OFFSET
1,1
COMMENTS
3, 5, 17, 257 and 65537 are the only known Fermat primes. The counting function p(N) seems to follow the law: p(N)~c*N^(4/3*gamma) where c is a positive constant and gamma the Euler constant. If so, the sequence is infinite.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[65538, 130000], PrimeQ[ #-3]&&PrimeQ[ #-5]&&PrimeQ[ #-17]&&PrimeQ[ #-257]&&PrimeQ[ #-65537]&] (* Stefan Steinerberger, Mar 31 2006 *)
Select[Range[65538, 200000], And@@PrimeQ[#-{3, 5, 17, 257, 65537}]&] (* Harvey P. Dale, Apr 27 2012 *)
With[{c=2^2^Range[0, 4]+1}, Select[Range[65538, 130000], AllTrue[#-c, PrimeQ]&]] (* Harvey P. Dale, Feb 07 2024 *)
PROG
(PARI) { n=0; for (m=1, 10^9, if(isprime(m - 3) && isprime(m - 5) && isprime(m - 17) && isprime(m - 257) && isprime(m - 65537), write("b063825.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 01 2009
(Magma) [n: n in [65700..2*10^5] | IsPrime(n-3) and IsPrime(n-5) and IsPrime(n-17) and IsPrime(n-257) and IsPrime(n-65537)]; // Vincenzo Librandi, Aug 26 2015
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Felice Russo, Aug 21 2001
STATUS
approved