Eric Hahn wrote:

>  M727 - 94.3716% probability - 2 factors
>  M727 - 52.8693% probability - 3 factors
>  M727 -  6.0014% probability - 4+ factors
>  M727 - 91.1834% probability - 313-bit min. factor size
>  M727 - 93.0447% probability - 428-bit max. factor size

It's impossible for these to be both true, since their product would then
have 741 bits.

>  M727 - 21.7336% probability - highly composite factors

What does this mean?

>  M751 - 83.8467% probability - 2 factors
>  M751 - 74.2974% probability - 3 factors
>  M751 - 19.5801% probability - 4+ factors
>  M751 - 87.2999% probability - 281-bit min. factor size
>  M751 - 81.0003% probability - 526-bit max. factor size

Ditto 807 bits.

>  M751 - 30.1716% probability - highly composite factors

Is M751 now the smallest unfactorised composite Mersenne?  What is the
smallest Mersenne not completely factorised?

Regards

Daran G.


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