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New prime number result
Posted:
Sep 8, 2009 7:47 PM


Using Nvidia's CUDA HPC system I just got a new result in primality testing.
If n < 97921 and n is a 42162995SPRP 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=8d5ab3be62894b098e1fdb37f6d927b0 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 MillerRabin primality test.
if n < 176,609,441 and n is a 2346211568SPRP and 3056093627SPRP then n is prime.
This is following Steve's recent 10x improvement in this test, as described in the referenced white paper.
Dave McAllister



