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

1,1

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)

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A060792 A119519 A233661 * A186086 A236733 A015310

Adjacent sequences: A131642 A131643 A131644 * A131646 A131647 A131648

Keyword

base,nonn

Author

Tanya Khovanova, Sep 08 2007

Extensions

Definition corrected by Arkadiusz Wesolowski, Feb 12 2011

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

Status

approved