Monday, March 18, 2013

997

997 is a prime number. It is the largest three-digit prime.

997 is the smallest prime of the form 10p - p, where p is prime (3).

997 is the smallest prime whose sum of digits (25) is an odd composite number.

997 is the smallest prime p such that the sum of the digits of p (9 + 9 + 7 = 25) is not prime, but the sum of the squares of the digits is prime (92 + 92 + 72 = 211).

997 is the smallest prime p such that the sum of the digits of p (9 + 9 + 7 = 25) is not prime, but the sum of the cubes of the digits is prime (93 + 93 + 73 = 1801).

997 has a representation as a sum of two squares: 997 = 62 + 312.

997 is the hypotenuse of a primitive Pythagorean triple: 9972 = 3722 + 9252.


Sourcea: Number Gossip and Prime Curios!

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