Hi,
I wondered if someone already have checked if the last mersenne numbers +2 are double primes?
like 3+5, 5+7, 9+11, 11+13 or
824 633 702 441 and 824 633 702 443
regards Bjoern
Mp + 2 is divisible by 3 for odd p and thus cannot be prime.
Mp - 2 however can, in theory, be prime and form a twin prime with a Mersenne prime. A list of the status of Mp - 2 for known Mersenne primes can be found on Will Edgington's page, http://www.garlic.com/~wedgingt/mersenne.html
Try the M3status.txt link right at the top.
As you see most Mp - 2 have known factors, some others have failed probable primality tests.
However you will notice that for the present record prime, M13466917, no status is listed for M13466917 - 2. This is because no factors are known, nor has a primality test been done yet. I have searched for factors in vain up to almost 10^13 and am planning to do a primality test, but I'm still not determined which program to use for optimal speed.
There is also an older discussion on the Mersenne forums on this subject, see http://www.mersenneforum.org/viewtopic.php?t=108
Regards, Alex
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