Extreme sieving
 

I was playing around with tpsieve and found five factors at p=10P and two factors at p=100P:

10000006224344089 | 4184379*2^481439+1
10000012821412039 | 6681861*2^482663+1
10000013413645747 | 3946077*2^483496-1
10000016097203239 | 4692531*2^483533+1
10000017044013187 | 1852539*2^482057-1
100000111903220981 | 2995515*2^480627-1
100000274118432799 | 9555297*2^480626-1

Could someone verify these factors (using a software other than tpsieve) to make sure that those k/n pairs really are divisible by those factors? Also, if these factors are indeed valid, what's the max p value of tpsieve? I know it's beyond the optimal TPS sieving depth, but I'd still like to know what tpsieve is capable of.

On another note, does anyone want to try beating my records?

[quote=MooMoo2;230223]I was playing around with tpsieve and found five factors at p=10P and two factors at p=100P:

10000006224344089 | 4184379*2^481439+1
10000012821412039 | 6681861*2^482663+1
10000013413645747 | 3946077*2^483496-1
10000016097203239 | 4692531*2^483533+1
10000017044013187 | 1852539*2^482057-1
100000111903220981 | 2995515*2^480627-1
100000274118432799 | 9555297*2^480626-1

Could someone verify these factors (using a software other than tpsieve) to make sure that those k/n pairs really are divisible by those factors? Also, if these factors are indeed valid, what's the max p value of tpsieve? I know it's beyond the optimal TPS sieving depth, but I'd still like to know what tpsieve is capable of.

On another note, does anyone want to try beating my records?[/quote]
All verified with PARI/GP. FYI, the command I used is:
[I]Mod(number,factor)[/I]
It returns something like this:
[I]%1 = Mod(0, factor)[/I]
If the 0 had been anything else, the factor would not have divided the number.

There's probably a more efficient way to do this, but I'm not particularly savvy with PARI.

BTW @gribozavr: you might want to remove these factors from the sieve file next time you do that. It's only a few factors, but hey, no reason to waste them. :smile:

Factors saved :)

[QUOTE=mdettweiler;230233]All verified with PARI/GP. FYI, the command I used is:
[I]Mod(number,factor)[/I]
It returns something like this:
[I]%1 = Mod(0, factor)[/I]
If the 0 had been anything else, the factor would not have divided the number.

There's probably a more efficient way to do this, but I'm not particularly savvy with PARI.[/QUOTE]

Slow way:
[code]Mod(4184379*2^481439+1, 10000006224344089)[/code]

Fast way:
[code]4184379*Mod(2, 10000006224344089)^481439+1[/code]

The slow way requires working with a 144,935-digit number, while the fast way uses nothing with more than 33 digits. In this case the difference is negligible (26 microseconds vs. 1 microsecond) but when the numbers get large it's a big deal.