666 (number)

666 (Six hundred sixty-six in American English, Six hundred and sixty-six elsewhere) is the Number of the Beast in the Christian Bible, in the Book of Revelation. There is also a house music group named "666". For the year, see AD 666.

666
Cardinal Six hundred and sixty-six
Ordinal 666th
Factorization
Roman numeral DCLXVI
Binary 1010011010
Hexadecimal 29A

666
Cardinal	Six hundred and sixty-six
Ordinal	666th
Factorization
Roman numeral	DCLXVI
Binary	1010011010
Hexadecimal	29A

Mathematics

Naturally enough, 666 also has many mathematical properties, some more interesting than others:

666 in binary translates to 1010011010

666 is the 667th non-negative integer.
666 = 2 × 3² × 37 is the 333rd even number and the 544th composite number. (The 666th composite number is 806 = 2 × 13 × 31). 666 is the 260th non square-free number: {4, 8, 9, 12, 16, 18, 20, 24, ..., 648, 650, 652, 656, 657, 660, 664, 666, ...}. The 666th non square-free number is 1701.
666 is not a prime (it is quite evidently divisible by 2, 3 and 111). The 666th prime is 4973. 666 is not a lucky number. The 666th lucky number is 5559.
666 has 12 divisors: {1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666}. The sum of its divisors is 1482. The first numbers in the interval [1, 10⁶] that have the same sum of divisors are 666, 1017, 1481. The sum of its proper divisors is 816>666, so 666 is the 162th abundant number. 666 has 3 distinct prime divisors {2, 3, 37} (&omega(666) = ω(2 × 3² × 37) = ω(2) + ω(3²) + ω(37) = 1+1+1=3) and a total of 4 prime divisors (Ω(666)=...=4).
By Euler's totient function φ(666) = 216. 666 is the 14th number with this value of φ: {247, 259, 327, 333, 351, 399, 405, 436, 494, 518, 532, 648, 654, 666, ...}
The harmonic mean of the digits of 666 is an integer: 3/(1/6 + 1/6 + 1/6) = 6. 666 is the 54th number with this property.
666 is the 25th repdigit.
666 is the 76th palindromic number in base 10 and it is also the sum of two consecutive palindromic primes: 666=313+353. It is the 62th palindromic composite number.
The sum of all the integers from 1 to 36 inclusive is 666. This means 666 is the 36th triangular number. (The 666th triangular number, on the other hand, (1+2+3+...+664+665+666) is 222111.)

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A prime reciprocal magic square based on 1/149 in base 10 has a magic total of 666.
6^(6^6) or 6⁴⁶⁶⁵⁶ is 36,306 digits long. Its first 150 digits are:

26591197721532267796824894043879185949053422002699

24300660432789497073559873882909121342292906175583

03244068282650672342560163577559027938964261261109...

The sum of the digits 1 through 146 of this number is 666, as is the sum of its digits 2 through 148 and its digits 2 through 149.