[math-fun] Re New Mersenne Prime
Why is the new prime M(p) not the 48th known? As Charles Greathouse says, GIMPS is a distributed project. So, inevitably, any unfinished Lucas-residue computations on smaller M(p) will have to be completed, and verified as correct, before it is 'certain' where this new prime is in the sequence of prime M(p). It was precisely this systematic twin-sourcing that was missing before my work with the ICL DAP team in the 1980s set that standard. Slowinski 'aimed' the early CRAYs at the next prime M(p). Second-sourcing known-factors and zero Lucas-residues indicating prime M(p) is obviously not a problem. The latest prime find has been sourced four independent ways already. Naturally, people want to find the next record M(p) or even the first 100m-digit prime M(p) - so there is a bit of a resource-blight behind the largest M(p). Fortunately, older machines with less memory cache tend to be given this second-sourcing task. http://mersenne.org/primenet/ (Primenet Summary, Work Distribution Map) indicates that: - there's quite a bit of LR second-sourcing to be done in the 'p in (26m, 44m)' range - below 58m, over 67,000 M(p) have not had a single LR-test, let alone two, - curiously, some validated LR-testing effort is being put in on a few M(p) with p = ~195m Some analysis of the results-distribution would indicate what the balance of effort is on second-sourcing LRs, 1st-LR-testing below the largest prime M(p) and 1st LR-testing above the new record. Suffice it to say that the 6-year time-lag (in placing the 42nd prime M(p) AS the 42nd prime M(p)) is a measure of the lack of second-sourcing effort. Guy http://www.reading.ac.uk/sse/about/staff/g-haworth.aspx http://centaur.reading.ac.uk/view/creators/90000763.default.html
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Guy Haworth