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Numbers k such that 101*k + 997 is prime.
3

%I #31 Aug 17 2024 16:07:33

%S 0,14,26,30,32,44,50,54,56,60,72,92,102,110,114,116,126,140,144,152,

%T 162,176,182,192,204,206,212,234,240,242,252,296,320,324,326,330,360,

%U 366,372,386,390,396,404,410,416,444,450,452,462,474,480,494,506,512,516

%N Numbers k such that 101*k + 997 is prime.

%C 101 and 997 are the smallest and largest three-digit primes.

%H Daniel Starodubtsev, <a href="/A105583/b105583.txt">Table of n, a(n) for n = 1..10000</a>

%e If k=0, then 101*k + 997 = 997 (prime).

%e If k=110, then 101*k + 997 = 12107 (prime).

%t Select[Range[520],PrimeQ[101#+997]&] (* _Stefano Spezia_, Aug 02 2024 *)

%o (Magma) [n: n in [0..100000] | IsPrime(101*n + 997)]; // _Vincenzo Librandi_, Nov 13 2010

%o (PARI) is(n)=isprime(101*n+997) \\ _Charles R Greathouse IV_, Jun 06 2017

%Y Cf. A105679.

%K nonn,easy

%O 1,2

%A _Parthasarathy Nambi_, May 06 2005