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

Author

Parthasarathy Nambi, May 06 2005

Keywords

• nonn
• easy

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

Examples

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

Crossrefs

Cf. A105679.

Programs

Magma

[n: n in [0..800] | IsPrime(9973*n + 1009)]; // Vincenzo Librandi, Sep 14 2015

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 *)

PARI

is(n)=isprime(9973*n+1009) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Stefan Steinerberger, Feb 12 2006