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%I #18 Mar 21 2024 06:45:16
%S 2,101,211,367,409,419,461,557,673,709,769,937,967,1009,1201,1259,
%T 1709,1831,1889,2141,2221,2309,2351,2411,2437,2539,2647,2837,2879,
%U 3011,3019,3041,3049,3079,3163,3217,3221,3359,3389,3499,3593,3671,3709,3833,3851
%N Erdős primes: primes p such that all p-k! for 1 <= k! < p are composite.
%C Numbers of Erdős primes <= 10^j for j = 1,2,3, ... are 1, 1, 13, 95, 901, 7875, 71140, 646242, 5901409, ... For large j the asymptotic law seems to be #E(10^j) ~ (1/8)*(10^j/(j*log(10))). If so the sequence is infinite.
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A2, p. 11.
%H Amiram Eldar, <a href="/A064152/b064152.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..7875 from T. D. Noe)
%t q[n_] := Module[{k = 1}, While[k! < n && ! PrimeQ[n - k!], k++]; k! >= n]; Select[Prime[Range[550]], q] (* _Amiram Eldar_, Mar 21 2024 *)
%o (PARI) { n=0; for (m=1, 10^9, p=prime(m); k=f=b=1; while ((f*=k) < p, if (isprime(p-f), b=0; break); k++); if (b, write("b064152.txt", n++, " ", p); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 09 2009
%Y Cf. A000142, A065381.
%K easy,nonn
%O 1,1
%A _Felice Russo_, Sep 13 2001
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