A100595 Numbers k such that (prime(k)-1)! + prime(k)^9 is prime.
9, 10, 17, 137
Offset: 1
Examples
a(1) = 9 because (prime(9)-1)! + prime(9)^9 = (23-1)! + 23^9 = 1124000729578760341463 is the smallest prime of this form. a(2) = 10 because (prime(10)-1)! + prime(10)^9 = (29-1)! + 29^9 = 304888344611713875008649975869 is the 2nd smallest prime of this form. a(3) = 17, but prime(17) = 59 yields a number that would take 2 full lines of this page; and a(4) = 137 because prime(137) = 773 yields a prime of this form which is 1975 digits long. Note also that 773 = prime(137) = prime(prime(34)).
Programs
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Mathematica
lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^9], AppendTo[lst, n]], {n, 12^2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *) -
PARI
is(k) = ispseudoprime((prime(k)-1)! + prime(k)^9); \\ Jinyuan Wang, Apr 11 2020
Formula
Numbers k such that (prime(k)-1)! + prime(k)^9 is prime, where prime(k) is the k-th prime.
Comments