A268475 Numbers n such that n^3 +/- 2 and 3*n +/- 2 are all prime.

435, 555, 2415, 31635, 38025, 44835, 80625, 88335, 97455, 98505, 99435, 124335, 142065, 145095, 165375, 176055, 204765, 246435, 279225, 293475, 310095, 315555, 332085, 344745, 348735, 376935, 392415, 443595, 462105, 467385, 482355, 581415, 609555, 626775, 636015

Offset: 1

Author

K. D. Bajpai, Feb 05 2016

Keywords

• nonn

Comments

All the terms in this sequence are congruent to 0 (mod 5).

Each term in this sequence yields two sets of cousin prime pairs i.e., for n = 435 -> {82312877, 82312873} and {1307, 1303}.

All terms are congruent to 15 mod 30. - Robert Israel, Feb 05 2016

Examples

			435 is in the sequence because 435^3 + - 2 =  82312877, 82312873; 3*435 + - 2 = 1307, 1303 are all prime.
555 is in the sequence because 555^3 + - 2 =  170953877, 170953873; 3*555 + - 2 = 1667, 1663 are all prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A024893, A090121, A108701, A153183, A157834.

Programs

Magma

[n : n in [1..1e5] | IsPrime(n^3 + 2) and IsPrime(n^3 - 2) and IsPrime(3*n + 2) and IsPrime(3*n - 2)];

Maple

select(n -> andmap(isprime, [n^3 + 2, n^3 - 2, 3*n + 2, 3*n - 2]), [seq(p, p=1.. 10^6)]);

Mathematica

Select[Range[1000000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[3 # + 2] && PrimeQ[3 # - 2] &]

PARI

for(n = 1,1e5, if( isprime(n^3 + 2) && isprime(n^3 - 2) && isprime(3*n + 2) && isprime(3*n - 2), print1(n ", ")))