8807

This number is a prime.

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Prime 8807 has an unusual property: it's equal to the average of its nearest square and nearest triangular number. The nearest square to 8807 is 8836 = 94^2, the nearest triangular number is 8778, and (8836 + 8778)/2 = 8807. There are only two other 4-digit primes with this property, 1667 and 9431. [Keith]