The verification computers are typically quite fast, massively multicore beasts. The verification time would probably be a few months on a typical machine. Charles Greathouse Analyst/Programmer Case Western Reserve University On Fri, Feb 8, 2013 at 3:49 PM, Guy Haworth <g.haworth@reading.ac.uk> wrote:

Simon Plouffe's estimate - 'more than 2 months' - for the minimum time to run a Lucas-residue test on an M(p) ... is way over the mark.

http://mersenne.org/ reports that the three confirmations of the latest prime M(p) took 3.6, 4.5 and 6 days.

The main reason for confirming that prime M(p) are 'likely' to be the Nth prime M(p) by size, and 'proved' to be so ... is the residue of first- and second-LR-tests to be run.

http://mersenne.org/report_milestones/default.php gives notice of: a) prime M(p), b) residual first-LR-testing of prime exponents 'p', and c) residual dual sourcing of Lucas residues for M(p)

Thus, 51,552 M(p) smaller than the latest record prime M(p) have not even been LR-tested once ... and 565,667 have not been tested twice.

I have not heard of any M(p) being seen as composite and then later as prime ... so accuracy has apparently been good in GIMPS territory.

Note that the 46th and 47th prime M(p) found were both smaller than the 45th. That was a first for GIMPS but not a first overall.

Guy

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