A242518 Primes p for which p^n - 2 is prime for n = 1, 3, 5 and 7.

201829, 2739721, 6108679, 7883329, 9260131, 9309721, 9917389, 14488249, 15386491, 15876481, 16685299, 16967191, 18145279, 20566969, 20869129, 21150991, 23194909, 25510189, 28406929, 34669909, 35039311, 36795169, 37912141, 39083521, 39805639

Offset: 1

Author

Abhiram R Devesh, May 17 2014

Keywords

• nonn

Comments

This is a subsequence of A242517.

Examples

			p = 201829  (prime)
p - 2 = 201827 (prime)
p^3 - 2 = 8221493263045787 (prime)
p^5 - 2 = 334902077869420623790640147 (prime)
p^7 - 2 = 13642217803107967058507788317851080907 (prime)
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..150 (first 100 terms from Abhiram R Davesh)

Crossrefs

Cf. A242517, A240126, A001359, A006512.

Programs

Mathematica

Select[Prime[Range[25*10^5]],AllTrue[#^{1,3,5,7}-2,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 26 2015 *)

Python

import sympy
n=2
while n>1:
    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 sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True and sympy.ntheory.isprime(n4)== True:
        print(n, " , " , n1, " , ", n2, " , ", n3, " , ", n4)
    n=sympy.ntheory.nextprime(n)