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A063825 Numbers k such that k-3, k-5, k-17, k-257, and k-65537 are all primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A268912 A168667 A170781 * A253043 A170790 A043678
KEYWORD
easy,nice,nonn
AUTHOR
Felice Russo, Aug 21 2001
STATUS
approved

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Last modified July 21 18:17 EDT 2024. Contains 374475 sequences. (Running on oeis4.)