OFFSET
1,1
COMMENTS
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.
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A2, p. 11.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..7875 from T. D. Noe)
MATHEMATICA
q[n_] := Module[{k = 1}, While[k! < n && ! PrimeQ[n - k!], k++]; k! >= n]; Select[Prime[Range[550]], q] (* Amiram Eldar, Mar 21 2024 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Felice Russo, Sep 13 2001
STATUS
approved