A186086 Beastly primes (version 1): either 666 followed by 0's and a 1 or 7 at the right end or a palindrome with 666 in the center, 0's surrounding these digits, and 1 or 7 at both ends.

6661, 16661, 66601, 76667, 700666007, 6660000000001, 666000000000001, 700000666000007, 70000006660000007, 6660000000000000000000000007, 66600000000000000000000000007, 1000000000000066600000000000001

Offset: 1

Author

Arkadiusz Wesolowski, Feb 12 2011

Keywords

• nonn
• base
• dumb

Comments

Differs from A131645 in that 26669, 46663, 56663, 66617, 66629, 66643, 66653, 66683, 66697, 96661, 96667, 106661, 106663, 106669, 116663, 146669, 166601, 166603, 166609, 166613, 166619, 166627, 166631, 166643, 166657, 166667, 166669, 166679, are not included here.

76667 is the largest beastly prime that does not contain the digit "0".

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..33
• Chris Caldwell, The Prime Glossary, Beastly prime
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6661
• R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations (May 2001), p. 5
• Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)
• Eric Weisstein's World of Mathematics, Beast Number

Crossrefs

Cf. A046720, A051003, A131645, A164968, A196023, A138563, A186630, A186538, A156166, A186521.

Programs

Mathematica

e = 14; p = 666*10^n + 1; q = (10^(n + 2) + 666)*10^n + 1; Select[Union[Table[p, {n, 2*e}], Table[p + 6, {n, 2*e}], Table[q, {n, e}], Table[q + 6*10^(2*n + 2) + 6, {n, e}]], PrimeQ] (* Arkadiusz Wesolowski, Sep 21 2011 *)
Module[{nn=35,bp1,bp2,bp3,bp4}, bp1=FromDigits/@ Table[Join[PadRight[ {6,6,6},n1,0],{1}],{n1,3,nn}]; bp2=FromDigits/@ Table[Join[ PadRight[ {6,6,6},n2,0],{7}], {n2,3,nn}]; bp3=FromDigits/@ Table[Join[PadRight[ {1},n3,0], {6,6,6},PadLeft[ {1},n3,0]],{n3,1,nn/2}];bp4=FromDigits/@ Table[Join[PadRight[{7},n3,0],{6,6,6}, PadLeft[ {7},n3,0]],{n3,1,nn/2}]; Select[Sort[Join[bp1,bp2,bp3,bp4]],PrimeQ]] (* Harvey P. Dale, Jan 18 2017 *)

Extensions

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

a(10)-a(12) from Charles R Greathouse IV, Feb 12 2011