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Old 2016-08-14, 18:09   #4
GP2
 
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Sep 2003

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By convention, if an exponent is fully factored, the largest factor is omitted from the database (in both mersenne.org and mersenne.ca).

Storing it would be redundant, since it easily calculated by dividing the Mersenne number itself by all of its other factors. And in most cases (although not here), it is many orders of magnitude larger than the next largest factor, so there would be enormous storage costs, for example:

M5240707 = 75392810903 * (a probable prime with 1.5776 million digits)


Note that the 273 fully factored Mersenne exponents up to and including M63703 really are fully factored, with primality certificates calculated for the remaining cofactor using programs like Primo, whereas all larger "fully factored" Mersenne exponents (of which 30 are known) are only "probably fully factored".

Last fiddled with by GP2 on 2016-08-14 at 18:15
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