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

Author

Abhiram R Devesh, Jun 11 2014

Keywords

• nonn
• easy

Comments

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

Examples

			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).
		

Links

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

Crossrefs

Cf. A046132.

Programs

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)