A063825 Numbers k such that k-3, k-5, k-17, k-257, and k-65537 are all primes.

65704, 66364, 72106, 74764, 80686, 80914, 82474, 85456, 85834, 89074, 89674, 92644, 94564, 95806, 97006, 97384, 97864, 98644, 100804, 101284, 102004, 105256, 108964, 113044, 113176, 119704, 121024, 121954, 123736, 125644, 127294, 129226

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

Cf. A063799, A019434.

Sequence in context: A268912 A168667 A170781 * A253043 A170790 A043678

Adjacent sequences: A063822 A063823 A063824 * A063826 A063827 A063828

Keyword

easy,nice,nonn

Author

Felice Russo, Aug 21 2001

Status

approved