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A117706
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Numbers k such that 6^k - k^6 is prime.
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10
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OFFSET
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1,2
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COMMENTS
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Comment from Donovan Johnson: A117705 and A117706 are both Fermat probable prime to four bases. They have also passed a Miller-Rabin primality test in five randomly chosen bases. I checked the n values up to 70000 for A117705 and n values up to 60000 for A117706. No additional primes or probable primes were found.
From the Lifchitz link: 100193 and 114433 are also in this sequence. - Robert Price, Mar 27 2019
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LINKS
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EXAMPLE
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a(2)=7 because 6^7 - 7^6 = 162287 is prime.
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MATHEMATICA
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Do[If[PrimeQ[(6^n-n^6)], Print[n]], {n, 1, 3000}]
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PROG
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(PARI) for(x=1, 1e5, ispseudoprime(p=6^x-x^6)&&print1(x", ")) \\ M. F. Hasler, Aug 20 2014
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Apr 13 2006, Jan 08 2008
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STATUS
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approved
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