How many perfect numbers + 1 are prime

UoPTucson · 2020-01-28, 14:27

I noticed that some primes are of the form (perfect number + 1), while some P.N. + 1 are not prime. Has anybody looked at checking the primarily of (P.N. + 1)?

R. Gerbicz · 2020-01-28, 15:23

See http://oeis.org/A061644 .

R.D. Silverman · 2020-01-28, 18:14

Quote:

Originally Posted by UoPTucson

I noticed that some primes are of the form (perfect number + 1), while some P.N. + 1 are not prime. Has anybody looked at checking the primarily of (P.N. + 1)?

If we assume that Sam Wagstaff's analysis of the distribution of Mersenne primes
is correct, we should expect finitely many.

ATH · 2020-01-28, 21:56

See post #10 here:
https://www.mersenneforum.org/showthread.php?t=10336

So far 4 primes and 1 unknown in the 51 known perfect numbers + 1.

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2020-01-28, 14:27	#1
UoPTucson Jul 2019 1 Posts	How many perfect numbers + 1 are prime I noticed that some primes are of the form (perfect number + 1), while some P.N. + 1 are not prime. Has anybody looked at checking the primarily of (P.N. + 1)?

2020-01-28, 15:23	#2
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 1484₁₀ Posts	See http://oeis.org/A061644 .

2020-01-28, 21:56	#4
ATH Einyen Dec 2003 Denmark 3⁵·13 Posts	See post #10 here: https://www.mersenneforum.org/showthread.php?t=10336 So far 4 primes and 1 unknown in the 51 known perfect numbers + 1.