Wednesday, December 11, 2013

689

689 = 13 x 53.

689 is the smallest strobogrammatic brilliant number. Deleting the middle digit gives the smallest strobogrammatic semiprime (69).

689 is the sum of three consecutive primes and seven consecutive primes: 689 = 227 + 229 + 233 = 83 + 89 + 97 + 101 + 103 + 107 + 109.

689 has two representations as a sum of two squares: 689 = 82 + 252 = 172 + 202.

689 is the hypotenuse of two primitive Pythagorean triples: 6892 = 1112 + 6802 = 4002 + 5612.

689 is the smallest number that can be written as the sum of three distinct squares in nine ways.

689 is 373 in base 14.


Source: Prime Curios!

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