20141203, 08:36  #1 
"M49"
Dec 2014
Austria
2^{3}×3 Posts 
SophieGermain primes as Mersenne exponents
Suppose, an exponent p (1 mod 4) yields a Mersenne Prime M^{p}=2^{p}1.
If q = 2*p1 (3 mod 4), will the resulting M_{q} be composite? If yes, why? q is a SophieGermain prime. Thanks in advance! 
20141203, 12:40  #2  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10,061 Posts 
Quote:


20141203, 12:47  #3 
"M49"
Dec 2014
Austria
18_{16} Posts 
No, only p is a SGP, not q. Sorry for mixing this up!
Nevertheless, can q yield a Mersenne Prime? 
20141203, 12:50  #4  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10,061 Posts 
Then q is 2p+1 ?
You cannot have Quote:


20141203, 12:52  #5 
"M49"
Dec 2014
Austria
2^{3}×3 Posts 
And of course q = 2*p+1, not 2*p1, as I posted before!
So q is a safe prime! There are 8 known Mersenne Prime exponents so far, which are SophieGermain Primes as well, namely 2 3 5 89 9689 21701 859433 43112609 2 of them have associated safe primes, which also result in a Mersenne prime. M5 and M7 My question is: Are there any more possible of this special kind? Last fiddled with by ProximaCentauri on 20141203 at 13:51 
20141203, 14:22  #6 
"M49"
Dec 2014
Austria
2^{3}×3 Posts 
To be sure about this, i will be "LucasLehmering" 2^{(2*43112609+1)}1

20141203, 17:13  #7 
"Curtis"
Feb 2005
Riverside, CA
3^{3}×11×19 Posts 

20141203, 18:47  #8 
"M49"
Dec 2014
Austria
2^{3}·3 Posts 
Maybe sure was the wrong word.
But I see a strong correlation between Mersenne prime exponents, SophieGermain Primes and Twin primes. By now 16 of the 48 Mersenne prime exponents are also part of a TWINPRIME, this is 1/3 of all known. 2 3 5 7 13 17 19 31 61 107 521 1279 4423 110503 132049 20996011 21 of 48 Mersenne prime exponents either share the property of being a SGP (SophieGermain Prime) and/or being a part of a TWINPrime. 2, 3 and 5 have both properties! This is nearly 50% of all, 43,75% to be exact! So I will concentrate on these exponents with above mentioned attributes in the future. Just a strong feeling, no proof at all! 
20141203, 19:40  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10,061 Posts 
No, this ("I see a strong correlation") is properly called apophenia.
Or a clustering illusion, or any of the interrelated cognitive biases. 
20141203, 20:18  #10 
"M49"
Dec 2014
Austria
24_{10} Posts 
I am not suffering "onset schizophrenia" like u wanted to tell me, Serge!!!
Don´t worry and take care of yourself pls! 
20141203, 21:24  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10,061 Posts 
Now, you see? You just saw another pattern that you wanted to see  where there was none. Everyone sees them; not everyone knows proper statistics.

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