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 A064152 Erdos primes: primes p such that all p-k! for 1<=k!

%I

%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 Erdos primes: primes p such that all p-k! for 1<=k!<p are composite.

%C Numbers of Erdos 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*ln(10))). If so the sequence is infinite.

%D R. K. Guy, Unsolved Problems in Number Theory, A16.

%H T. D. Noe, <a href="/A064152/b064152.txt">Table of n, a(n) for n=1..7875</a>

%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)) ) } [From _Harry J. Smith_, Sep 09 2009]

%K easy,nonn,changed

%O 1,1

%A _Felice Russo_, Sep 13 2001

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Last modified May 20 02:52 EDT 2013. Contains 225446 sequences.