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Primes p such that 5^p - 4 is also prime.
0

%I #23 Aug 18 2024 20:10:49

%S 5,7,47

%N Primes p such that 5^p - 4 is also prime.

%C If it exists, a(4) > 48091. - _J.W.L. (Jan) Eerland_, Nov 13 2022

%C If it exists, a(4) > 2*10^5 (cf. comment by _Tyler NeSmith_ in A059613). - _Michael S. Branicky_, Aug 17 2024

%F A000040 INTERSECT A059613. - _R. J. Mathar_, Apr 15 2010

%e For p=5, 5^5-4=3121; p=7, 5^7-4=78121; p=47, 5^47-4= 710542735760100185871124267578121

%o (Magma) [p: p in PrimesUpTo(3500) | IsPrime(5^p-4)];

%o (PARI) is(n)=isprime(n) && isprime(5^n-4) \\ _Charles R Greathouse IV_, Sep 06 2016

%Y Cf. A000040, A059613.

%K nonn,more,bref

%O 1,1

%A _Vincenzo Librandi_, Mar 14 2010