A030432 Primes of form 10n+7.

7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217, 1237

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn
• easy
• base

Comments

Union of A132231 and A039949. - Ray Chandler, Apr 07 2009

5 is not quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014

Also primes of the form 5n+2 with positive n. - Danny Rorabaugh, Feb 20 2016

Intersection of A000040 and A017353. - Iain Fox, Dec 30 2017

Links

• Michael B. Porter, Table of n, a(n) for n = 1..100000
• A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.

Crossrefs

Cf. A030430 (10n+1), A030431 (10n+3), A030433 (10n+9).

Cf. A045357, A045380, A049509, A102342.

Programs

Magma

[n: n in [7..1240 by 10] | IsPrime(n)]; // Bruno Berselli, Apr 06 2011

Mathematica

Select[Prime@Range[210], Mod[ #, 10] == 7 &] (* Ray Chandler, Nov 07 2006 *)

PARI

is(n)=n%10==7 && isprime(n) \\ Charles R Greathouse IV, Jul 01 2013

PARI

lista(nn) = forprime(p=7, nn, if(p%10==7, print1(p, ", "))) \\ Iain Fox, Dec 30 2017

Sage

[10*n+7 for n in range(124) if is_prime(10*n+7)] # Danny Rorabaugh, Feb 20 2016

Formula

a(n) = 10*A102342(n) + 7.

a(n) ~ 4n log n. - Charles R Greathouse IV, Jul 01 2013

Extensions

Extended by Ray Chandler, Nov 07 2006