Friday, October 23, 2009

2501

2501 = 41 x 61.

2501 is the product of the only two primes (41 and 61) that can be the last two digits of a perfect fourth power. If you replace the 5 by a 4, you get a fourth power: 2401 = 74.

2501 is a pentagonal number, having the form n(3n – 1)/2. In this case, n = 41.

2501 has two representations as a sum of two squares: 2501 = 12 + 502 = 102 + 492.

2501 is the hypotenuse of two primitive Pythagorean triples: 25012 = 1002 + 24992 = 9802 + 23012.


Project
2501, from the film and manga Ghost in the Shell, is an artificial intelligence program that develops sapience.

Source:
Prime Curios!

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