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%I
%S 23,29,59,61,67,71,79,83,109,137,139,149,193,227,233,239,251,257,269,
%T 271,277,293,307,311,317,359,379,383,389,397,401,419,431,449,461,463,
%U 467,479,499,503,521,557,563,569,571,577,593,599,601,607
%N Pillai primes: p such that there exists an integer m such that m!+1 is 0 mod p and p is not 1 mod m.
%D G. E. Hardy and M. V. Subbarao, A modified problem of Pillai and some related questions, Amer. Math. Monthly 109 (2002), no. 6, 554-559.
%H T. D. Noe and Charles R Greathouse IV, <a href="/A063980/b063980.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Noe)
%t ok[p_] := (r = False; Do[If[Mod[m! + 1, p] == 0 && Mod[p, m] != 1, r = True; Break[]], {m, 2, p}]; r); Select[Prime /@ Range[111], ok] (* From Jean-François Alcover, Apr 22 2011 *)
%t nn=1000; fact=1+Rest[FoldList[Times,1,Range[nn]]]; t={}; Do[p=Prime[i]; m=2; While[m<p && !(Mod[p,m]!=1 && Mod[fact[[m]],p]==0), m++]; If[m<p, AppendTo[t,p]], {i,2,PrimePi[nn]}]; t (* T. D. Noe, Apr 22 2011 *)
%o (PARI) is(p)=my(t=Mod(5040,p)); for(m=8, p-2, t*=m; if(t==-1 && p%m!=1, return(isprime(p)))); 0 \\ _Charles R Greathouse IV_, Feb 10 2013
%Y Smallest m is given in A063828, largest in A211411.
%K nonn,nice
%O 1,1
%A _R. K. Guy_, Sep 08 2001
%E More terms from David W. Wilson, Sep 08, 2001
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