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Old 2015-05-19, 19:03   #2
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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That is a nice sequence. And good thinking about converting it into the k-series (A258081); one needs a compact representation for a simple sieve and whatnot.

Technically, this series is not as fast as Mersenne's (wall clock wise), because for all terms generic mod reduction on a generic FFT size will be used (making the proof at least twice slower than a similar-sized Mp or a GFN or a cyclotomic GenUni number). My bet for a viz-a-viz Mersenne contender for the largest known prime is between the latter two classes; all they need is a GIMPS' size crowd to follow.

I'll double check your terms with PFGW and scripts. I'll start with writing a quick-and-dirty sieve, maybe tonight.
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