A048636 Primes of the form prime^3 + 2.

29, 127, 24391, 357913, 571789, 1442899, 5177719, 18191449, 30080233, 73560061, 80062993, 118370773, 127263529, 131872231, 318611989, 344472103, 440711083, 461889919, 590589721, 756058033, 865523179, 1095912793, 1298596573, 1341919729, 1524845953, 1697936059

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn

Comments

The first terms in the intersection with A092402, i.e., of the form p + 2^3, are (18191449, 1341919729, 2588282119, 3532642669, 16445197009, ...). - M. F. Hasler, Jan 13 2025

Examples

			a(2) = 127 = 5^3 + 2 and 5 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Crossrefs

Cf. A048637.

Cf. A092402 (primes of the form p + 8), A321891 (union of the two); A188764 (primes of the form (product of distinct primes^3) + 2).

Programs

Maple

select(isprime, [ithprime(i)^3+2$i=1..300])[];  # Alois P. Heinz, Jan 13 2025

Mathematica

lst={};Do[s=Prime[n]^3;If[PrimeQ[p=s+2], AppendTo[lst, p]], {n, 6!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 26 2008 *)

PARI

forprime (p=2,1100,if(isprime(p^3+2),print1(p^3+2,", "))) \\ Hugo Pfoertner, Oct 30 2018