On 22 Apr 2001, at 20:37, Spike Jones wrote:
> Nathan I liked your comment about the largest genuine composite:
> a number known to be composite but for which none of the factors
> are known. I suppose we could set up a computer to arbitrarily
> generate a few million 20 digit primes by factoring, then multiply
> them all together to get the largest known composite number for which
> none of the factors would be "known", eh? spike
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
1775*2^332181+1 is prime! (100000 digits) Discovered 22-Apr-2001
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