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%I #85 Jun 13 2022 02:27:17
%S 2,3,5,17,29,31,53,59,101,277,647,1061,2381,2833,3613,3853,3929,5297,
%T 7417,90217,122219,173191,256199,336353,485977,591827,1059503
%N Numbers k such that 3^k - 2^k is prime.
%C Some of the larger entries may only correspond to probable primes.
%C The 1137- and 1352-digit values associated with the terms 2381 and 2833 have been certified prime with Primo. - _Rick L. Shepherd_, Nov 12 2002
%C Or, numbers k such that A001047(k) is prime. - _Zak Seidov_, Sep 17 2006
%C 3^k - 2^k were proved prime for k = 3613, 3853, 3929, 5297, 7417 with Primo. - _David Harrison_, Jun 08 2011
%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=3%5En-2%5En&action=Search">PRP Records</a>.
%H R. Miles, <a href="https://doi.org/10.1090/S0002-9947-2013-05829-1">Synchronization points and associated dynamical invariants</a>, Trans. Amer. Math. Soc. 365 (2013), 5503-5524.
%H Primality certificates for <a href="http://oeis.hddkillers.com/A057468/">3613 to 7417</a>
%t Select[Prime@ Range@ 941, PrimeQ[3^# - 2^#] &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 and modified by _Robert G. Wilson v_, Mar 15 2017 *)
%t ParallelMap[ If[ PrimeQ[3^# - 2^#], #, Nothing] &, Prime@ Range@ 941] (* _Robert G. Wilson v_, Jun 28 2017 *)
%o (PARI) select(p->ispseudoprime(3^n-2^n), primes(100)) \\ _Charles R Greathouse IV_, Feb 11 2011
%Y Cf. A058765, A000043 (Mersenne primes), A001047 (3^n-2^n).
%Y Subset of A000040.
%K nonn,hard,nice,more
%O 1,1
%A _Robert G. Wilson v_, Sep 09 2000
%E a(20) = 90217 found by _Mike Oakes_, Feb 23 2001
%E Terms a(21) = 122219, a(22) = 173191, a(23) = 256199 were found by _Mike Oakes_ in 2003-2005. Corresponding numbers of decimal digits are 58314, 82634, 122238.
%E a(24) = 336353 found by _Mike Oakes_, Oct 15 2007. It corresponds to a probable prime with 160482 decimal digits.
%E a(25) = 485977 found by _Mike Oakes_, Sep 06 2009; it corresponds to a probable prime with 231870 digits. - _Mike Oakes_, Sep 08 2009
%E a(26) = 591827 found by _Mike Oakes_, Aug 25 2009; it corresponds to a probable prime with 282374 digits.
%E a(27) = 1059503 found by _Mike Oakes_, Apr 12 2012; it corresponds to a probable prime with 505512 digits. - _Mike Oakes_, Apr 14 2012
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