My Math Forum Primes of the form Sigma(Sigma(x))

 Number Theory Number Theory Math Forum

 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 :2^13-1 (3937)=8191 (57337)=131071 :2^17-1 (172011)=524287:2^19-1 (253921)=5242872^19-1 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 counter-example for it and what do you think? Last edited by skipjack; August 8th, 2018 at 08:51 AM.

 Tags form, primes, sigmasigmax

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post John Travolski Real Analysis 3 September 3rd, 2017 04:36 AM Keroro Algebra 4 June 10th, 2012 06:32 PM ilovetheflowguy Algebra 2 May 23rd, 2012 08:14 AM luketapis Calculus 2 March 27th, 2012 11:30 AM rudrax Economics 1 May 26th, 2011 01:09 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top