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 A171376 Numbers n such that 1 + 3*10^n + 100^n is prime. 2
 0, 1, 2, 3, 4, 11, 14, 16, 92, 133, 153, 378, 448, 785, 1488, 1915, 2297, 3286, 4755, 5825, 7820, 34442, 34941 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)