Friday, February 20, 2009

641

641 is a prime number. It is a Sophie Germain prime because 2 x 641 + 1 = 1283, which is also prime.

Leonhard Euler found the first counterexample to Fermat's conjecture that 22^n + 1 is always prime, when he discovered in 1742 that 22^5 + 1 is divisible by 641. All factors of 22^n + 1 are of the form k x 2n + 1 + 1. In this case 641 = 10 x 26 + 1.

641 has a representation as a sum of two squares: 641 = 42 + 252.

641 and 643 form a twin prime pair.

641 is the hypotenuse of a primitive Pythagorean triple: 6412 = 2002 + 6092.


The telephone area code 641 covers the central portion of Iowa.

Source: D. Wells. 1997. The Penguin Dictionary of Curious and Interesting Numbers, rev. ed.
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