On Saturday 05 April 2003 20:33, Alexander Kruppa wrote: > Bjoern Hoffmann wrote: > > 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.
I would think that running Miller's Test (for strong pseudoprimes) would be worthwhile... this _should_ take about the same time as a Lucas-Lehmer test on the associated Mersenne number, but there may be a problem with fast calculation modulo (2^p-3). It might be possible to modify PRP (Woltman) and/or Proth (Gallot) to perform this test without an enormous amount of effort. Even without a shortcut for modulo (2^p-3) working, the run time should be "reasonable" on a fast PC system. Proth may also give some clues about constructing a Lucas sequence to perform a proper primality test, though the run time is likely to be a lot longer than a Fermat/Miller pseudoprime test & isn't worth the effort of starting unless the number is found to be a probable prime. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
