Extreme sieving

[MooMoo2]

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?

[mdettweiler]

Originally Posted by MooMoo2

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?

All verified with PARI/GP. FYI, the command I used is:
Mod(number,factor)
It returns something like this:
%1 = Mod(0, factor)
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.

[gribozavr]

Factors saved :)

[CRGreathouse]

Originally Posted by mdettweiler

All verified with PARI/GP. FYI, the command I used is:
Mod(number,factor)
It returns something like this:
%1 = Mod(0, factor)
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.

Slow way:

Mod(4184379*2^481439+1, 10000006224344089)

Fast way:

4184379*Mod(2, 10000006224344089)^481439+1

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.