Beast Number

Author

Eric W. Weisstein
March 23, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Numbers/BeastNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BeastNumber.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Identities

Total[((((Prime[Range[7]])))^2)]==666

Total[Prime[Range[7]]^2]

(EulerPhi[666])==6 6 6

EulerPhi[666]==6 6 6

(1^6)-(2^6)+(3^6)==666

1^6-2^6+3^6

1+2+3+4+567+89==666

1+2+3+4+567+89

123+456+78+9==666

123+456+78+9

9 + 87 + 6 + 543 + 21==666

9+87+6+543+21

(Subscript[T, 6 6])==666

TriangularNumber[6 6]

Total[First[RealDigits[π-3,10,144]]]==666

Total[First[RealDigits[Pi-3,10,144]]]

144==(6+6) (6+6)

144==(6+6)(6+6)

Total[ToCharacterCode[ToUpperCase["Indonesia"]]]==666

Total[ToCharacterCode[ToUpperCase["Indonesia"]]]

Honaker

{#,DigitCount[#,10,6]}&[666^6]

DigitCount[%,10,6]

ϕ Identities

Wang

-2 sin(666 °)==ϕ

-2Sin[666Degree]

-2 cos(6 6 6 °)==ϕ

-2Cos[6 6 6Degree]

-(sin(666 °)+cos(6 6 6 °))==ϕ

-(Sin[666 Degree]+Cos[6 6 6 Degree])

Barbosa

-(sin(666 °)+cos((666^666) °))==ϕ

-(Sin[666 Degree]+Cos[666^666 Degree])//FullSimplify

{Cos[6 6 6 Degree],Cos[(6^6)6Degree],Cos[(6^(6^6))Degree],Cos[666^666 Degree]}

Equal@@%

Sums

(∑_i^(6 6))i==666

Sum[i,{i,6 6}]

(Mod[((∑_(n=0)^5)(2048^n)), 691])==666

Mod[Sum[2048^n,{n,0,5}],691]

(∑_n^666)2 (((-1))^n) n==666

Erik Åström, Mar 30, 2006

Sum[2(((-1))^n)n,{n,666}]