A232450 Largest prime factor of the Belphegor number B(n) = (10^(n+3) + 666)*10^(n+1) + 1.

16661, 1103, 1417831, 1143749, 14282381, 11699423, 1950071, 7503425119, 3837692792387, 145857793, 76607717987, 1755833757671518620617, 17416012536871141, 1000000000000066600000000000001, 16540928199996367, 744657085412168192717253704669

Offset: 0

Author

Stanislav Sykora, Nov 24 2013

Keywords

• nonn

Comments

The Belphegor numbers (A232449), though not often prime themselves (see A232448), tend to contain very large prime factors and are therefore hard to factorize.

Links

• Stanislav Sykora and Amiram Eldar, Table of n, a(n) for n = 0..64 (terms 0..44 from Stanislav Sykora)
• Clifford A. Pickover, Belphegor's Prime: 1000000000000066600000000000001
• Wikipedia, Belphegor's prime

Crossrefs

Cf. A232448 (indices of Belphegor primes), A232449 (Belphegor numbers).

Programs

Mathematica

Table[FactorInteger[(10^(n + 3) + 666)*10^(n + 1) + 1][[-1, 1]], {n, 20}] (* T. D. Noe, Nov 25 2013 *)

PARI

default(factor_proven,1);
Belphegor(k)=(10^(k+3)+666)*10^(k+1)+1;
LargestPrimeFactor(k)={local(f);f=factor(k);return(f[#f[,1],1])};
nmax=40; v=vector(nmax);
for (n=0,#v-1,v[n+1]=LargestPrimeFactor(Belphegor(n));print(v[n+1]))