No, it decreases, and eventually becomes identically zero.
All prime factors of M(p) must be of the form 2kp+1. Once p reaches 2^58 we
can guarantee that there are no factors of this form which are less than 59
bits!
Paul
> -----Original Message-----
> From: Stefan Struiker [mailto:[EMAIL PROTECTED]]
> Sent: 04 August 2000 17:11
> To: [EMAIL PROTECTED]
> Subject: Mersenne: Likelihood Of Small Factors
>
>
> Question:
>
> From a number theoretic point of view, does the
> likelihood of small (52 through 59 bits) factors increase
> with exponent size?
>
> Regards,
> Stefanovic
>
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