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A057468
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Numbers k such that 3^k - 2^k is prime.
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123
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2, 3, 5, 17, 29, 31, 53, 59, 101, 277, 647, 1061, 2381, 2833, 3613, 3853, 3929, 5297, 7417, 90217, 122219, 173191, 256199, 336353, 485977, 591827, 1059503
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OFFSET
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1,1
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COMMENTS
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Some of the larger entries may only correspond to probable primes.
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
3^k - 2^k were proved prime for k = 3613, 3853, 3929, 5297, 7417 with Primo. - David Harrison, Jun 08 2011
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LINKS
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MATHEMATICA
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ParallelMap[ If[ PrimeQ[3^# - 2^#], #, Nothing] &, Prime@ Range@ 941] (* Robert G. Wilson v, Jun 28 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,hard,nice,more
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AUTHOR
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EXTENSIONS
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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.
a(24) = 336353 found by Mike Oakes, Oct 15 2007. It corresponds to a probable prime with 160482 decimal digits.
a(25) = 485977 found by Mike Oakes, Sep 06 2009; it corresponds to a probable prime with 231870 digits. - Mike Oakes, Sep 08 2009
a(26) = 591827 found by Mike Oakes, Aug 25 2009; it corresponds to a probable prime with 282374 digits.
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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STATUS
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approved
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