A097954 Numbers k such that 7*10^k + 9 is prime.
1, 2, 4, 6, 11, 12, 13, 35, 46, 57, 128, 156, 263, 353, 396, 429, 783, 982, 1058, 1563, 1695, 1816, 1937, 4236, 4431, 6858, 9898, 13145, 16646, 20891, 63351, 105296, 113693, 121144, 163780, 234915, 284751
Offset: 1
Examples
k=2 we get 7*10^2+9 = 7*100+9 = 709, which is prime.
Links
- Makoto Kamada, Prime numbers of the form 700...009.
- Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.
- Index entries for primes involving repunits.
Crossrefs
Cf. A101130.
Programs
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Magma
[n: n in [0..400] |IsPrime(7*10^n + 9)]; // Vincenzo Librandi, Sep 06 2015
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Mathematica
Do[ If[ PrimeQ[ 7*10^n + 9], Print[ n ]], {n, 0, 10000}] (* Robert G. Wilson v, Jan 19 2005 *) Select[Range[0, 10000], PrimeQ[7 10^# + 9] &] (* Vincenzo Librandi, Sep 06 2015 *) -
PARI
is(n)=ispseudoprime(7*10^n+9) \\ Charles R Greathouse IV, Jun 13 2017
Formula
a(n) = A101130(n) + 1.
Extensions
a(19)-a(27) from Robert G. Wilson v, Jan 19 2005
a(28)-a(31) from Kamada data by Robert Price, Dec 14 2010
a(32)-a(35) from Robert Price, Sep 05 2015
a(36)-a(37) from Robert Price, Jul 10 2023
Comments