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First differences of A062481.
1

%I #9 Jun 25 2021 23:14:40

%S 7,235,16141,48811741,13011865891,232617453293191,143882557561868665,

%T 8862794004464425240057,99999991137061880347498904071,

%U 191843424957750480504146841291811

%N First differences of A062481.

%C a(1), a(3) and a(6) are the only primes found for n up to 10000 using The C/Gmp program in the link which is 17 times faster than the PARI routine. We read large blocks of primes into memory and test in memory.

%C If another prime exists, it is larger than 418977 digits.

%C A concept of order can be introduced here by researching and analyzing the next-nextprime, next-next-nextprime etc.

%H C.L. Hilliard,<a href="http://groups.google.com/group/prime-index-powers/web/c-gmp-prime-indices-to-prime-power">Primes less than 3 trillion</a>

%F a(n) = A062481(n+1) - A062481(n).

%e For n = 3, 4^7 - 3^3 = 16141, the 3rd entry in the sequence.

%o (PARI) ppower(n) = { for(x=1,n, y=(x+1)^prime(x+1)-x^prime(x); print1(y",") ); }

%K nonn

%O 1,1

%A _Cino Hilliard_, May 15 2009

%E Edited by _R. J. Mathar_, May 17 2009