A243817 Primes p for which p - 4 and p^3 - 4 are primes.

11, 17, 23, 41, 83, 101, 131, 227, 311, 383, 491, 503, 773, 827, 881, 887, 971, 1097, 1283, 1301, 1451, 1493, 1877, 2141, 2243, 2273, 2351, 2687, 2861, 2957, 3533, 3881, 3947, 4007, 4517, 4643, 5231, 5237, 5573, 5741, 6203, 7211, 7541, 7883, 7937, 8741, 9137, 9551, 10337, 11447

Offset

1,1

Comments

This is a subsequence of A046132: Larger member p+4 of cousin primes (p, p+4).

Links

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

Example

p = 11 is in this sequence because p - 4 = 7  (prime) and p^3 - 4 = 1327 (prime).
p = 17 is in this sequence because p - 4 = 13  (prime) and p^3 - 4 = 4909 (prime).

Prog

(Python)
import sympy.ntheory as snt
n=5
while n>1:
....n1=n-4
....n2=((n**3)-4)
....##Check if n1 and n2 are also primes.
....if snt.isprime(n1)== True and snt.isprime(n2)== True:
........print(n, n1, n2)
....n=snt.nextprime(n)

Crossrefs

Cf. A046132.

Sequence in context: A099722 A031505 A094524 * A098412 A261918 A136342

Adjacent sequences: A243814 A243815 A243816 * A243818 A243819 A243820

Keyword

nonn,easy

Author

Abhiram R Devesh, Jun 11 2014

Status

approved