A171376 Numbers k such that 1 + 3*10^k + 100^k is prime.

0, 1, 2, 3, 4, 11, 14, 16, 92, 133, 153, 378, 448, 785, 1488, 1915, 2297, 3286, 4755, 5825, 7820, 34442, 34941

Offset: 1

Author

Jason Earls, Dec 07 2009

Keywords

• more
• nonn

Comments

All primes were certified with WinPFGW.

a(24) > 35000. - Serge Batalov, Dec 20 2015

Examples

			4 is in the sequence because 10^8 + 3 * 10^4 + 1 = 100030001 is prime.
		

Links

• Chris K. Caldwell, Prime Pages, Database Search Output

Crossrefs

Cf. A082622.

Cf. A171411, A171459, A171514, A171554.

Programs

Magma

[n: n in [0..4*10^2] | IsPrime(1+3*10^n+100^n)]; // Vincenzo Librandi, Dec 22 2015

Mathematica

Select[Range@ 1000, PrimeQ[1 + 3 10^# + 100^#] &] (* Michael De Vlieger, Dec 18 2015 *)

PARI

\\sieve for the candidates:
{
lim=10^9; ns=6*10^5; pp=10^7; s=vectorsmall(ns);
forprime(p=11,lim,if(kronecker(5,p)==1,o=znorder(t=Mod(10,p));
  q=sqrt(Mod(5,p));r=znlog((q-3)/2,t,o);
  if(r,forstep(n=r,ns,o,s[n]=1);forstep(n=o-r,ns,o,s[n]=1)));
  if(p>pp,pp+=10000000;print1(p" ")));
for(n=1,ns,if(!s[n],write("sieve_out_10301NGm1.txt", n)));
}
\\quick initial check for small sequence members
for(n=0,2297,if(ispseudoprime((10^n+3)*10^n+1),print1(n", ")))
\\ Serge Batalov, Dec 17 2015

Formula

a(n) = (A100028(n-1) - 1)/2 for n>1. - Jeppe Stig Nielsen, Oct 06 2024

Extensions

a(21)-a(23) from Serge Batalov, Dec 20 2015