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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 :2^13-1 (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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded 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

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