496*387^496+1 is prime.
472*391^472+1 is prime.
408*392^408-1 is prime.
522*392^522-1 is prime.

[QUOTE=3.14159;233733]It tries an N+1 once in a while;

Why is it slower for k * b^n ± 1 numbers anyway?[/QUOTE]
Primo is intended as a proving tool for general-form primes--i.e., primes for which no "shortcuts" for primality proof exist. Primo will work on any number, but for numbers of special forms (like k*b^n+-1) there are faster ways to attain a proof (in this case, an N-1/N+1 test with PFGW, LLR, or Proth).

This is the reason why most of the primes on the top-5000 list are of special forms (mostly ones that end in a +1 or -1, some way or another) rather than just big long strings of digits.

[QUOTE=lorgix;233754]496*387^496+1 is prime.
472*391^472+1 is prime.
408*392^408-1 is prime.
522*392^522-1 is prime.[/QUOTE]

4 entries for category 8, Generalized Cullen/Woodall.

Verifications:

[code]Primality testing 496*387^496+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using zero-padded FFT length 640 on 496*387^496+1
Calling Brillhart-Lehmer-Selfridge with factored part 62.99%
496*387^496+1 is prime! (0.0932s+0.0339s)

Done.
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]

Primality testing 472*391^472+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using zero-padded FFT length 640 on 472*391^472+1
Calling Brillhart-Lehmer-Selfridge with factored part 52.42%
472*391^472+1 is prime! (0.0700s+0.0007s)

Done.
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]

Primality testing 408*392^408-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using zero-padded FFT length 512 on 408*392^408-1
Calling Brillhart-Lehmer-Selfridge with factored part 65.00%
408*392^408-1 is prime! (0.1752s+0.0007s)

Done.
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]

Primality testing 522*392^522-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using zero-padded FFT length 640 on 522*392^522-1
Calling Brillhart-Lehmer-Selfridge with factored part 65.04%
522*392^522-1 is prime! (0.3144s+0.0006s)

Done.[/code]

4 entries for category 8 accepted.

And, based on those timings, it seems PFGW is better with +1 numbers than -1 numbers.

I wonder how Fermat's factoring algorithm would be coded in PARI/GP.

(I tried 10870*5^2587-1 so I could try to catch the N+1. It instead offered N-1. It seems as if Primo always rejects the shortcut on special-form numbers.)

use induction

More Cullen/Woodall;

510*399^510+1
511*400^511+1
539*400^539-1


...and it's approaching midnight in my time zone so; G'night!

[QUOTE=lorgix;233769]More Cullen/Woodall;

510*399^510+1
511*400^511+1
539*400^539-1


...and it's approaching midnight in my time zone so; G'night![/QUOTE]

Three entries for Generalized Cullen-Woodall; And, g'night to you as well!

Verifications:


[code]Primality testing 510*399^510+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using zero-padded FFT length 640 on 510*399^510+1
Calling Brillhart-Lehmer-Selfridge with factored part 49.06%
510*399^510+1 is prime! (0.0527s+0.0006s)

Done.
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]

Primality testing 511*400^511+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using zero-padded FFT length 640 on 511*400^511+1
Running N-1 test using base 11
Special modular reduction using zero-padded FFT length 640 on 511*400^511+1
Calling Brillhart-Lehmer-Selfridge with factored part 53.62%
511*400^511+1 is prime! (0.1014s+0.0006s)

Done.
PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]

Primality testing 539*400^539-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using zero-padded FFT length 640 on 539*400^539-1
Calling Brillhart-Lehmer-Selfridge with factored part 53.62%
539*400^539-1 is prime! (0.3056s+0.0007s)[/code]

Three entries accepted.

[QUOTE=lorgix;233769]More Cullen/Woodall;

....

...and it's approaching midnight in my time zone so; G'night![/QUOTE]

@G'night ... Europe is large !

Entry for #2: 61368*396^2686+1 (6983 digits)

Verification:

Primality testing 61368*396^2686+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Special modular reduction using zero-padded FFT length 3584 on 61368*396^2686+1
Calling Brillhart-Lehmer-Selfridge with factored part 40.06%
61368*396^2686+1 is prime! (1.5766s+0.0008s)

Done.

Now; For some fun;

Post prime factors of 10[sup]200![/sup]-1;

I'll do the honors to begin..

It is divisible by 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, well.. any prime under 44520.

Any factors > 211[sup]2[/sup]?

Here's one: 909091.

Another; 999999000001.

More: 5882353, 2906161, 52579, 333667, 99990001, 121499449, 1058313049, 265371653, 69857, 2071723, 5363222357, 21993833369, 2212394296770203368013, 247629013, 2028119, 909090909090909091, 1111111111111111111, 201763709900322803748657942361, 459691, 10838689, 1963506722254397, 2140992015395526641, 1056689261

Running under the assumption that since it has 200! digits, it should be divisible by all 10^n-1 (Reason: Length of period of 1/n. Ex: 10[sup]200![/sup]-1 is divisible by 7, since 200! is divisible by 6.)

[QUOTE=3.14159;233775]Post factors of 10[sup]200![/sup]-1;

I'll do the honors to begin..

It is divisible by 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313..[/QUOTE]

3[SUP]99[/SUP] * 7[SUP]33[/SUP] * 11[SUP]20[/SUP] * 13[SUP]17[/SUP] * 17[SUP]12[/SUP] * 19[sup]11[/sup] * 23[sup]9[/sup] * 29[sup]7[/sup] * 31[sup]7[/sup] * 37[sup]6[/sup] * 41[sup]5[/sup] * 43[sup]5[/sup] * 47[sup]5[/sup] * 53[sup]4[/sup] * 59[sup]4[/sup] * 61[sup]4[/sup] * 67[sup]3[/sup] * 71[sup]3[/sup] * 73[sup]3[/sup] * 79[sup]3[/sup] * 83[sup]3[/sup] * 89[sup]3[/sup] * 97[sup]3[/sup] * 101[sup]2[/sup] * 103[sup]2[/sup] * 107[sup]2[/sup] * 109[sup]2[/sup] * 113[sup]2[/sup] * 127[sup]2[/sup] * 131[sup]2[/sup] * 137[sup]2[/sup] * 139[sup]2[/sup] * 149[sup]2[/sup] * 151[sup]2[/sup] * 157[sup]2[/sup] * 163[sup]2[/sup] * 167[sup]2[/sup] * 173[sup]2[/sup] * 179[sup]2[/sup] * 181[sup]2[/sup] * 191[sup]2[/sup] * 193[sup]2[/sup] * 197[sup]2[/sup] * 199[sup]2[/sup] * (463# / 199#) * 487[sup]2[/sup] * 491 * 499 * 509 * 521 * 523 * 541 * 547 * 557 * 569 * 571 * 577 * 593 * 599 * 601 * 607 * 613 * 617 * 619 * 631 * 641 * 643 * 647 * 653 * 659 * 661 * 673 * 677 * 683 * 691 * 701 * 709 * 727 * 733 * 739 * 743 * 751 * 757 * 761 * 769 * 773 * 787 * 797 * 809 * 811 * 821 * 823 * 827 * 829 * 853 * 857 * 859 * 877 * 881 * 883 * 907 * 911 * 919 * 929 * 937 * 941 * 947 * 953 * 967 * 971 * 977 * 991 * 997 * 1009 * 1013 * 1021 * 1031 * 1033 * 1039 * 1049 * 1051 * 1061 * 1063 * 1069 * 1087 * 1091 * 1093 * 1097 * 1103 * 1117 * 1123 * 1129 * 1151 * 1153 * 1163 * 1171 * 1181 * 1193 * 1201 * 1213 * 1217 * 1223 * 1231 * 1237 * 1249 * 1259 * 1277 * 1279 * 1289 * 1291 * 1297 * 1301 * 1303 * 1321 * 1327 * 1361 * 1373 * 1381 * 1409 * 1423 * 1427 * 1429 * 1433 * 1451 * 1453 * 1459 * 1471 * 1481 * 1483 * 1489 * 1499 * 1511 * 1531 * 1549 * 1553 * 1559 * 1567 * 1571 * 1583 * 1597 * 1601 * 1607 * 1609 * 1613 * 1621 * 1657 * 1667 * 1669 * 1693 * 1697 * 1709 * 1721 * 1723 * 1741 * 1747 * 1753 * 1777 * 1783 * 1787 * 1789 * 1801 * 1811 * 1831 * 1847 * 1861 * 1871 * 1873 * 1877 * 1889 * 1901 * 1931 * 1933 * 1951 * 1973 * 1979 * 1993 * 1999 * 2003 * 2011 * 2017 * 2029 * 2053 * 2069 * 2081 * 2087 * 2089 * 2113 * 2129 * 2131 * 2137 * 2141 * 2143 * 2161 * 2179 * 2213 * 2221 * 2237 * 2243 * 2251 * 2267 * 2269 * 2273 * 2281 * 2287 * 2293 * 2297 * 2311 * 2333 * 2339 * 2341 * 2347 * 2351 * 2357 * 2371 * 2377 * 2381 * 2389 * 2393 * 2399 * 2417 * 2423 * 2437 * 2441 * 2467 * 2473 * 2503 * 2521 * 2531 * 2539 * 2543 * 2549 * 2551 * 2557 * 2591 * 2593 * 2609 * 2617 * 2621 * 2633 * 2647 * 2657 * 2663 * 2671 * 2683 * 2687 * 2689 * 2699 * 2707 * 2713 * 2719 * 2729 * 2731 * 2741 * 2753 * 2789 * 2791 * 2801 * 2833 * 2843 * 2851 * 2857 * 2861 * 2887 * 2897 * 2917 * 2927 * 2939 * 2953 * 2969 * 2971 * 3001 * 3011 * 3037 * 3041 * 3049 * 3061 * 3067 * 3079 * 3083 * 3089 * 3109 * 3121 * 3137 * 3163 * 3169 * 3181 * 3187 * 3191 * 3217 * 3221 * 3251 * 3257 * 3259 * 3271 * 3299 * 3301 * 3307 * 3313 * 3319 * 3323 * 3329 * 3331 * 3359 * 3361 * 3389 * 3391 * 3407 * 3433 * 3457 * 3461 * 3469 * 3499 * 3511 * 3527 * 3529 * 3539 * 3541 * 3547 * 3557 * 3571 * 3581 * 3583 * 3613 * 3617 * 3631 * 3637 * 3659 * 3673 * 3691 * 3697 * 3701 * 3709 * 3719 * 3727 * 3739 * 3761 * 3769 * 3793 * 3797 * 3821 * 3823 * 3851 * 3853 * 3877 * 3881 * 3889 * 3907 * 3911 * 3917 * 3923 * 3931 * 3943 * 4001 * 4003 * 4013 * 4019 * 4021 * 4027 * 4049 * 4051 * 4057 * 4093 * 4111 * 4129 * 4153 * 4159 * 4177 * 4201 * 4217 * 4219 * 4229 * 4231 * 4241 * 4243 * 4261 * 4271 * 4273 * 4289 * 4297 * 4327 * 4357 * 4397 * 4409 * 4421 * 4423 * 4441 * 4447 * 4451 * 4463 * 4481 * 4483 * 4513 * 4523 * 4561 * 4583 * 4591 * 4603 * 4621 * 4637 * 4649 * 4651 * 4657 * 4663 * 4673 * 4691 * 4721 * 4729 * 4733 * 4751 * 4759 * 4789 * 4801 * 4817 * 4831 * 4861 * 4877 * 4889 * 4903 * 4931 * 4933 * 4951 * 4957 * 4967 * 4969 * 4973 * 4993 * 4999 * 5003 * 5011 * 5023 * 5051 * 5077 * 5081 * 5101 * 5107 * 5113 * 5147 * 5153 * 5167 * 5171 * 5209 * 5227 * 5233 * 5237 * 5279 * 5281 * 5333 * 5347 * 5351 * 5407 * 5413 * 5419 * 5431 * 5437 * 5441 * 5477 * 5479 * 5501 * 5503 * 5519 * 5521 * 5531 * 5563 * 5569 * 5573 * 5581 * 5591 * 5641 * 5651 * 5653 * 5657 * 5659 * 5669 * 5689 * 5701 * 5741 * 5743 * 5779 * 5783 * 5791 * 5801 * 5821 * 5839 * 5843 * 5849 * 5851 * 5857 * 5869 * 5881 * 5897 * 5923 * 5953 * 5981 * 5987 * 6007 * 6029 * 6043 * 6053 * 6073 * 6091 * 6101 * 6113 * 6121 * 6133 * 6143 * 6151 * 6163 * 6211 * 6217 * 6229 * 6257 * 6263 * 6271 * 6299 * 6301 * 6323 * 6329 * 6337 * 6343 * 6359 * 6361 * 6373 * 6397 * 6421 * 6427 * 6449 * 6451 * 6469 * 6481 * 6491 * 6521 * 6529 * 6551 * 6553 * 6563 * 6571 * 6577 * 6581 * 6637 * 6661 * 6673 * 6679 * 6689 * 6701 * 6709 * 6733 * 6761 * 6763 * 6781 * 6791 * 6803 * 6833 * 6841 * 6863 * 6869 * 6883 * 6917 * 6947 * 6949 * 6959 * 6961 * 6967 * 6971 * 6977 * 6997 * 7001 * 7019 * 7039 * 7057 * 7069 * 7103 * 7121 * 7129 * 7151 * 7177 * 7193 * 7211 * 7229 * 7237 * 7243 * 7253 * 7297 * 7309 * 7321 * 7333 * 7349 * 7351 * 7393 * 7411 * 7417 * 7451 * 7459 * 7477 * 7481 * 7487 * 7489 * 7499 * 7507 * 7537 * 7541 * 7547 * 7549 * 7561 * 7591 * 7603 * 7621 * 7639 * 7669 * 7673 * 7681 * 7687 * 7723 * 7741 * 7753 * 7789 * 7829 * 7841 * 7853 * 7867 * 7873 * 7877 * 7879 * 7901 * 7907 * 7919 * 7937 * 7951 * 7993 * 8009 * 8011 * 8017 * 8053 * 8059 * 8081 * 8093 * 8101 * 8123 * 8161 * 8171 * 8179 * 8191 * 8209 * 8221 * 8233 * 8237 * 8263 * 8269 * 8273 * 8297 * 8317 * 8353 * 8363 * 8419 * 8429 * 8443 * 8447 * 8461 * 8467 * 8501 * 8513 * 8521 * 8527 * 8537 * 8581 * 8641 * 8647 * 8663 * 8669 * 8681 * 8689 * 8693 * 8713 * 8731 * 8737 * 8741 * 8761 * 8779 * 8803 * 8807 * 8821 * 8837 * 8849 * 8867 * 8893 * 8929 * 8933 * 8941 * 8951 * 8969 * 8971 * 9001 * 9007 * 9011 * 9029 * 9041 * 9043 * 9049 * 9091 * 9103 * 9109 * 9127 * 9151 * 9157 * 9181 * 9199 * 9203 * 9239 * 9241 * 9257 * 9281 * 9283 * 9293 * 9311 * 9323 * 9343 * 9349 * 9397 * 9413 * 9421 * 9431 * 9433 * 9439 * 9461 * 9463 * 9473 * 9491 * 9521 * 9547 * 9551 * 9601 * 9613 * 9629 * 9631 * 9649 * 9661 * 9677 * 9689 * 9697 * 9719 * 9721 * 9769 * 9781 * 9791 * 9803 * 9811 * 9829 * 9851 * 9857 * 9859 * 9871 * 9883 * 9901 * 9907 * 9923 * 9929 * 9941 * 9967 * ...

[QUOTE=Charles;233781]3[SUP]99[/SUP] * 7[SUP]33[/SUP] * 11[SUP]20[/SUP] * 13[SUP]17[/SUP] * 17[SUP]12[/SUP] * 19[sup]11[/sup] * 23[sup]9[/sup] * 29[sup]7[/sup] * 31[sup]7[/sup] * 37[sup]6[/sup] * 41[sup]5[/sup] * 43[sup]5[/sup] * 47[sup]5[/sup] * 53[sup]4[/sup] * 59[sup]4[/sup] * 61[sup]4[/sup] * 67[sup]3[/sup] * 71[sup]3[/sup] * 73[sup]3[/sup] * 79[sup]3[/sup] * 83[sup]3[/sup] * 89[sup]3[/sup] * 97[sup]3[/sup] * 101[sup]2[/sup] * 103[sup]2[/sup] * 107[sup]2[/sup] * 109[sup]2[/sup] * 113[sup]2[/sup] * 127[sup]2[/sup] * 131[sup]2[/sup] * 137[sup]2[/sup] * 139[sup]2[/sup] * 149[sup]2[/sup] * 151[sup]2[/sup] * 157[sup]2[/sup] * 163[sup]2[/sup] * 167[sup]2[/sup] * 173[sup]2[/sup] * 179[sup]2[/sup] * 181[sup]2[/sup] * 191[sup]2[/sup] * 193[sup]2[/sup] * 197[sup]2[/sup] * 199[sup]2[/sup] * (463# / 199#) * 487[sup]2[/sup] * 491 * 499 * 509 * 521 * 523 * 541 * 547 * 557 * 569 * 571 * 577 * 593 * 599 * 601 * 607 * 613 * 617 * 619 * 631 * 641 * 643 * 647 * 653 * 659 * 661 * 673 * 677 * 683 * 691 * 701 * 709 * 727 * 733 * 739 * 743 * 751 * 757 * 761 * 769 * 773 * 787 * 797 * 809 * 811 * 821 * 823 * 827 * 829 * 853 * 857 * 859 * 877 * 881 * 883 * 907 * 911 * 919 * 929 * 937 * 941 * 947 * 953 * 967 * 971 * 977 * 991 * 997 * 1009 * 1013 * 1021 * 1031 * 1033 * 1039 * 1049 * 1051 * 1061 * 1063 * 1069 * 1087 * 1091 * 1093 * 1097 * 1103 * 1117 * 1123 * 1129 * 1151 * 1153 * 1163 * 1171 * 1181 * 1193 * 1201 * 1213 * 1217 * 1223 * 1231 * 1237 * 1249 * 1259 * 1277 * 1279 * 1289 * 1291 * 1297 * 1301 * 1303 * 1321 * 1327 * 1361 * 1373 * 1381 * 1409 * 1423 * 1427 * 1429 * 1433 * 1451 * 1453 * 1459 * 1471 * 1481 * 1483 * 1489 * 1499 * 1511 * 1531 * 1549 * 1553 * 1559 * 1567 * 1571 * 1583 * 1597 * 1601 * 1607 * 1609 * 1613 * 1621 * 1657 * 1667 * 1669 * 1693 * 1697 * 1709 * 1721 * 1723 * 1741 * 1747 * 1753 * 1777 * 1783 * 1787 * 1789 * 1801 * 1811 * 1831 * 1847 * 1861 * 1871 * 1873 * 1877 * 1889 * 1901 * 1931 * 1933 * 1951 * 1973 * 1979 * 1993 * 1999 * 2003 * 2011 * 2017 * 2029 * 2053 * 2069 * 2081 * 2087 * 2089 * 2113 * 2129 * 2131 * 2137 * 2141 * 2143 * 2161 * 2179 * 2213 * 2221 * 2237 * 2243 * 2251 * 2267 * 2269 * 2273 * 2281 * 2287 * 2293 * 2297 * 2311 * 2333 * 2339 * 2341 * 2347 * 2351 * 2357 * 2371 * 2377 * 2381 * 2389 * 2393 * 2399 * 2417 * 2423 * 2437 * 2441 * 2467 * 2473 * 2503 * 2521 * 2531 * 2539 * 2543 * 2549 * 2551 * 2557 * 2591 * 2593 * 2609 * 2617 * 2621 * 2633 * 2647 * 2657 * 2663 * 2671 * 2683 * 2687 * 2689 * 2699 * 2707 * 2713 * 2719 * 2729 * 2731 * 2741 * 2753 * 2789 * 2791 * 2801 * 2833 * 2843 * 2851 * 2857 * 2861 * 2887 * 2897 * 2917 * 2927 * 2939 * 2953 * 2969 * 2971 * 3001 * 3011 * 3037 * 3041 * 3049 * 3061 * 3067 * 3079 * 3083 * 3089 * 3109 * 3121 * 3137 * 3163 * 3169 * 3181 * 3187 * 3191 * 3217 * 3221 * 3251 * 3257 * 3259 * 3271 * 3299 * 3301 * 3307 * 3313 * 3319 * 3323 * 3329 * 3331 * 3359 * 3361 * 3389 * 3391 * 3407 * 3433 * 3457 * 3461 * 3469 * 3499 * 3511 * 3527 * 3529 * 3539 * 3541 * 3547 * 3557 * 3571 * 3581 * 3583 * 3613 * 3617 * 3631 * 3637 * 3659 * 3673 * 3691 * 3697 * 3701 * 3709 * 3719 * 3727 * 3739 * 3761 * 3769 * 3793 * 3797 * 3821 * 3823 * 3851 * 3853 * 3877 * 3881 * 3889 * 3907 * 3911 * 3917 * 3923 * 3931 * 3943 * 4001 * 4003 * 4013 * 4019 * 4021 * 4027 * 4049 * 4051 * 4057 * 4093 * 4111 * 4129 * 4153 * 4159 * 4177 * 4201 * 4217 * 4219 * 4229 * 4231 * 4241 * 4243 * 4261 * 4271 * 4273 * 4289 * 4297 * 4327 * 4357 * 4397 * 4409 * 4421 * 4423 * 4441 * 4447 * 4451 * 4463 * 4481 * 4483 * 4513 * 4523 * 4561 * 4583 * 4591 * 4603 * 4621 * 4637 * 4649 * 4651 * 4657 * 4663 * 4673 * 4691 * 4721 * 4729 * 4733 * 4751 * 4759 * 4789 * 4801 * 4817 * 4831 * 4861 * 4877 * 4889 * 4903 * 4931 * 4933 * 4951 * 4957 * 4967 * 4969 * 4973 * 4993 * 4999 * 5003 * 5011 * 5023 * 5051 * 5077 * 5081 * 5101 * 5107 * 5113 * 5147 * 5153 * 5167 * 5171 * 5209 * 5227 * 5233 * 5237 * 5279 * 5281 * 5333 * 5347 * 5351 * 5407 * 5413 * 5419 * 5431 * 5437 * 5441 * 5477 * 5479 * 5501 * 5503 * 5519 * 5521 * 5531 * 5563 * 5569 * 5573 * 5581 * 5591 * 5641 * 5651 * 5653 * 5657 * 5659 * 5669 * 5689 * 5701 * 5741 * 5743 * 5779 * 5783 * 5791 * 5801 * 5821 * 5839 * 5843 * 5849 * 5851 * 5857 * 5869 * 5881 * 5897 * 5923 * 5953 * 5981 * 5987 * 6007 * 6029 * 6043 * 6053 * 6073 * 6091 * 6101 * 6113 * 6121 * 6133 * 6143 * 6151 * 6163 * 6211 * 6217 * 6229 * 6257 * 6263 * 6271 * 6299 * 6301 * 6323 * 6329 * 6337 * 6343 * 6359 * 6361 * 6373 * 6397 * 6421 * 6427 * 6449 * 6451 * 6469 * 6481 * 6491 * 6521 * 6529 * 6551 * 6553 * 6563 * 6571 * 6577 * 6581 * 6637 * 6661 * 6673 * 6679 * 6689 * 6701 * 6709 * 6733 * 6761 * 6763 * 6781 * 6791 * 6803 * 6833 * 6841 * 6863 * 6869 * 6883 * 6917 * 6947 * 6949 * 6959 * 6961 * 6967 * 6971 * 6977 * 6997 * 7001 * 7019 * 7039 * 7057 * 7069 * 7103 * 7121 * 7129 * 7151 * 7177 * 7193 * 7211 * 7229 * 7237 * 7243 * 7253 * 7297 * 7309 * 7321 * 7333 * 7349 * 7351 * 7393 * 7411 * 7417 * 7451 * 7459 * 7477 * 7481 * 7487 * 7489 * 7499 * 7507 * 7537 * 7541 * 7547 * 7549 * 7561 * 7591 * 7603 * 7621 * 7639 * 7669 * 7673 * 7681 * 7687 * 7723 * 7741 * 7753 * 7789 * 7829 * 7841 * 7853 * 7867 * 7873 * 7877 * 7879 * 7901 * 7907 * 7919 * 7937 * 7951 * 7993 * 8009 * 8011 * 8017 * 8053 * 8059 * 8081 * 8093 * 8101 * 8123 * 8161 * 8171 * 8179 * 8191 * 8209 * 8221 * 8233 * 8237 * 8263 * 8269 * 8273 * 8297 * 8317 * 8353 * 8363 * 8419 * 8429 * 8443 * 8447 * 8461 * 8467 * 8501 * 8513 * 8521 * 8527 * 8537 * 8581 * 8641 * 8647 * 8663 * 8669 * 8681 * 8689 * 8693 * 8713 * 8731 * 8737 * 8741 * 8761 * 8779 * 8803 * 8807 * 8821 * 8837 * 8849 * 8867 * 8893 * 8929 * 8933 * 8941 * 8951 * 8969 * 8971 * 9001 * 9007 * 9011 * 9029 * 9041 * 9043 * 9049 * 9091 * 9103 * 9109 * 9127 * 9151 * 9157 * 9181 * 9199 * 9203 * 9239 * 9241 * 9257 * 9281 * 9283 * 9293 * 9311 * 9323 * 9343 * 9349 * 9397 * 9413 * 9421 * 9431 * 9433 * 9439 * 9461 * 9463 * 9473 * 9491 * 9521 * 9547 * 9551 * 9601 * 9613 * 9629 * 9631 * 9649 * 9661 * 9677 * 9689 * 9697 * 9719 * 9721 * 9769 * 9781 * 9791 * 9803 * 9811 * 9829 * 9851 * 9857 * 9859 * 9871 * 9883 * 9901 * 9907 * 9923 * 9929 * 9941 * 9967 * ...[/QUOTE]

Woah.

But still, any prime under 44520 divides 10[sup]200![/sup] -1.

Large factor; 3660574762725521461527140564875080461079917.

Also, doesn't 5261 or 5237, or 503 divide this number?

Larger factor; 109399846855370537540339266842070119107662296580348039.

Even larger; 651871849785243820958119684233142982170536938147349501049955875423544371888519632103159753836519854149224951224466197.