623

623 = 7 x 89.

623 is a number that cannot be written as a sum of three squares.

623 - 6*2*3 and 623 + 6*2*3 are prime numbers: 587 and 659.

623 is the sum of three distinct positive cubes: 623 = 4³ + 6³ + 7³.

A Uranus-Neptune conjunction in Virgo occurred in the year 623.

Source: Prime Curios!