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 2021-02-11, 18:41 #1 bur   Aug 2020 2×5×17 Posts Proth primes with k = 1281979 Because I was interested how sieving worked and also wanted to test Proth20 (proth testing for GPU), I started looking at 1281979 * 2^n +1. That k is large enough not to get into PG's various Proth subprojects. Also it's prime, which I find interesting since it means there can be a lot of small factors in 1281979 * 2^n + 1 so sieving will be quite efficient. Of course it also means the probability for smaller primes is low, so it evens out. And it's my birthday. ;) Sieving Range: 100 000 < n < 4 100 000 Factors: p < 290e12 I sieved with sr1sieve on a Pentium G870 which took about 6 months. I stopped when finding a factor took about 2 hours. 66272 candidates remained. I know now I should have sieved to much higher n, but I didn't know that when I began. Primality testing Software is LLR2, n < 1 200 000 was tested on the Pentium G870. Now I switched to a Ryzen 9 3900X. For n = 1 200 000 a test takes 460 s, for n = 2 300 000 it takes 1710 s, showing nicely how well the approximation "double the digits, quadruple the time" can be applied. At least as long as FFT and L3 sizes match. Results Code: For n < 1 000 000 k = digits 2 7 (not a Proth) 142 49 202 67 242 79 370 118 578 180 614 191 754 233 6430 1942 7438 2246 10474 3159 11542 3481 45022 13559 46802 14095 70382 21194 74938 22565 367310 110578 485014 146010 Next milestone is n = 1 560 000 at which point any prime would be large enough to enter Caldwell's Top 5000. Last fiddled with by bur on 2021-02-11 at 18:46