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Primes p such that the largest prime factor of p^5 + 1 is less than p.
2

%I #22 Jun 19 2024 01:54:42

%S 1753,2357,7103,9749,13441,16453,21467,22739,25153,28409,29059,33247,

%T 33347,36781,42853,51427,57751,58453,62347,65777,66593,69119,72923,

%U 78643,80407,83591,85619,89909,91411,99409,101209,101363,113171,124337

%N Primes p such that the largest prime factor of p^5 + 1 is less than p.

%H Amiram Eldar, <a href="/A102327/b102327.txt">Table of n, a(n) for n = 1..10000</a>

%F Solutions to {A006530(1 + p^5) < p} where p is a prime.

%e p = 1753, 1 + p^5 = 16554252702583994 = 2*41*151*691*877*1361*1621, so the largest prime factor is 1621 < p = 1753.

%t Select[Prime[Range[15000]], Max[PrimeFactorList[1 + #^5]] < # &] (* _Ray Chandler_, Jan 08 2005 *)

%t Select[Prime[Range[12000]],FactorInteger[#^5+1][[-1,1]]<#&] (* _Harvey P. Dale_, Mar 14 2011 *)

%o (PARI) isok(p)= isprime(p) && (vecmax(factor(p^5+1)[,1]) < p); \\ _Michel Marcus_, Jul 11 2018

%Y Cf. A000040, A006530, A065091, A073501.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 05 2005

%E Extended by _Ray Chandler_, Jan 08 2005