A070157 Numbers k such that k-1, k+1, k^2+1, k^4+1 and k^8+1 are all prime numbers.
4, 19380, 9443670, 11054760, 15992070, 22482330, 32557380, 51102510, 57978840, 60549240, 64671570, 84045960, 89757960, 111316170, 112821690, 116433510, 171124380, 171418650, 183082350, 196694760, 197021160, 241803240, 266498460
Offset: 1
Keywords
Examples
19380 is a term since 19380-1 = 19379, 19380+1 = 19381, 19380^2+1 = 375584401, 19380^4+1 = 141063641523360001 and 19380^8+1 = 19898950959831015581425689600000001 are primes.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
Do[p = Prime[n] + 1; If[ PrimeQ[p + 1] && PrimeQ[1 + p^2] && PrimeQ[1 + p^4] && PrimeQ[1 + p^8], Print[p]], {n, 1, 115000000}] Select[Range[2665*10^5],AllTrue[{#-1,#+1,#^2+1,#^4+1,#^8+1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 03 2019 *) -
PARI
is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+1) && isprime(k^4+1) && isprime(k^8+1); \\ Amiram Eldar, Jun 26 2024
Extensions
Edited and extended by Robert G. Wilson v, May 04 2002