A242327 Primes p for which (p^n) + 2 is prime for n = 1, 3, 5, and 7.

132749, 1175411, 3940799, 5278571, 11047709, 12390251, 15118769, 21967241, 22234871, 26568929, 31809959, 32229341, 32969591, 35760551, 38704661, 43124831, 43991081, 49248971, 50227211, 51140861, 53221631, 55568171, 59446109, 63671651, 71109161, 76675589

Offset: 1

Author

Abhiram R Devesh, May 10 2014

Keywords

• nonn

Comments

Subsequence of A001359 and A048637.

Examples

			p = 132749 (prime);
p + 2 = 132751 (prime);
p^3 + 2 = 2339342304585751 (prime);
p^5 + 2 = 41224584878413873150038751 (prime);
p^7 + 2 = 726471878470342746448722269536491751 (prime).
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A001359, A006512, A048637.

Programs

PARI

isok(p) = isprime(p) && isprime(p+2) && isprime(p^3+2) && isprime(p^5+2) && isprime(p^7+2); \\ Michel Marcus, May 15 2014

Python

import sympy
from sympy.ntheory import isprime, nextprime
n=2
while True:
    n1=n+2
    n2=n**3+2
    n3=n**5+2
    n4=n**7+2
    ##.Check if n1, n2, n3 and n4 are also primes
    if all(isprime(x) for x in [n1, n2, n3, n4]):
        print(n, ", ", n1, ", ", n2, ", ", n3, ", ", n4)
    n=nextprime(n)

Sage

def is_A242327(n):
    return is_prime(n) and all([is_prime(n^(2*k+1)+2) for k in range(4)])
filter(is_A242327, range(3940800)) # Peter Luschny, May 15 2014