Six hundred sixty-six
Six hundred sixty-six, or 666, is the Number of the Beast in the Christian Bible, in the the Book of Revelation.
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} (ω(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.
See also: six hundred
For the year, see 666 AD.
Referenced By
List of numbers | Mark of the Beast | Number 600 | Number 666 | Number of the Beast (Bible) | Number of the Beast (Biblical) | Number of the Beast (eschatology) | Number of the Beast (mathematics) | Number of the Beast (numerology) | Number of the Beast (theology) | Six hundred
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