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A093804
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Primes p such that p! + 1 is also prime.
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3
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OFFSET
| 1,1
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COMMENTS
| Or, numbers n such that Sum_{d|n} d! is prime.
The prime 26951 from A002981 (n!+1 is prime) is a member since Sum_{d|n} d! = n!+1 if n is prime. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 30 2005
a(n) are the primes in A002981[n] = {0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, ...} Numbers n such that n! + 1 is prime. Corresponding primes of the form p! + 1 are listed in A103319[n] = {3, 7, 39916801, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 23 2006
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LINKS
| Chris K. Caldwell, The List of Largest Known Primes, 110059! + 1
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EXAMPLE
| Sum_{d|3} d! = 1! + 3! = 7 is prime, so 3 is a member.
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MAPLE
| seq(`if`(isprime(ithprime(n)!+1), ithprime(n), NULL), n=1..25); # Nathaniel Johnston, Jun 28 2011
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MATHEMATICA
| Select[Prime[Range[5! ]], PrimeQ[ #!+1]&] (*From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 17 2009*)
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CROSSREFS
| Cf. A062363, A002981, A038507, A088332, A103319.
Sequence in context: A006497 A038912 A019361 * A084121 A088747 A007756
Adjacent sequences: A093801 A093802 A093803 * A093805 A093806 A093807
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KEYWORD
| more,hard,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), May 19 2004
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EXTENSIONS
| One more term from Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 23 2006
Added a(8)=110059 (found on June 11, 2011, by PrimeGrid), Arkadiusz Wesolowski, Jun 28 2011
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