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Topic: New prime number result
Replies: 5   Last Post: Sep 9, 2009 10:17 AM

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David McAllister

Posts: 1
Registered: 9/8/09
New prime number result
Posted: Sep 8, 2009 7:47 PM
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Using Nvidia's CUDA HPC system I just got a new result in primality
testing.

If n < 97921 and n is a 42162995-SPRP then n is prime.

I exhaustively tested all bases less than 2^32 and found that 42162995
is the base that yields correct primality testing up to the highest n.

I don't know how many applications require fast primality testing of
numbers only in that limited range (less than 2..97921) but now it can
be done with a single strong probably prime test, rather than two.

This work was done using my modifications to Steve Worley's code,
available from http://www.nvidia.com/object/cuda_home.html#state=detailsOpen;aid=8d5ab3be-6289-4b09-8e1f-db37f6d927b0
or http://www.gpgpgpu.com/gecco2009/6.pdf.

I also used Steve's code, unmodified, to generate a new, slightly
better pair of bases for the Miller-Rabin primality test.

if n < 176,609,441 and n is a 2346211568-SPRP and 3056093627-SPRP then
n is prime.

This is following Steve's recent 10x improvement in this test, as
described in the referenced white paper.

Dave McAllister



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