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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A024670 (sum of two cubes).

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

Sequence in context: A142043 A175600 A142417 * A044385 A044766 A342450

Adjacent sequences: A217715 A217716 A217717 * A217719 A217720 A217721

Keyword

nonn

Author

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

Status

approved