Re: Probable Prime Number

bassam king karzeddin wrote:
Dear All

I would like to introduce the following conjecture about prime factorization without having a proof or a counter example or a reference.

The Conjecture:

"If, n = (p^2 + q^2) / 2, where, (p, q) are odd prime numbers, then, (n) has at most three distinct odd prime numbers factors"

And, It follows as a result another sub conjecture with above mention conditions :

"If, (50) divides (p^2 +q^2), then the result is a good probable prime number"

I will be gratfull for some one who will kindly provide a counter example or a reference

Thanking your comments

My Best Regards

Bassam Karzeddin

Manager of Engineering and Projects Circle

Al Hussein Bin Talal University
Ma'an - Jordan

So I wrote I few lines of Matlab code to check your conjecture for all combinations of primes p<1e3 and q<1e3:

function test

clc
p = primes(1e3);
for i = 2:length(p)
for j = i:length(p)
n = (p(i)^2 + p(j)^2)/2;
factors_n = factor(n);
if length(unique(factors_n)) > 3
disp([sprintf('p=%4d, q=%4d, factors: ', p(i), p(j)) num2str(factors_n)]);
end
end
end

I think your conjecture failed, given the output list below. It certainly failed...

p= 3, q= 811, factors: 5 17 53 73
p= 3, q= 821, factors: 5 5 13 17 61
p= 3, q= 991, factors: 5 17 53 109
p= 7, q= 641, factors: 5 13 29 109
p= 7, q= 719, factors: 5 13 41 97
p= 7, q= 809, factors: 5 29 37 61
p= 7, q= 839, factors: 5 17 41 101
p= 7, q= 919, factors: 5 13 73 89
p= 11, q= 367, factors: 5 13 17 61
p= 11, q= 653, factors: 5 13 17 193
p= 11, q= 673, factors: 5 5 13 17 41
p= 11, q= 857, factors: 5 17 29 149
p= 17, q= 709, factors: 5 13 53 73
p= 17, q= 929, factors: 5 13 29 229
p= 19, q= 373, factors: 5 13 29 37
p= 19, q= 953, factors: 5 13 29 241
p= 19, q= 977, factors: 5 17 41 137
p= 23, q= 401, factors: 5 13 17 73
p= 23, q= 449, factors: 5 17 29 41
p= 23, q= 479, factors: 5 13 29 61
p= 23, q= 619, factors: 5 17 37 61
p= 23, q= 769, factors: 5 13 29 157
p= 29, q= 677, factors: 5 17 37 73
p= 29, q= 887, factors: 5 17 41 113
p= 31, q= 443, factors: 5 13 37 41
p= 31, q= 607, factors: 5 17 41 53
p= 31, q= 787, factors: 5 17 41 89
p= 37, q= 569, factors: 5 13 41 61
p= 37, q= 821, factors: 5 17 29 137
p= 37, q= 991, factors: 5 5 13 17 89
p= 41, q= 283, factors: 5 13 17 37
p= 41, q= 523, factors: 5 13 29 73
p= 41, q= 647, factors: 5 13 53 61
p= 41, q= 653, factors: 5 13 37 89
p= 41, q= 827, factors: 5 17 37 109
p= 41, q= 907, factors: 5 13 17 373
p= 43, q= 461, factors: 5 13 17 97
p= 43, q= 631, factors: 5 13 17 181
p= 43, q= 661, factors: 5 17 29 89
p= 43, q= 761, factors: 5 13 41 109
p= 43, q= 839, factors: 5 13 61 89
p= 47, q= 509, factors: 5 17 29 53
p= 47, q= 883, factors: 13 17 29 61
p= 47, q= 911, factors: 5 13 37 173
p= 53, q= 281, factors: 5 13 17 37
p= 59, q= 563, factors: 5 5 13 17 29
p= 61, q= 397, factors: 5 13 17 73
p= 61, q= 487, factors: 5 13 17 109
p= 61, q= 877, factors: 5 5 13 29 41
p= 61, q= 929, factors: 13 17 37 53
p= 67, q= 439, factors: 5 13 37 41
p= 67, q= 601, factors: 5 13 29 97
p= 67, q= 659, factors: 5 17 29 89
p= 67, q= 809, factors: 5 13 37 137
p= 67, q= 829, factors: 5 13 17 313
p= 71, q= 277, factors: 5 13 17 37
p= 71, q= 743, factors: 5 17 29 113
p= 71, q= 823, factors: 5 13 29 181
p= 71, q= 997, factors: 5 5 13 29 53
p= 79, q= 673, factors: 5 17 37 73
p= 79, q= 733, factors: 5 13 37 113
p= 79, q= 863, factors: 5 13 53 109
p= 83, q= 599, factors: 5 13 29 97
p= 83, q= 859, factors: 5 13 17 337
p= 83, q= 911, factors: 5 13 41 157
p= 89, q= 613, factors: 5 17 37 61
p= 89, q= 647, factors: 5 13 17 193
p= 89, q= 757, factors: 5 13 41 109
p= 89, q= 883, factors: 5 17 41 113
p= 97, q= 269, factors: 5 13 17 37
p= 97, q= 439, factors: 5 17 29 41
p= 97, q= 641, factors: 5 13 53 61
p= 101, q= 353, factors: 5 13 17 61
p= 101, q= 557, factors: 5 5 13 17 29
p= 101, q= 977, factors: 5 13 41 181
p= 103, q= 359, factors: 5 13 29 37
p= 103, q= 599, factors: 5 17 41 53
p= 103, q= 811, factors: 5 13 53 97
p= 103, q= 941, factors: 5 13 61 113
p= 107, q= 431, factors: 5 13 37 41
p= 107, q= 479, factors: 5 13 17 109
p= 107, q= 881, factors: 5 17 41 113
p= 109, q= 467, factors: 5 13 29 61
p= 109, q= 997, factors: 5 17 61 97
p= 113, q= 449, factors: 5 13 17 97
p= 113, q= 631, factors: 5 13 29 109
p= 113, q= 761, factors: 5 13 29 157
p= 113, q= 839, factors: 5 13 37 149
p= 113, q= 877, factors: 13 17 29 61
p= 127, q= 509, factors: 5 13 29 73
p= 127, q= 661, factors: 5 5 13 17 41
p= 131, q= 853, factors: 5 13 17 337
p= 131, q= 953, factors: 5 37 41 61
p= 131, q= 983, factors: 5 5 13 17 89
p= 137, q= 251, factors: 5 13 17 37
p= 137, q= 659, factors: 5 5 13 17 41
p= 137, q= 769, factors: 5 17 37 97
p= 137, q= 919, factors: 5 13 29 229
p= 139, q= 617, factors: 5 13 17 181
p= 139, q= 683, factors: 5 13 37 101
p= 139, q= 797, factors: 5 29 37 61
p= 149, q= 373, factors: 5 13 17 73
p= 149, q= 503, factors: 5 13 29 73
p= 149, q= 883, factors: 5 17 53 89
p= 149, q= 919, factors: 13 17 37 53
p= 149, q= 953, factors: 5 13 17 421
p= 151, q= 467, factors: 5 13 17 109
p= 151, q= 773, factors: 5 17 41 89
p= 157, q= 239, factors: 5 13 17 37
p= 157, q= 811, factors: 5 13 29 181
p= 163, q= 419, factors: 5 17 29 41
p= 163, q= 719, factors: 5 13 37 113
p= 163, q= 941, factors: 5 5 17 29 37
p= 167, q= 601, factors: 5 13 41 73
p= 167, q= 641, factors: 5 17 29 89
p= 167, q= 751, factors: 5 13 29 157
p= 167, q= 809, factors: 5 13 29 181
p= 167, q= 811, factors: 5 17 37 109
p= 167, q= 991, factors: 5 13 17 457
p= 173, q= 331, factors: 5 13 29 37
p= 173, q= 409, factors: 5 13 37 41
p= 173, q= 631, factors: 5 13 37 89
p= 173, q= 709, factors: 5 13 17 241
p= 173, q= 821, factors: 5 17 41 101
p= 179, q= 223, factors: 5 13 17 37
p= 179, q= 457, factors: 5 13 17 109
p= 179, q= 593, factors: 5 17 37 61
p= 179, q= 937, factors: 5 17 53 101
p= 181, q= 577, factors: 5 13 29 97
p= 181, q= 653, factors: 5 17 37 73
p= 181, q= 827, factors: 5 13 37 149
p= 181, q= 877, factors: 5 17 53 89
p= 181, q= 983, factors: 5 5 13 29 53
p= 191, q= 577, factors: 5 17 41 53
p= 191, q= 683, factors: 5 13 53 73
p= 193, q= 211, factors: 5 13 17 37
p= 193, q= 439, factors: 5 13 29 61
p= 193, q= 809, factors: 5 13 17 313
p= 197, q= 419, factors: 5 13 17 97
p= 197, q= 601, factors: 5 13 17 181
p= 197, q= 769, factors: 5 29 41 53
p= 199, q= 397, factors: 5 13 37 41
p= 199, q= 617, factors: 5 13 53 61
p= 199, q= 643, factors: 5 5 13 17 41
p= 199, q= 677, factors: 5 17 29 101
p= 199, q= 683, factors: 5 13 17 229
p= 199, q= 787, factors: 5 13 37 137
p= 199, q= 983, factors: 5 17 61 97
p= 211, q= 397, factors: 5 17 29 41
p= 211, q= 587, factors: 5 13 41 73
p= 211, q= 613, factors: 5 13 53 61
p= 211, q= 977, factors: 5 5 13 29 53
p= 211, q= 997, factors: 5 17 41 149
p= 223, q= 601, factors: 5 13 29 109
p= 223, q= 859, factors: 5 17 41 113
p= 227, q= 659, factors: 5 13 37 101
p= 227, q= 919, factors: 5 13 61 113
p= 229, q= 457, factors: 5 17 29 53
p= 229, q= 563, factors: 5 17 41 53
p= 229, q= 727, factors: 5 13 41 109
p= 229, q= 883, factors: 5 13 37 173
p= 229, q= 937, factors: 5 13 17 421
p= 229, q= 967, factors: 5 17 37 157
p= 233, q= 541, factors: 5 13 17 157
p= 233, q= 853, factors: 13 17 29 61
p= 239, q= 467, factors: 5 13 29 73
p= 239, q= 727, factors: 5 5 13 17 53
p= 239, q= 757, factors: 5 29 41 53
p= 239, q= 863, factors: 5 17 53 89
p= 239, q= 883, factors: 5 13 41 157
p= 241, q= 277, factors: 5 13 17 61
p= 241, q= 373, factors: 5 13 37 41
p= 241, q= 607, factors: 5 13 17 193
p= 241, q= 617, factors: 5 17 29 89
p= 241, q= 743, factors: 5 17 37 97
p= 241, q= 947, factors: 5 17 41 137
p= 251, q= 373, factors: 5 17 29 41
p= 251, q= 613, factors: 5 17 29 89
p= 251, q= 787, factors: 5 13 29 181
p= 251, q= 877, factors: 5 13 37 173
p= 251, q= 953, factors: 5 17 29 197
p= 257, q= 271, factors: 5 13 29 37
p= 257, q= 509, factors: 5 13 41 61
p= 257, q= 661, factors: 5 13 53 73
p= 257, q= 691, factors: 5 13 37 113
p= 257, q= 739, factors: 5 13 17 277
p= 263, q= 401, factors: 5 13 29 61
p= 263, q= 431, factors: 5 13 37 53
p= 263, q= 661, factors: 5 13 17 229
p= 269, q= 397, factors: 5 13 29 61
p= 269, q= 617, factors: 5 5 13 17 41
p= 269, q= 643, factors: 5 13 37 101
p= 269, q= 787, factors: 5 13 17 313
p= 271, q= 523, factors: 5 13 17 157
p= 271, q= 557, factors: 5 17 37 61
p= 271, q= 907, factors: 5 13 61 113
p= 277, q= 541, factors: 5 17 41 53
p= 277, q= 881, factors: 5 17 29 173
p= 281, q= 443, factors: 5 13 29 73
p= 281, q= 937, factors: 5 13 17 433
p= 283, q= 401, factors: 5 13 17 109
p= 283, q= 661, factors: 5 13 41 97
p= 283, q= 809, factors: 5 17 29 149
p= 283, q= 911, factors: 5 17 53 101
p= 293, q= 919, factors: 5 13 17 421
p= 293, q= 971, factors: 5 13 41 193
p= 307, q= 521, factors: 5 13 29 97
p= 307, q= 571, factors: 5 13 53 61
p= 307, q= 599, factors: 5 5 13 17 41
p= 307, q= 701, factors: 5 5 13 17 53
p= 307, q= 769, factors: 5 17 37 109
p= 307, q= 859, factors: 5 13 37 173
p= 311, q= 317, factors: 5 13 37 41
p= 311, q= 853, factors: 5 13 17 373
p= 311, q= 983, factors: 5 13 13 17 37
p= 313, q= 421, factors: 5 13 29 73
p= 313, q= 499, factors: 5 13 17 157
p= 313, q= 521, factors: 5 17 41 53
p= 313, q= 601, factors: 5 17 37 73
p= 313, q= 827, factors: 13 17 29 61
p= 313, q= 839, factors: 5 17 53 89
p= 313, q= 941, factors: 5 5 13 17 89
p= 313, q= 971, factors: 5 29 37 97
p= 317, q= 401, factors: 5 17 29 53
p= 317, q= 571, factors: 5 13 17 193
p= 317, q= 701, factors: 5 13 29 157
p= 317, q= 911, factors: 5 13 17 421
p= 331, q= 347, factors: 5 13 29 61
p= 331, q= 563, factors: 5 13 17 193
p= 331, q= 797, factors: 5 13 17 337
p= 331, q= 937, factors: 5 17 37 157
p= 337, q= 811, factors: 5 13 17 349
p= 337, q= 821, factors: 5 17 41 113
p= 337, q= 941, factors: 5 5 13 29 53
p= 347, q= 499, factors: 5 17 41 53
p= 347, q= 839, factors: 5 13 17 373
p= 347, q= 929, factors: 5 5 13 17 89
p= 347, q= 941, factors: 5 17 61 97
p= 349, q= 563, factors: 5 17 29 89
p= 349, q= 797, factors: 5 17 61 73
p= 349, q= 887, factors: 5 13 29 241
p= 353, q= 491, factors: 5 13 29 97
p= 353, q= 509, factors: 5 17 37 61
p= 353, q= 601, factors: 5 13 37 101
p= 359, q= 443, factors: 5 13 41 61
p= 359, q= 467, factors: 5 13 17 157
p= 359, q= 547, factors: 5 13 37 89
p= 359, q= 857, factors: 5 13 29 229
p= 359, q= 859, factors: 13 17 37 53
p= 359, q= 883, factors: 5 13 29 241
p= 367, q= 431, factors: 5 5 13 17 29
p= 367, q= 499, factors: 5 17 37 61
p= 367, q= 691, factors: 5 13 17 277
p= 373, q= 599, factors: 5 17 29 101
p= 379, q= 643, factors: 5 17 29 113
p= 379, q= 683, factors: 5 17 37 97
p= 379, q= 757, factors: 5 13 37 149
p= 379, q= 887, factors: 5 13 17 421
p= 383, q= 659, factors: 5 13 41 109
p= 383, q= 797, factors: 13 17 29 61
p= 383, q= 971, factors: 5 13 17 17 29
p= 389, q= 463, factors: 5 13 29 97
p= 389, q= 467, factors: 5 17 41 53
p= 389, q= 593, factors: 5 13 53 73
p= 389, q= 863, factors: 5 13 61 113
p= 389, q= 967, factors: 5 13 61 137
p= 397, q= 659, factors: 5 13 29 157
p= 397, q= 911, factors: 5 17 37 157
p= 401, q= 887, factors: 5 13 37 197
p= 401, q= 907, factors: 5 5 13 17 89
p= 409, q= 503, factors: 5 13 53 61
p= 409, q= 823, factors: 5 13 73 89
p= 409, q= 863, factors: 5 5 17 29 37
p= 419, q= 557, factors: 5 13 37 101
p= 419, q= 743, factors: 5 13 29 193
p= 419, q= 823, factors: 5 17 29 173
p= 419, q= 857, factors: 5 17 53 101
p= 419, q= 947, factors: 5 13 73 113
p= 419, q= 997, factors: 5 29 37 109
p= 421, q= 673, factors: 5 29 41 53
p= 421, q= 727, factors: 5 13 61 89
p= 421, q= 883, factors: 5 13 17 433
p= 431, q= 503, factors: 5 17 29 89
p= 431, q= 653, factors: 5 13 17 277
p= 431, q= 773, factors: 5 29 37 73
p= 431, q= 877, factors: 5 17 41 137
p= 433, q= 449, factors: 5 13 41 73
p= 433, q= 461, factors: 5 13 17 181
p= 433, q= 631, factors: 5 5 13 17 53
p= 433, q= 859, factors: 5 37 41 61
p= 433, q= 971, factors: 5 17 61 109
p= 433, q= 991, factors: 5 29 37 109
p= 439, q= 557, factors: 5 13 53 73
p= 439, q= 743, factors: 5 13 17 337
p= 439, q= 821, factors: 13 17 37 53
p= 439, q= 947, factors: 5 13 17 17 29
p= 443, q= 769, factors: 5 17 41 113
p= 443, q= 919, factors: 5 29 37 97
p= 443, q= 941, factors: 5 13 53 157
p= 449, q= 487, factors: 5 17 29 89
p= 449, q= 673, factors: 5 29 37 61
p= 449, q= 797, factors: 5 13 41 157
p= 449, q= 997, factors: 5 13 17 541
p= 457, q= 569, factors: 5 13 17 241
p= 457, q= 751, factors: 5 5 13 29 41
p= 457, q= 757, factors: 13 17 29 61
p= 457, q= 809, factors: 5 13 29 229
p= 457, q= 829, factors: 5 13 61 113
p= 461, q= 587, factors: 5 17 29 113
p= 461, q= 607, factors: 5 13 41 109
p= 461, q= 953, factors: 5 13 37 233
p= 463, q= 521, factors: 5 13 37 101
p= 463, q= 701, factors: 5 13 61 89
p= 463, q= 911, factors: 5 13 29 277
p= 467, q= 491, factors: 5 17 37 73
p= 479, q= 523, factors: 5 13 53 73
p= 479, q= 617, factors: 5 17 37 97
p= 479, q= 673, factors: 5 13 29 181
p= 479, q= 937, factors: 5 37 41 73
p= 487, q= 619, factors: 5 17 41 89
p= 487, q= 739, factors: 5 29 37 73
p= 487, q= 919, factors: 5 13 53 157
p= 487, q= 971, factors: 5 13 29 313
p= 491, q= 587, factors: 5 5 13 17 53
p= 491, q= 643, factors: 5 29 37 61
p= 491, q= 977, factors: 5 13 17 541
p= 499, q= 653, factors: 5 17 29 137
p= 499, q= 857, factors: 5 5 13 17 89
p= 499, q= 877, factors: 5 17 53 113
p= 499, q= 883, factors: 5 13 41 193
p= 503, q= 761, factors: 5 13 37 173
p= 503, q= 839, factors: 5 13 17 433
p= 503, q= 929, factors: 5 5 13 17 101
p= 503, q= 941, factors: 5 17 37 181
p= 509, q= 523, factors: 5 13 17 241
p= 509, q= 727, factors: 5 17 41 113
p= 509, q= 757, factors: 5 13 37 173
p= 509, q= 907, factors: 5 13 53 157
p= 521, q= 853, factors: 5 5 13 29 53
p= 521, q= 857, factors: 5 17 61 97
p= 521, q= 887, factors: 5 29 41 89
p= 523, q= 691, factors: 5 13 53 109
p= 523, q= 821, factors: 5 13 37 197
p= 541, q= 547, factors: 5 13 29 157
p= 541, q= 677, factors: 5 13 53 109
p= 541, q= 787, factors: 5 5 17 29 37
p= 541, q= 883, factors: 5 13 73 113
p= 541, q= 953, factors: 5 29 41 101
p= 547, q= 619, factors: 5 13 29 181
p= 547, q= 709, factors: 5 17 53 89
p= 547, q= 811, factors: 5 13 17 433
p= 557, q= 809, factors: 5 13 41 181
p= 557, q= 881, factors: 5 13 61 137
p= 563, q= 761, factors: 5 13 61 113
p= 563, q= 929, factors: 5 13 29 313
p= 569, q= 587, factors: 5 13 53 97
p= 569, q= 593, factors: 5 17 29 137
p= 569, q= 857, factors: 5 29 41 89
p= 569, q= 947, factors: 5 13 41 229
p= 571, q= 577, factors: 5 13 37 137
p= 571, q= 733, factors: 5 13 29 229
p= 571, q= 827, factors: 5 13 17 457
p= 571, q= 907, factors: 5 17 29 233
p= 571, q= 967, factors: 5 13 89 109
p= 577, q= 599, factors: 5 13 17 313
p= 577, q= 701, factors: 5 13 17 373
p= 577, q= 761, factors: 5 5 17 29 37
p= 587, q= 601, factors: 5 13 61 89
p= 587, q= 751, factors: 5 13 29 241
p= 587, q= 809, factors: 5 5 13 29 53
p= 587, q= 881, factors: 5 13 37 233
p= 593, q= 859, factors: 5 13 17 17 29
p= 593, q= 911, factors: 5 13 61 149
p= 593, q= 919, factors: 5 37 53 61
p= 599, q= 613, factors: 5 17 29 149
p= 599, q= 733, factors: 5 13 61 113
p= 599, q= 853, factors: 5 13 61 137
p= 599, q= 883, factors: 5 17 37 181
p= 599, q= 953, factors: 5 17 29 257
p= 599, q= 967, factors: 5 13 37 269
p= 601, q= 653, factors: 5 17 41 113
p= 601, q= 823, factors: 5 17 41 149
p= 601, q= 877, factors: 5 17 61 109
p= 601, q= 977, factors: 5 13 29 349
p= 607, q= 643, factors: 13 17 29 61
p= 607, q= 761, factors: 5 13 37 197
p= 607, q= 839, factors: 5 13 73 113
p= 613, q= 761, factors: 5 17 41 137
p= 613, q= 829, factors: 5 13 13 17 37
p= 619, q= 907, factors: 5 17 41 173
p= 619, q= 937, factors: 5 13 89 109
p= 619, q= 953, factors: 5 29 61 73
p= 631, q= 757, factors: 5 17 29 197
p= 631, q= 977, factors: 5 17 73 109
p= 641, q= 643, factors: 5 13 17 373
p= 641, q= 683, factors: 5 13 17 397
p= 641, q= 853, factors: 5 17 37 181
p= 641, q= 877, factors: 5 13 29 313
p= 643, q= 719, factors: 5 13 17 421
p= 647, q= 659, factors: 5 17 29 173
p= 647, q= 691, factors: 5 13 61 113
p= 647, q= 701, factors: 5 17 53 101
p= 647, q= 739, factors: 5 13 41 181
p= 647, q= 769, factors: 5 13 17 457
p= 653, q= 661, factors: 5 13 29 229
p= 653, q= 691, factors: 5 13 17 409
p= 653, q= 839, factors: 5 17 61 109
p= 653, q= 929, factors: 5 5 17 37 41
p= 659, q= 883, factors: 5 17 37 193
p= 659, q= 953, factors: 5 17 53 149
p= 661, q= 757, factors: 5 13 17 457
p= 673, q= 691, factors: 5 13 17 421
p= 673, q= 739, factors: 5 5 13 29 53
p= 673, q= 769, factors: 5 13 29 277
p= 673, q= 809, factors: 5 37 41 73
p= 677, q= 811, factors: 5 5 13 17 101
p= 677, q= 859, factors: 5 37 53 61
p= 677, q= 991, factors: 5 17 37 229
p= 683, q= 719, factors: 5 5 13 17 89
p= 683, q= 823, factors: 13 29 37 41
p= 683, q= 971, factors: 5 13 37 293
p= 691, q= 907, factors: 5 13 73 137
p= 691, q= 997, factors: 5 37 41 97
p= 701, q= 733, factors: 5 13 41 193
p= 701, q= 863, factors: 5 13 37 257
p= 709, q= 823, factors: 5 13 29 313
p= 709, q= 887, factors: 5 5 17 37 41
p= 709, q= 997, factors: 5 13 29 397
p= 719, q= 827, factors: 5 29 41 101
p= 719, q= 977, factors: 5 37 41 97
p= 727, q= 919, factors: 5 17 41 197
p= 727, q= 941, factors: 5 13 73 149
p= 733, q= 859, factors: 5 13 17 577
p= 743, q= 751, factors: 5 5 13 17 101
p= 743, q= 881, factors: 5 13 17 601
p= 751, q= 947, factors: 5 13 17 661
p= 757, q= 821, factors: 5 13 53 181
p= 757, q= 971, factors: 5 17 37 241
p= 761, q= 953, factors: 5 13 17 673
p= 769, q= 907, factors: 5 13 73 149
p= 773, q= 971, factors: 5 13 17 17 41
p= 787, q= 971, factors: 5 13 61 197
p= 797, q= 859, factors: 5 17 41 197
p= 811, q= 853, factors: 5 17 29 281
p= 811, q= 887, factors: 5 17 29 293
p= 811, q= 983, factors: 5 17 41 233
p= 821, q= 887, factors: 5 13 17 661
p= 821, q= 907, factors: 5 13 29 397
p= 823, q= 929, factors: 5 13 17 17 41
p= 823, q= 941, factors: 5 17 29 317
p= 827, q= 911, factors: 5 5 13 17 137
p= 829, q= 977, factors: 5 13 73 173
p= 829, q= 983, factors: 5 37 41 109
p= 839, q= 853, factors: 5 37 53 73
p= 839, q= 997, factors: 5 13 37 353
p= 853, q= 991, factors: 5 17 89 113
p= 857, q= 941, factors: 5 13 17 733
p= 859, q= 967, factors: 5 13 17 757
p= 881, q= 947, factors: 5 13 17 757
p= 911, q= 983, factors: 5 13 41 337
p= 947, q= 991, factors: 5 13 97 149
p= 983, q= 991, factors: 5 17 73 157
.

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