Number analysis
666
The Number of the Beast in Revelation 13:18, and a triangular number.
The Number of the Beast in Revelation 13:18, and a triangular number.
The number itself
- Value
- 666
- Digits
- 3
- Digit sum
- 18
- Reversed
- 666
- Palindrome
- Yes
6 + 6 + 6
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reads the same in both directions.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2 × 3^2 × 37
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 661 ← → 673
Divisible by 2.
Composite — it factors as 2 × 3^2 × 37.
3 distinct prime factors, 4 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 12 between them.
Divisors
- Sum of divisors σ(n)
- 1,482
- Aliquot sum
- 816
- Classification
- Abundant
1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The proper divisors — everything except n itself.
Its proper divisors overshoot by 150.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- Yes
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Goldbach pair
- 5 + 661
15² + 21² = 666
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.
Shapes and sequences
- Triangular number
- Yes — the 36th
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 113 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 18 — 666 ÷ 18 = 37.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 1010011010
- Octal
- 1232
- Hexadecimal
- 29A
- Base 36
- II
- Roman numerals
- DCLXVI
- In words
- six hundred and sixty-six
- Scientific notation
- 6.66 × 10^2
Is 666 a prime number?
Composite — it factors as 2 × 3^2 × 37.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 666 their own way.
- Morse code
- − · · · · − · · · · − · · · ·
- Devanagari
- ६६६
- Tamil
- ௬௱௬௰௬
- Thai
- ๖๖๖
References
Further reading: Wikipedia · MathWorld · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.