A243780 Primes p for which p^i + 4 is prime for i = 1, 3 and 5.

7, 5503, 8779, 14629, 15877, 21013, 23599, 51199, 61483, 70237, 78163, 79333, 80149, 96667, 113089, 113359, 133153, 140053, 149377, 150889, 184039, 198967, 228199, 251287, 255637, 295843, 301123, 303613, 356929, 382843, 385393, 393709, 420037, 457363, 458119

Offset: 1

Author

Abhiram R Devesh, Jun 10 2014

Keywords

• nonn
• easy

Comments

This is a subsequence of:

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

A243583: Primes p for which p + 4 and p^3 + 4 are prime.

Examples

			p=7 is in this sequence as p + 4, p^3 + 4, p^5 + 4 (11, 347, 16811) are all prime.
p=5503 is in this sequence as p + 4 = 5507 (prime), p^3 + 4 = 166647398531 (prime) and p^5 + 4 = 5046584669419727747 (prime).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..250 from Abhiram R Devesh)

Crossrefs

Cf. A023200, A243583.

Programs

Mathematica

Select[Range[500000], PrimeQ[#] && AllTrue[#^{1, 3, 5} + 4, PrimeQ] &] (* Amiram Eldar, Apr 04 2020 *)

PARI

s=[]; forprime(p=2, 200000, if(isprime(p+4) && isprime(p^3+4) && isprime(p^5+4), s=concat(s, p))); s \\ Colin Barker, Jun 11 2014

Python

import sympy.ntheory as snt
n=2
while n>1:
    n1=n+4
    n2=((n**3)+4)
    n3=((n**5)+4)
    ##Check if n1 , n2 and n3 are also primes.
    if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True:
        print(n,n1,n2,n3)
    n=snt.nextprime(n)