20200814, 21:44  #1 
Mar 2016
2^{2}×67 Posts 
is the factorisation of Mp1 an advantage ?
A peaceful and pleasant night for you,
if I know the factorisation or a part of the factorisation of Mp1 do I have any advantages for checking the primality ? (Mp should be a Mersenne number) Or in other words, is the factorisation of p1 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 
20200814, 22:05  #2  
"Robert Gerbicz"
Oct 2005
Hungary
11·127 Posts 
Quote:
since rMp1=2*(2^(p1)1). Last fiddled with by R. Gerbicz on 20200814 at 22:07 

20200814, 22:13  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3^{3}×13^{2} Posts 

20200816, 10:34  #4 
"Jeppe"
Jan 2016
Denmark
5·31 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 
20200816, 11:51  #5  
Jun 2003
2^{3}×587 Posts 
Quote:


20200817, 20:49  #6 
"Jeppe"
Jan 2016
Denmark
5·31 Posts 
Oops, that is right. It should have been 2^n2 for n prime, or 2*(2^(n1)  1). /JeppeSN

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