## Re: Sub-KP square testing

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• Phil: To find the 5 top triplets at http://www.ltkz.demon.co.uk/ktuplets.htm#largest3 I had recourse to sub-BLS square testing:
Message 1 of 3 , Oct 3, 2002
Phil: To find the 5 top triplets at
http://www.ltkz.demon.co.uk/ktuplets.htm#largest3
I had recourse to sub-BLS square testing:
http://groups.yahoo.com/group/primeform/message/2723
but it was, as you may infer from the cubic Ansatz,
rather mild; pfgw asked only for -x5231887
David
• ... Ah yes, I saw that announcement while I was on holiday, but didn t have enough time to congratulate you there and then. It s nice to see clever, but easily
Message 2 of 3 , Oct 4, 2002
> Phil: To find the 5 top triplets at
> http://www.ltkz.demon.co.uk/ktuplets.htm#largest3
> I had recourse to sub-BLS square testing:
> http://groups.yahoo.com/group/primeform/message/2723
> but it was, as you may infer from the cubic Ansatz,
> rather mild; pfgw asked only for -x5231887

Ah yes, I saw that announcement while I was on holiday, but didn't have
enough time to congratulate you there and then. It's nice to see clever,
but easily accessible, maths smarts bear fruit.

Only 6 minutes work, by the looks of it. Scaling up indicates that 10^12
might take (on a similarly sized number) over 2 years. I reckon a sieve
should do that range in minutes.

I wonder if some bizarre kinky 3-way divide-and-conquer CRT
split/sort/combining method would win the race though. (That's all most of
these square tests are - checking simultanious modular properties)

However, I guess the efficacity of either will have to remain unknown
until someone actually encounters such a situation where they need just
2 extra digits, and they've already ECMed like Billy-oh. I trust they'll
pipe up when they do (David? Andy? Anyone?!). Well in advance, that is,
if they're interested in the CRT one - it's just random firings in my
brain at the moment, but it's just a gut feel that it should work, and
my guts are usually right. However, the GenSv method is ready to roll
as we speak.

Phil

=====
First rule of Factor Club - you do not talk about Factor Club.
Second rule of Factor Club - you DO NOT talk about Factor Club.
Third rule of Factor Club - when the cofactor is prime, or you've trial-
divided up to the square root of the number, the factoring is over.

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