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

11, 971, 1877, 2861, 8741, 12641, 13163, 16763, 28283, 29021, 30707, 36713, 41957, 42227, 58967, 98717, 105971, 115127, 128663, 138641, 160817, 164093, 167441, 190763, 205607, 210173, 211067, 228341, 234197, 237977, 246473, 249107, 276557, 295433, 312233

Offset: 1

Author

Abhiram R Devesh, Jun 11 2014

Keywords

• nonn
• easy

Comments

This is a subsequence of the following:

A046132: Larger member p+4 of cousin primes (p, p+4).

A243817: Primes p for which p - 4 and p^3 - 4 are primes.

Examples

			p = 11 is in this sequence because p - 4 = 7  (prime), p^3 - 4 = 1327 (prime) and p^5 - 4 = 161047 (prime).
p = 971 is in this sequence because p - 4 = 967  (prime), p^3 - 4 = 915498607 (prime) and p^5 - 4 = 863169625893847 (prime).
		

Links

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

Crossrefs

Cf. A046132, A243817.

Programs

Mathematica

Select[Range[300000], PrimeQ[#] && AllTrue[#^{1, 3, 5} - 4, PrimeQ] &] (* Amiram Eldar, Apr 04 2020 *)
Select[Prime[Range[27000]],AllTrue[#^{1,3,5}-4,PrimeQ]&] (* Harvey P. Dale, Jan 04 2021 *)

Python

import sympy.ntheory as snt
n=5
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)