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

0, 28, 36, 70, 76, 78, 106, 124, 136, 168, 184, 198, 208, 216, 226, 234, 238, 246, 258, 294, 300, 304, 318, 348, 364, 366, 370, 394, 418, 436, 454, 468, 474, 496, 556, 570, 588, 598, 604, 616, 660, 688, 696, 714, 736, 738, 744, 748

Offset

1,2

Comments

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

The theorem of Dirichlet shows that this sequence is infinite. - Stefan Steinerberger, Feb 12 2006

Links

Table of n, a(n) for n=1..48.

Example

If k=0, then 9973*k + 1009 = 1009 (prime).
If k=168, then 9973*k + 1009 = 1676473 (prime).

Mathematica

For[n = 1, n < 1000, n++, If[PrimeQ[(9973*n + 1009)], Print[n]]] (* Stefan Steinerberger, Feb 12 2006 *)
Select[Range[0, 1000], PrimeQ[9973 # + 1009] &] (* Vincenzo Librandi, Sep 14 2015 *)

Prog

(Magma) [n: n in [0..800] | IsPrime(9973*n + 1009)]; // Vincenzo Librandi, Sep 14 2015
(PARI) is(n)=isprime(9973*n+1009) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A105679.

Sequence in context: A061900 A048023 A359529 * A192226 A323005 A080983

Adjacent sequences: A105707 A105708 A105709 * A105711 A105712 A105713

Keyword

nonn,easy

Author

Parthasarathy Nambi, May 06 2005

Extensions

More terms from Stefan Steinerberger, Feb 12 2006

Status

approved