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August 8th, 2018, 03:10 AM  #1 
Newbie Joined: Aug 2018 From: Turkey Posts: 1 Thanks: 0 Math Focus: Prime numbers  Primes of the form Sigma(Sigma(x))
Hi, I checked for the primes of the form sigma(sigma(x)). (Sigma(x) : sum of divisors of x) and it is prime for the x values x>1; x=3, 2667, 3937,57337,172011,253921 and all the primes of this form I found are Mersenne primes. sigma(sigma(3))=7 ......... ............(2667)=8191 :2^131 (3937)=8191 (57337)=131071 :2^171 (172011)=524287:2^191 (253921)=5242872^191 and all the x values>3 are products of Mersenne primes; 2667=3*7*127, 3937=31*127 ,... 253921=31*8191 I know that if Sigma(x) is prime than x has to be a square. So if Sigma(Sigma(x)) is prime than Sigma(x) has to be a square. I couldn't find any prime of this form that is not a Mersenne prime. Are all the primes of this form Mersenne primes? I don't know whether there is a proof about it; can you find a counterexample for it and what do you think? Last edited by skipjack; August 8th, 2018 at 08:51 AM. 

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