login
A102326
Primes p such that the largest prime divisor of p^4+1 is less than p.
3
10181, 14051, 18979, 25253, 57173, 58013, 60101, 62497, 65951, 66541, 69457, 75931, 82241, 82261, 84229, 87721, 88339, 88819, 91499, 92333, 95917, 99523, 105557, 107747, 109229, 118493, 118927, 137339, 146291, 155399, 157019
OFFSET
1,1
COMMENTS
Primes in A309562. - Robert Israel, Aug 09 2019
LINKS
EXAMPLE
p = 10181, 1+p^4 = 10743894862923122 = 2*17*1657*4657*5113*8009, so the largest prime factor is 8009 < p = 10181.
MAPLE
filter:= proc(p) max(numtheory:-factorset(p^4+1)) < p end proc:
select(filter, [seq(ithprime(i), i=1..20000)]); # Robert Israel, Aug 09 2019
MATHEMATICA
<<NumberTheory`NumberTheoryFunctions` Select[Prime[Range[15000]], Max[PrimeFactorList[1 + #^4]] < # &] (* Ray Chandler, Jan 08 2005 *)
Select[Prime[Range[15000]], FactorInteger[#^4+1][[-1, 1]]<#&] (* Harvey P. Dale, Feb 27 2017 *)
PROG
(PARI) isok(p) = isprime(p) && (vecmax(factor(p^4+1)[, 1]) < p); \\ Michel Marcus, Jul 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 05 2005
EXTENSIONS
Extended by Ray Chandler, Jan 08 2005
STATUS
approved