A243861 Primes p for which p^i - 4 is prime for i = 1, 3, 5 and 7.

971, 12641, 205607, 228341, 276557, 412343, 1012217, 1101323, 1902881, 2171021, 2477411, 2692121, 4116377, 4311677, 6060953, 6182993, 6388913, 6444863, 8341121, 8551451, 9507527, 10523141, 10997411, 11444093, 14101361, 14656307, 14813147, 15435587, 17337521

Offset: 1

Author

Abhiram R Devesh, Jun 12 2014

Keywords

• nonn
• easy

Comments

Subsequence of A243818: Primes p for which p^i - 4 is prime for i = 1, 3 and 5.

Examples

			Prime p=971 is in this sequence because p-4 = 967 (prime), p^3-4 = 915498607 (prime),  p^5-4 = 863169625893847 (prime), and p^7-4 = 813831713247384370687 (prime).
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A023200, A243583, A243780, A243818.

Programs

Python

import sympy.ntheory as snt
n=2
while n>1:
    n1=n-4
    n2=((n**3)-4)
    n3=((n**5)-4)
    n4=((n**7)-4)
    ##Check if n1 , n2, n3 and n4 are also primes.
    if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True and snt.isprime(n4)== True:
        print(n, n1, n2, n3, n4)
    n=snt.nextprime(n)