login
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.
8
6661, 16661, 66601, 76667, 700666007, 6660000000001, 666000000000001, 700000666000007, 70000006660000007, 6660000000000000000000000007, 66600000000000000000000000007, 1000000000000066600000000000001
OFFSET
1,1
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
Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)
Eric Weisstein's World of Mathematics, Beast Number
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 *)
KEYWORD
nonn,base,dumb
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Feb 12 2011
a(10)-a(12) from Charles R Greathouse IV, Feb 12 2011
STATUS
approved