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 2020-08-14, 21:44 #1 bhelmes     Mar 2016 11F16 Posts is the factorisation of Mp-1 an advantage ? A peaceful and pleasant night for you, if I know the factorisation or a part of the factorisation of Mp-1 do I have any advantages for checking the primality ? (Mp should be a Mersenne number) Or in other words, is the factorisation of p-1 helpful ? I know the theorem of Pocklington for proofing primality https://en.wikipedia.org/wiki/Pockli...primality_test Thanks in advance if you spend me some lines Bernhard
2020-08-14, 22:05   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

26108 Posts

Quote:
 Originally Posted by bhelmes if I know the factorisation or a part of the factorisation of Mp-1 do I have any advantages for checking the primality ?
Probably there is no advantage for that, but any odd factor of Mp-1 could give a non-trival factor of another Mersenne number (with prime index),
since r|Mp-1=2*(2^(p-1)-1).

Last fiddled with by R. Gerbicz on 2020-08-14 at 22:07

2020-08-14, 22:13   #3
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

217048 Posts

Quote:
 Originally Posted by bhelmes Or in other words, is the factorisation of Mp-1 helpful ?
N=Mp are a beautiful example of being proven with >>33.33% N+1 factorization (indeed, 100%).
Factorization of N-1 is needless, when you have a 100% N+1 factorization.

 2020-08-16, 10:34 #4 JeppeSN     "Jeppe" Jan 2016 Denmark 2·34 Posts Agree with Batalov; for proving primality of M_p, since the full factorization of M_p + 1 is trivial, we do not gain anything from the factorization of M_p - 1. Of course, it may be fun to find the factorization anyway; here is a factordb query for tiny examples. /JeppeSN
2020-08-16, 11:51   #5
axn

Jun 2003

17×281 Posts

Quote:
 Originally Posted by JeppeSN Of course, it may be fun to find the factorization anyway; here is a factordb query for tiny examples.

2020-08-17, 20:49   #6
JeppeSN

"Jeppe"
Jan 2016
Denmark

2×34 Posts

Quote:
 Originally Posted by axn You linked to Mp-2.
Oops, that is right. It should have been 2^n-2 for n prime, or 2*(2^(n-1) - 1). /JeppeSN

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