# 641

This number is a prime.

A prime whose digits are consecutive nonprime digits reversed.

Pulsars (rapidly spinning neutron stars) have been observed to spin up to 641 times per second.

In 1732, Euler found that 2^2^5 + 1, the first composite Fermat number, is divisible by 641.

641 divides all the Generalized Fermat numbers of the form (2^*a**5^*b*)^2^5 + 1,
where *a* is odd and *b* is even, or *a* is even and *b* is odd. [Gallot]

641 = 4^{2} + 25^{2} = 2^{4} + 5^{4} = (1^{2} + 1^{2})^{4} + (1^{2} + 2^{2})^{4}. [Melo]

2^{641} - 1 was the smallest Mersenne number that had not been completely factored prior to the 21st century. [Cerias]

Replacing each digit *d* of 641 with *d* copies of the digit *d* produces another prime, i.e., 641 becomes 66666644441, which is also prime. If we apply the same transform using 66666644441, yet another prime is formed. [Honaker]

The Ford 641 Workmaster is an antique farm tractor. They have been known to crop up at the annual Lee County Tobacco & Fall Festival in Pennington Gap, Virginia (the birthplace of one of the authors).

641 is the smallest prime factor of 4^16 + 1 , written with all the digits of 641 . [Capelle]

The largest sexy prime quadruplet less than a thousand starts at 641. I.e., 641+6, 641+6+6, and 641+6+6+6, are also prime. [Opao]

The leading 641 digits in the decimal expansion of the square root of three is prime. [Carmody]

641 can be written as 10 * 2^{6} + 1.

The Great Library of Alexandria, home to such mathematicians as Euclid, Archimedes, Eratosthenes, Apollonius, and Pappus, had disappeared before the arrival of the Muslim Arab armies in A.D. 641.

Room 641A is an alleged intercept facility operated by AT&T for the U.S. National Security Agency. [McCranie]

First of seven consecutive primes that remain that way if you eliminate their first digit. [Silva]

The largest 3-digit number n such that (10^n+1)/11 is prime. [Loungrides]

The only non-titanic prime of form 2^x+5^x, for x a composite number (x=4). [Loungrides]

The least number in the smallest set of four consecutive odd numbers that are primes or pseudoprime (base-2). [Gupta]

The sum of all the palindromes from 1 up to 101 is prime, i.e., 1+2+3+...+9+11+22+33+...+99+101 = 641. [Loungrides]