A217718 Primes of the form x^3 + y^3 - 1, where x and y are primes.

53, 151, 467, 2539, 3527, 6983, 7109, 30133, 31121, 31247, 34703, 41957, 50777, 59581, 62819, 68947, 69263, 75041, 79631, 81703, 91673, 98711, 106019, 109297, 110681, 159013, 183329, 205721, 228311, 228383, 231893, 239147, 256031, 256771, 295901, 302959, 312929

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Mar 21 2013

Keywords

• nonn

Comments

A number is in this sequence if it is prime, and can be expressed as p1^3 + p2^3 - 1, where p1 and p2 are also prime.

There are 175 numbers in the sequence < 10^7: a(175) = 83^3 + 211^3 - 1 = 9965717.

Examples

			3527 is in the sequence, because 11^3 + 13^3 - 1 = 3527, and 11, 13, and 3527 are all prime.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..1890

Crossrefs

Cf. A024670 (sum of two cubes).

Cf. A214175 (primes that are one more than the sum of two prime cubes).

Programs

Mathematica

mx = 25; Union[Select[Flatten[Table[Prime[a]^3 + Prime[b]^3 - 1, {a, mx}, {b, a, mx}]], # < Prime[mx]^3 && PrimeQ[#] &]] (* T. D. Noe, Mar 29 2013 *)