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A058302
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Primes p such that p | ((p-1)/2)! -1.
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2
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3, 23, 31, 59, 71, 83, 107, 139, 151, 167, 211, 223, 239, 251, 271, 283, 307, 311, 331, 359, 379, 439, 463, 467, 487, 499, 547, 587, 643, 647, 659, 719, 751, 811, 827, 859, 883, 907, 911, 919, 967, 971, 983, 1031, 1039, 1063, 1103, 1163, 1171, 1223
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| p | (p-1)! +1 iff p is a prime (Wilson's theorem). All of the above primes are congruent to 3 (mod 4).
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LINKS
| Math Overflow, Primes P such that ((P-1)/2)!=1 mod P [From T. D. Noe (noe(AT)sspectra.com), Feb 24 2010]
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MATHEMATICA
| Select[ Range[ 1225 ], PrimeQ[ # ] && Mod[ ((# - 1)/2)! - 1, # ] == 0 & ]
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PROG
| (Pari) forprime(p=3, 10^4, if( Mod(((p-1)/2)!, p)==1, print1(p, ", "))); /* Joerg Arndt, Apr 12 2011 */
(MAGMA) [p: p in PrimesInInterval(3, 1230) | IsDivisibleBy(Factorial((p-1) div 2)-1, p)]; // Bruno Berselli, Apr 13 2011
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CROSSREFS
| Cf. A055939.
Sequence in context: A133023 A098946 A191086 * A133213 A138465 A006598
Adjacent sequences: A058299 A058300 A058301 * A058303 A058304 A058305
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 08 2000
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