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

1,1

Comments

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

Links

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

Example

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).

Prog

(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)

Crossrefs

Cf. A023200, A243583, A243780, A243818.

Sequence in context: A345790 A257975 A217161 * A171771 A206089 A217162

Adjacent sequences: A243858 A243859 A243860 * A243862 A243863 A243864

Keyword

nonn,easy

Author

Abhiram R Devesh, Jun 12 2014

Status

approved