2 4 2 10 2 10 2 6 4 6 2 10 6 6 8 6 4 2 6 |
|
421
|
|
|
|
|
|
|
4 6 8 4 6 2 4 14 4 6 2 4 6 2 6 6 4 12 2 6 6 4 12 2 10 2 4 2 4 6 2 6 6 10 6 2 |
|
422
|
|
|
|
|
|
|
10 2 6 4 6 8 4 2 4 2 12 6 4 6 2 4 6 2 12 4 2 4 8 6 4 2 6 10 2 10 6 2 4 6 2 6 |
|
423
|
|
|
|
|
|
|
4 2 4 6 6 2 6 4 2 10 6 8 6 4 2 4 8 6 4 6 2 10 2 6 6 10 6 2 6 4 2 4 2 10 14 4 |
|
424
|
|
|
|
|
|
|
2 10 2 10 2 4 6 6 2 10 2 6 4 14 4 2 4 2 4 8 6 4 6 2 4 6 2 6 6 6 4 6 2 6 4 6 |
|
425
|
|
|
|
|
|
|
12 2 12 4 2 4 6 2 6 4 2 4 6 6 8 4 2 6 4 6 8 4 2 4 2 18 4 6 12 2 6 6 4 2 4 6 2 |
|
426
|
|
|
|
|
|
|
12 4 2 12 10 2 4 2 4 6 2 6 4 6 6 8 6 4 2 6 4 6 8 4 2 4 6 8 6 12 4 6 2 6 10 2 |
|
427
|
|
|
|
|
|
|
4 6 2 6 4 2 6 10 2 10 2 4 2 4 6 8 4 2 4 12 2 6 4 2 6 10 12 2 4 6 8 6 4 6 2 4 |
|
428
|
|
|
|
|
|
|
6 2 6 10 2 4 6 2 10 2 4 2 10 2 10 2 4 6 8 6 6 4 6 6 2 6 4 2 6 4 6 8 4 2 6 4 8 |
|
429
|
|
|
|
|
|
|
6 4 6 2 4 6 8 6 4 2 10 2 6 4 2 4 2 10 12 2 4 2 4 8 6 4 2 4 12 2 6 4 12 6 8 4 |
|
430
|
|
|
|
|
|
|
2 4 2 4 8 6 10 6 6 2 12 4 2 4 6 2 6 4 2 4 2 12 10 2 6 4 6 2 6 4 2 4 6 6 8 4 2 |
|
431
|
|
|
|
|
|
|
6 10 8 4 6 2 4 8 10 6 2 4 8 6 6 4 2 4 6 8 4 6 2 10 2 10 2 4 2 10 2 6 4 2 4 6 |
|
432
|
|
|
|
|
|
|
6 2 6 6 6 4 6 8 6 4 2 4 8 10 8 4 6 2 6 6 4 2 4 14 4 2 4 2 10 2 10 2 4 2 4 6 2 |
|
433
|
|
|
|
|
|
|
10 2 10 8 6 4 8 4 6 8 4 6 2 4 8 6 4 6 2 4 6 8 6 4 6 6 2 6 6 4 2 10 2 10 2 4 6 |
|
434
|
|
|
|
|
|
|
6 2 6 4 2 10 6 2 6 6 6 4 6 12 2 4 2 12 6 4 6 2 4 8 12 4 2 4 8 6 4 2 4 2 10 2 |
|
435
|
|
|
|
|
|
|
10 8 4 6 2 6 4 6 6 6 2 6 4 2 10 6 8 6 4 2 4 14 4 6 2 4 6 2 6 6 6 10 2 6 4 2 4 |
|
436
|
|
|
|
|
|
|
12 12 2 4 2 10 2 6 6 4 6 6 2 10 2 6 4 14 4 2 4 2 4 8 6 4 6 2 4 6 2 6 6 4 2 4 |
|
437
|
|
|
|
|
|
|
6 2 6 4 2 16 2 16 ); |
|
438
|
|
|
|
|
|
|
|
|
439
|
|
|
|
|
|
|
# run if called directly, indirectly, directly par-packed, undirectly par-packed |
|
440
|
|
|
|
|
|
|
__PACKAGE__->run( \*STDOUT, @ARGV ) if !caller() || caller(0) =~ /^(PerlPowerTools::Packed|PAR)$/ || caller(1) eq 'PAR'; # modulino |
|
441
|
|
|
|
|
|
|
|
|
442
|
|
|
|
|
|
|
sub run { |
|
443
|
1014
|
|
|
1014
|
|
1136899
|
my ($self, $fh, @numbers) = @_; |
|
444
|
1014
|
50
|
|
|
|
3037
|
$fh = *STDOUT unless defined $fh; |
|
445
|
|
|
|
|
|
|
|
|
446
|
1014
|
|
|
|
|
3386
|
my $old = select $fh; |
|
447
|
|
|
|
|
|
|
|
|
448
|
1014
|
50
|
|
|
|
2875
|
if (@numbers) { |
|
449
|
1014
|
|
|
|
|
1889
|
foreach (@numbers) { |
|
450
|
1015
|
|
|
|
|
1947
|
factor($_); |
|
451
|
|
|
|
|
|
|
} |
|
452
|
|
|
|
|
|
|
} else { |
|
453
|
0
|
|
|
|
|
0
|
while (<>) { |
|
454
|
0
|
|
|
|
|
0
|
chomp; |
|
455
|
0
|
0
|
|
|
|
0
|
if (/^\s*(\S+)/) { |
|
456
|
0
|
|
|
|
|
0
|
factor($1); |
|
457
|
|
|
|
|
|
|
} |
|
458
|
|
|
|
|
|
|
} |
|
459
|
|
|
|
|
|
|
} |
|
460
|
|
|
|
|
|
|
|
|
461
|
1014
|
|
|
|
|
2629
|
select $old; |
|
462
|
|
|
|
|
|
|
|
|
463
|
1014
|
|
|
|
|
2699
|
exit 0; |
|
464
|
|
|
|
|
|
|
} |
|
465
|
|
|
|
|
|
|
|
|
466
|
|
|
|
|
|
|
sub factor { |
|
467
|
1015
|
|
|
1015
|
|
1802
|
my $n = shift; |
|
468
|
|
|
|
|
|
|
|
|
469
|
|
|
|
|
|
|
# Check input. |
|
470
|
|
|
|
|
|
|
|
|
471
|
1015
|
50
|
|
|
|
6550
|
unless ($n =~ /^\+?\d+$/) { |
|
472
|
0
|
|
|
|
|
0
|
warn "$0: `$n:' is not a valid positive integer\n"; |
|
473
|
0
|
|
|
|
|
0
|
return; |
|
474
|
|
|
|
|
|
|
} |
|
475
|
|
|
|
|
|
|
|
|
476
|
1015
|
50
|
66
|
|
|
3795
|
if ($n % 2 == 0 && ($n - 1) % 2 == 0) { |
|
477
|
0
|
|
|
|
|
0
|
warn "$0: `$n:' is too large\n"; |
|
478
|
0
|
|
|
|
|
0
|
return; |
|
479
|
|
|
|
|
|
|
} |
|
480
|
|
|
|
|
|
|
|
|
481
|
1015
|
50
|
|
|
|
3205
|
print "$n:" or die "$0: print failed: $!"; |
|
482
|
|
|
|
|
|
|
|
|
483
|
|
|
|
|
|
|
# Quick exit when the input is 0 or 1. |
|
484
|
|
|
|
|
|
|
|
|
485
|
1015
|
50
|
|
|
|
2097
|
if ($n < 2) { |
|
486
|
0
|
0
|
|
|
|
0
|
print "\n" or die "$0: print failed: $!"; |
|
487
|
0
|
|
|
|
|
0
|
return; |
|
488
|
|
|
|
|
|
|
} |
|
489
|
|
|
|
|
|
|
|
|
490
|
|
|
|
|
|
|
# First check the basis primes and the primes in the first round through |
|
491
|
|
|
|
|
|
|
# the wheel, i.e., all primes smaller than 17 + 30030. |
|
492
|
|
|
|
|
|
|
|
|
493
|
1015
|
|
|
|
|
1995
|
my $s = sqrt($n); |
|
494
|
1015
|
|
|
|
|
1770
|
for my $p (@primes) { |
|
495
|
17260
|
|
|
|
|
31650
|
until ($n % $p) { |
|
496
|
26
|
50
|
|
|
|
46
|
print " $p" or die "$0: print failed: $!"; |
|
497
|
26
|
|
|
|
|
25
|
$n /= $p; |
|
498
|
26
|
|
|
|
|
39
|
$s = sqrt($n); |
|
499
|
|
|
|
|
|
|
} |
|
500
|
17260
|
100
|
|
|
|
28083
|
last if $p > $s; |
|
501
|
|
|
|
|
|
|
} |
|
502
|
|
|
|
|
|
|
|
|
503
|
|
|
|
|
|
|
# Now start going through the wheel. We have already done the first round |
|
504
|
|
|
|
|
|
|
# above, so we start at $pinit + $circ rather than at $pinit. |
|
505
|
|
|
|
|
|
|
# |
|
506
|
|
|
|
|
|
|
# We could compare $f and $s in the innermost loop. That would cause the |
|
507
|
|
|
|
|
|
|
# algorithm to halt while we are going through the last round in the wheel |
|
508
|
|
|
|
|
|
|
# rather than after the round has completed. However, it is not worth the |
|
509
|
|
|
|
|
|
|
# added cost of performing this comparison every time $f in incremented. |
|
510
|
|
|
|
|
|
|
|
|
511
|
1015
|
|
|
|
|
1657
|
my $f = $pinit + $circ; # possible factor |
|
512
|
|
|
|
|
|
|
|
|
513
|
1015
|
|
|
|
|
2442
|
while ($f <= $s) { |
|
514
|
0
|
|
|
|
|
0
|
for my $gap (@gaps) { |
|
515
|
0
|
|
|
|
|
0
|
until ($n % $f) { |
|
516
|
0
|
0
|
|
|
|
0
|
print " $f" or die "$0: print failed: $!"; |
|
517
|
0
|
|
|
|
|
0
|
$n /= $f; |
|
518
|
0
|
|
|
|
|
0
|
$s = sqrt($n); |
|
519
|
|
|
|
|
|
|
} |
|
520
|
0
|
|
|
|
|
0
|
$f += $gap; |
|
521
|
|
|
|
|
|
|
} |
|
522
|
|
|
|
|
|
|
} |
|
523
|
|
|
|
|
|
|
|
|
524
|
|
|
|
|
|
|
# If there is anything left, it's a prime. |
|
525
|
|
|
|
|
|
|
|
|
526
|
1015
|
100
|
|
|
|
1972
|
unless ($n == 1) { |
|
527
|
1008
|
50
|
|
|
|
2826
|
print " $n" or die "$0: print failed: $!"; |
|
528
|
|
|
|
|
|
|
} |
|
529
|
|
|
|
|
|
|
|
|
530
|
1015
|
50
|
|
|
|
3073
|
print "\n" or die "$0: print failed: $!"; |
|
531
|
|
|
|
|
|
|
} |
|
532
|
|
|
|
|
|
|
|
|
533
|
|
|
|
|
|
|
1; |
|
534
|
|
|
|
|
|
|
|
|
535
|
|
|
|
|
|
|
__END__ |