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Primes of the form k*6^m +1 where k is a Mersenne prime (A000668) and m is an integer.
3

%I #24 Sep 15 2024 01:44:43

%S 19,43,109,1117,3889,40177,139969,326593,839809,4718557,5038849,

%T 5925313,18874333,52068097,1088391169,1874451457,6115248577,

%U 24461134273,1410554953729,2429289086977,31701630016513,118486616113153

%N Primes of the form k*6^m +1 where k is a Mersenne prime (A000668) and m is an integer.

%e (2^521-1)*6^959+1 is prime

%t Union[Flatten[Table[Select[p*6^Range[0, 30] + 1, # < 10^20 && PrimeQ[#] &], {p, {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951}}]]]

%t Union[Flatten[Table[Select[(2^MersennePrimeExponent[n]-1)6^Range[ 0,20]+ 1,PrimeQ],{n,20}]]] (* _Harvey P. Dale_, Aug 15 2021 *)

%o (Magma) // For the Mersenne prime 2^521-1, for example:

%o [n: n in [0..1000] | IsPrime((2^521-1)*6^n+1)];

%Y Cf. A000668, A185069.

%K nonn

%O 1,1

%A _Gilbert Mozzo_, Feb 18 2011

%E Partially edited by _N. J. A. Sloane_, Feb 19 2011