# 666

This number is a composite.

Just showing those entries submitted by 'Capelle': (Click here to show all)

666 can be expressed in different ways as a sum of different primes using all ten digits, i.e., 666 = 2 + 5 + 83 + 109 + 467 = 2 + 5 + 83 + 167 + 409 = 2 + 5 + 89 + 103 + 467 = 2 + 5 + 89 + 107 + 463. Note that it is the smallest even number and the smallest palindrome with this property. [Capelle]

π(6*6*6) = 47 is the only prime number p such that the
sum of the digits of 666^{p} is
equal to 666. If we define S(n) as the sum of the digits of
n, we can write that
S(666^{π(6*6*6)}) = 666. [Capelle]

666 = (3*5)^{2} +
(3*7)^{2}, written with all the
single-digit primes. Note that 666, which is formed from
the triangular number 6 repeated 3 (the only prime
triangular number) times, is the smallest triangular number
n = a^{2} +
b^{2} such that a, b and a+b are
triangular numbers. [Capelle]

If we define S(n) as the sum of the digits of n, then we
can write that
S((prime(6+6+6))^{6}) =
S(prime(6+6+6)) + S(prime(666)) + S(prime(6*6*6)), where
all the terms are prime. Note that 666 = (6+6+6) *
S((prime(6+6+6))^{6}). [Capelle]