625 = 54. It is a perfect fourth power.
Two fourth powers use the same digits: 54 = 625 and 44 = 256.
625 has two representations as a sum of two squares: 625 = 72 + 242 = 152 + 202.
625 is the hypotenuse of a primitive Pythagorean triple: 6252 = 3362 + 5272.
625 is a centered octagonal number.
625 is an automorphic number.
According to a 2010 White House news release, 625 people lost their health insurance every hour in 2009.
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