Thread: 2.2 million?
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Old 2003-02-21, 21:32   #4

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Default largest non-mersenne

Has anyone else thought about LLR, to find primes of the form k*2^n-1?

Since Mersennes primes are a subset of these Riesel primes, there should be plenty of testable k left, that yield frequent primes for n=1,2,3,4....

For example k=195 yields many primes.
I found 195*2^243999-1(73,545 digits)
is prime with LLR, within just a few hours.
In fact there should be k, that for all n are prime, with (k =< 2^n)
I dont expect anyone to find one soon but the implications are fascinating.
Especially with the definition of a Riesel number. A proof may be the only tangible evidence.

PS I notice k is seldomly prime, for Riesel primes.
Does anyone know the mechanism for this?