login
Primes p such that 100*p+1, 100*p+3, 100*p+7, and 100*p+9 are all prime.
3

%I #6 Mar 05 2023 13:04:23

%S 1657,2437,6073,10687,11677,13297,13399,33289,35869,40927,46093,57601,

%T 61933,77743,97927,125119,127447,130411,140827,141397,189229,217207,

%U 246439,271573,289987,292867,292969,297469,329803

%N Primes p such that 100*p+1, 100*p+3, 100*p+7, and 100*p+9 are all prime.

%e 125119, 12511901, 12511903, 12511907, and 12511909 are all prime, thus 125119 is a member of this sequence.

%t Select[Prime[Range[30000]],AllTrue[100#+{1,3,7,9},PrimeQ]&] (* _Harvey P. Dale_, Mar 05 2023 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(p) for p in range(10**6) if isprime(p) and isprime(100*p+1) and isprime(100*p+3) and isprime(100*p+7) and isprime(100*p+9)}

%Y Cf. A000040, A064687.

%K nonn

%O 1,1

%A _Derek Orr_, Jan 18 2014