OFFSET
1,1
COMMENTS
p | (p-1)! +1 iff p is a prime (Wilson's theorem). All of the above primes are congruent to 3 (mod 4).
Primes p such that p | ((p-3)/2)! +2. - Davide Rotondo, Jun 03 2024
REFERENCES
J. B. Cosgrave, A Mersenne-Wieferich Odyssey, Manuscript, May 2022. See Section 18.5.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
Math Overflow, Primes P such that ((P-1)/2)!=1 mod P [From T. D. Noe, Feb 24 2010]
MATHEMATICA
Select[ Range[ 1225 ], PrimeQ[ # ] && Mod[ ((# - 1)/2)! - 1, # ] == 0 & ]
Select[Prime[Range[200]], Divisible[((#-1)/2)!-1, #]&] (* Harvey P. Dale, Aug 29 2022 *)
PROG
(PARI) forprime(p=3, 10^4, if( Mod(((p-1)/2)!, p)==1, print1(p, ", "))); /* Joerg Arndt, Apr 12 2011 */
(PARI) is(p)=isprime(p) && p%4==3 && if(p>9, qfbclassno(-p)%4, p)==3 \\ Charles R Greathouse IV, Nov 04 2013
(Magma) [p: p in PrimesInInterval(3, 1230) | IsDivisibleBy(Factorial((p-1) div 2)-1, p)]; // Bruno Berselli, Apr 13 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Dec 08 2000
STATUS
approved