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

1,1

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.

Links

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

Example

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).

Mathematica

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

Prog

(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)
(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

Crossrefs

Cf. A023200, A243583.

Sequence in context: A340292 A095155 A219893 * A246519 A062644 A103174

Adjacent sequences: A243777 A243778 A243779 * A243781 A243782 A243783

Keyword

nonn,easy

Author

Abhiram R Devesh, Jun 10 2014

Status

approved