Quote:
Originally Posted by Uncwilly
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