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A302333 Wagstaff primes related to The New Mersenne Conjecture that are the indices of perfect numbers in a list of centered 9-gonal numbers.

3, 11, 43, 2731, 43691, 174763, 715827883, 768614336404564651, 56713727820156410577229101238628035243

Offset: 1

Steve Homewood, Apr 05 2018

Let p be a Wagstaff prime related to The New Mersenne Conjecture. Then (3p-2)(3p-1)/2 gives the perfect number whose index it is.

			For p = 3, (3*3-2)*(3*3-1)/2 = 28 and for p = 11, (3*11-2)(3*11-1)/2 = 496.

Caldwell and Honaker, 56713...35243 (38-digits), Prime Curios!
Eric Weisstein's World of Mathematics, New Mersenne Prime Conjecture

Cf. A000979, A107360.

A185660 Numbers k such that (k^3 + 11*k) +/-1 is a twin prime pair.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 16, 17, 20, 22, 37, 44, 46, 48, 52, 57, 61, 63, 68, 69, 70, 72, 81, 84, 86, 94, 96, 99, 101, 106, 108, 112, 117, 123, 124, 134, 138, 162, 178, 189, 191, 193, 200, 202, 206, 223, 224, 229, 260, 264, 271, 279, 282, 294, 297

Offset: 1

G. L. Honaker, Jr., Feb 08 2011; proposed by Steve Homewood

nonn

			For k=9, the corresponding twin prime pair is {827, 829}.

G. C. Greubel, Table of n, a(n) for n = 1..5000
Prime curio for 829

Cf. A000040, A001097.

Select[Range[300], PrimeQ[#^3 + 11# - 1] && PrimeQ[#^3 + 11# + 1] &]
Select[Range[300],AllTrue[#^3+11#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 28 2014 *)

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User: Steve Homewood

A302333 Wagstaff primes related to The New Mersenne Conjecture that are the indices of perfect numbers in a list of centered 9-gonal numbers.

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