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Old 2021-02-11, 18:41   #1
bur
 
Aug 2020

2×5×17 Posts
Default 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
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