666
This number is a composite.
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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 666p is
equal to 666. If we define S(n) as the sum of the digits of
n, we can write that
S(666π(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 = a2 +
b2 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]