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#1 |
Mar 2016
33×11 Posts |
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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 |
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#2 | |
"Robert Gerbicz"
Oct 2005
Hungary
142910 Posts |
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since r|Mp-1=2*(2^(p-1)-1). Last fiddled with by R. Gerbicz on 2020-08-14 at 22:07 |
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#3 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22×7×331 Posts |
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#4 |
"Jeppe"
Jan 2016
Denmark
101001002 Posts |
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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 |
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#5 | |
Jun 2003
2·52·97 Posts |
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#6 |
"Jeppe"
Jan 2016
Denmark
2448 Posts |
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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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