A171376 Numbers n such that 1 + 3*10^n + 100^n 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

1,3

Comments

All primes were certified with WinPFGW.

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

Links

Table of n, a(n) for n=1..23.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A082622.

Sequence in context: A184806 A176541 A295721 * A317913 A141704 A061919

Adjacent sequences: A171373 A171374 A171375 * A171377 A171378 A171379

Keyword

more,nonn

Author

Jason Earls, Dec 07 2009

Extensions

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

Status

approved