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A064152
Erdős primes: primes p such that all p-k! for 1 <= k! < p are composite.
2
2, 101, 211, 367, 409, 419, 461, 557, 673, 709, 769, 937, 967, 1009, 1201, 1259, 1709, 1831, 1889, 2141, 2221, 2309, 2351, 2411, 2437, 2539, 2647, 2837, 2879, 3011, 3019, 3041, 3049, 3079, 3163, 3217, 3221, 3359, 3389, 3499, 3593, 3671, 3709, 3833, 3851
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
Sequence in context: A195903 A042249 A157338 * A162353 A088272 A125819
KEYWORD
easy,nonn
AUTHOR
Felice Russo, Sep 13 2001
STATUS
approved