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Old 2021-05-30, 19:25   #8
xilman's Avatar
May 2003
Down not across

1094910 Posts

Originally Posted by Uncwilly View Post
Only if there are several breakthroughs in quantum computing would testing of this be practical and TF would be useful.
Not necessarily.

A proof may be forthcoming that all Mersenne numbers with exponents of a particular form must be prime and all others must be composite.

Likewise, there may be a proof that M_n is composite for all n greater than an explicit bound. If that bound happens to be less than log_2(10^{12}) ...

I don't expect either theorem to be proven any time soon. if either is proven, the proposed computational effort will be wasted
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