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A105710 Numbers k such that 9973*k + 1009 is prime. 11

%I

%S 0,28,36,70,76,78,106,124,136,168,184,198,208,216,226,234,238,246,258,

%T 294,300,304,318,348,364,366,370,394,418,436,454,468,474,496,556,570,

%U 588,598,604,616,660,688,696,714,736,738,744,748

%N Numbers k such that 9973*k + 1009 is prime.

%C 1009 and 9973 are the smallest and largest four-digit primes, respectively.

%C The theorem of Dirichlet shows that this sequence is infinite. - _Stefan Steinerberger_, Feb 12 2006

%e If k=0, then 9973*k + 1009 = 1009 (prime).

%e If k=168, then 9973*k + 1009 = 1676473 (prime).

%t For[n = 1, n < 1000, n++, If[PrimeQ[(9973*n + 1009)], Print[n]]] (* _Stefan Steinerberger_, Feb 12 2006 *)

%t Select[Range[0, 1000], PrimeQ[9973 # + 1009] &] (* _Vincenzo Librandi_, Sep 14 2015 *)

%o (MAGMA) [n: n in [0..800] | IsPrime(9973*n + 1009)]; // _Vincenzo Librandi_, Sep 14 2015

%o (PARI) is(n)=isprime(9973*n+1009) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A105679.

%K nonn,easy

%O 1,2

%A _Parthasarathy Nambi_, May 06 2005

%E More terms from _Stefan Steinerberger_, Feb 12 2006

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Last modified July 13 17:54 EDT 2020. Contains 335689 sequences. (Running on oeis4.)