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A243817 Primes p for which p - 4 and p^3 - 4 are primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 23:31 EDT 2019. Contains 327207 sequences. (Running on oeis4.)