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A243583 Primes p for which p + 4 and p^3 + 4 are primes. 5
3, 7, 19, 79, 103, 109, 277, 379, 487, 967, 1489, 1663, 1867, 2857, 3019, 3253, 3613, 3697, 4003, 4783, 4969, 5413, 5437, 5503, 5569, 5647, 5923, 7477, 7669, 7687, 7699, 7789, 7933, 8233, 8779, 9007, 9319, 9547, 9739, 10597, 11257, 11467, 11593, 11827, 12037 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a subsequence of:

A023200: Primes p such that p + 4 is also prime.

A073573: Numbers n such that n^3 + 4 is prime.

LINKS

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

EXAMPLE

p = 3 is in this sequence because p + 4 = 7  (prime) and p^3 + 4 = 31 (prime).

p = 7 is in this sequence because p + 4 = 11  (prime) and p^3 + 4 = 347 (prime).

PROG

(Python)

import sympy.ntheory as snt

n=2

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)

(PARI) s=[]; forprime(p=2, 20000, if(isprime(p+4) && isprime(p^3+4), s=concat(s, p))); s \\ Colin Barker, Jun 11 2014

CROSSREFS

Cf. A023200, A073573.

Sequence in context: A163571 A217611 A322852 * A215487 A146037 A172514

Adjacent sequences:  A243580 A243581 A243582 * A243584 A243585 A243586

KEYWORD

nonn,easy

AUTHOR

Abhiram R Devesh, Jun 09 2014

STATUS

approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)