A131645 Beastly primes (version 2): primes containing 666 as a substring.

6661, 16661, 26669, 46663, 56663, 66601, 66617, 66629, 66643, 66653, 66683, 66697, 76667, 96661, 96667, 106661, 106663, 106669, 116663, 146669, 166601, 166603, 166609, 166613, 166619, 166627, 166631, 166643, 166657, 166667, 166669, 166679

Offset: 1

Author

Tanya Khovanova, Sep 08 2007

Keywords

• base
• nonn

Comments

These are the primes among the beastly numbers A051003.

There are several other definitions of beastly primes (see cross-references).

Asymptotic density n/log(n), since almost all primes are of this form.

Links

• Charles R Greathouse IV and Harry J. Smith, Table of n, a(n) for n = 1..20000
• Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)

Crossrefs

Cf. A051003, A186086, A046720, A138563, A232448, A321001.

Programs

Mathematica

Select[Range[300000], StringFreeQ[ToString[ # ], "666"] == False && PrimeQ[ # ] &]
Select[Prime[Range[300000]],!StringFreeQ[ToString[ # ],"666"]&] (* Zak Seidov, Jan 09 2009 *)

PARI

digitsIn(x) = 1 + log(x)\log(10)
allocatemem(932245000);
default(primelimit, 4294965247); m=1; forprime (p=6660, 68466670, d=digitsIn(p); for (i=1, d-3, t=10^i; u=p\t; x=u-(u\1000)*1000; if (x==666, print(m, " ", p); write("b131645.txt", m, " ", p); m++; break))) \\ Harry J. Smith, Jan 11 2009

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Oct 13 2015

Extensions

Definition corrected by Arkadiusz Wesolowski, Feb 12 2011

Edited by N. J. A. Sloane, Feb 12 2011