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 2^{2^n} + 1 is always prime, when he discovered in 1742 that 2^{2^5} + 1 is divisible by 641. All factors of 2^{2^n} + 1 are of the form k x 2^{n + 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.