678 = 2 x 3 x 113. It is the product of three distinct Sophie Germain primes (A157346).
678 is a member of the Fibonacci-like sequence starting with 1 and 7 (A022097).
The sum of the squares of the first 678 primes is a prime (A098561).
678 is the sum of eight positive fifth powers (A003353): 678 = 35 + 35 + 25 + 25 + 25 + 25 + 25 + 25.
678 and the 678th prime (5077) have only the digit 7 in common (A107938).
Source: What's Special About This Number?
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