A242326 Primes p for which p + 2, p^3 + 2 and p^5 + 2 are prime.

419, 2339, 14081, 45821, 46349, 51419, 56039, 68489, 70379, 108191, 112601, 115319, 131891, 132749, 256391, 267611, 278879, 314159, 328511, 342449, 361001, 385139, 424841, 433259, 470651, 489689, 519371, 573761, 664691, 691181, 694271

Offset: 1

Author

Abhiram R Devesh, May 10 2014

Keywords

• nonn

Comments

Subsequence of A001359 and A048637.

All the terms in the sequence are congruent to 2 mod 3. This sequence is a subsequence of A240110.

Also, congruent to (11, 29) mod 30. - Zak Seidov, May 18 2014

Also, subsequence of A216976. - Michel Marcus, May 18 2014

Examples

			419 is in the sequence because
p = 419 (prime),
p + 2 = 421 (prime),
p^3 + 2 = 73560061 (prime), and
p^5 + 2 = 12914277518101 (prime).
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A048637.

Programs

Magma

[p: p in PrimesUpTo(10^6)| IsPrime(p+2) and IsPrime(p^3+2)and IsPrime(p^5+2)]; // Vincenzo Librandi, May 11 2014

Mathematica

Select[Prime[Range[10^5]], PrimeQ[# + 2]&& PrimeQ[#^3 + 2]&& PrimeQ[#^5 + 2] &] (* Vincenzo Librandi, May 11 2014 *)