671 is a rhombic dodecahedral number.
671 is the 3-digit composite number (k) that yields the greatest percentage of primes from Leonhard Euler's formula x2 + x + k (453 out of 1000 possible primes).
671!/176! + 1 is prime.
671 is the magic constant for an 11 x 11 normal magic square.
671 is the solution for the n-queens problem, for n = 11.
Source: Prime Curios!