Hi Lucas

> Yesterday (and the day before), I went to the Illinois number theory
conference.
> There (2nd talk of yesterday) J. P. Selfridge announced that he would
> give away $1000 US for any factor found of a number which ought to be
> prime (he provided a list).  On that list was 2^(2^31-1)-1.
> To guard against errors in transmitions the factor is 295257526626031

p=295257526626031
I took 2, and squared it 31 times mod p. And got the result

2^(2^31)=2 mod p

Congratulations Lucas, it is indeed a factor of 2^(2^31-1)-1.... well done!
Had it already been shown that M(M(p)) is not necessarily prime?

Chris Nash
Lexington KY
UNITED STATES


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