Brian is likely to break his own record in about 5 months, with an LLtest of
2^40250087 -1 proceeding rapidly, with Stephan Grupp's simultaneous
test of the same number trailing by 11 days at the moment, both as
part of the continuing mersenne QA effort.
This candidate was P-1 tested by Brian, B1=360000, B2=1800000
after being trial factored by Nathan Russell last summer.
There are still some QA exponents available in the upper stratosphere
ranges for various forms of factoring, or LLtest. (These mostly require
cpu speeds above 500Mhz to complete LLtest in less than 5 years. Each.)
Ken
At 06:25 PM 4/23/2001 -0000, Brian J. Beesley wrote:
>
>If you allow a construction like that then, whatever number you
>suggest, I'll nominate a bigger one.
>
>AFAIK the largest number currently known to be composite but with no
>known factors is 2^33219281-1, the only 10 million digit Mersenne
>number which has been LL tested twice with matching final residual.
>(Rick Pali, 2000 & Brian Beesley, 2001) This number has been trial
>factored up to 2^68 and subjected to P-1 with B1=495000.
>
>Naturally I am happy to give up this claim to "fame" should a factor
>of this number be discovered, or when a larger number is eventually
>subjected to a definitive test for compositeness and cross-checked
>against the possibility of error.
>
>
>Regards
>Brian Beesley
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