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.

1001

1001 = 7 x 11 x 13.

To test a number for divisibility by any of the three divisors 7, 11, and 13 simultaneously, start by marking off the number to be tested in groups of three digits from the units position. Add the first, third, fifth, . . . groups and take away the total of the second, fourth, . . . groups. The number will be divisible by 7, 11, or 13 if the result is divisble by 7, 11, or 13 respectively.

1001 is the 11th pentatope number.

1001 is the fourth palindromic pentagonal number. The sequence of these numbers runs: 1, 5, 22, 1001, 2882, 15,251, . . .


In many cases, including the title One Thousand and One Arabian Nights, 1001 is meant to indicate a "big number" and need not be taken literally.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.

75

75 = 3 x 5²

75 is the smallest pandigital number in base 4: 75 is written as 1023 in base 4 and contains all the possible digits.

75 is 55 in base 14.

2⁷⁵ + 75 is a prime number.

Take the "digit sum" 7 + 5 = 12, then continue adding in pairs (as shown below). You reach 75.

7 + 5 = 12

5 + 12 = 17

12 + 17 = 29

17 + 29 = 46

29 + 46 = 75


Messier object M75 is a globular cluster in the constellation Sagittarius.

Source: Number Gossip

123

123 = 3 x 41.

123 is the 10th Lucas number.

123 x 2¹²³ - 1 is a prime number.

1234² - 123² - 456 is a prime number.

123 is a number of the form n² + 2, where n = 11.


The STS-123 space shuttle mission delivered the Japanese Kibo Logistics Module and the Canadian Dextre robotics system to the International Space Station in 2007.

Source: Prime Curios!

2101

2101 = 11 x 191.

2101 is a hendecagonal (11-gonal) number.

2101 is a centered heptagonal number.

2101 is a centered 10-gonal number.

2101 is a number n such that n, n + 1, and n + 2 are each the product of two primes: 2101 = 11 x 191, 2102 = 2 x 1051, 2103 = 3 x 701.

2101 is a number that yields a prime whenever a 1 is inserted anywhere in them, including the beginning or the end: 12101, 21101, and 21011 are all primes.


2101 Adonis was one of the first near-Earth asteroids to be discovered.

Source: On-Line Encyclopedia of Integer Sequences

920

920 = 2³ x 5 x 23.

920 is a truncated cube number.

920 is a number n such that n² is the sum of two successive primes: 920² = 846,400 = 423,191 + 423,209.

920 is the maximum number of regions into which 18 triangles divide the plane.

Telephone area code 920 covers Milwaukee, Wisconsin.

Source: What's Special About This Number

192

192 = 2⁶ x 3.

192 + 384 = 576, a pandigital sum where 384 = 2 x 192 and 576 = 3 x 192. There are three other such sums, starting with 219, 273, and 327.

192 is the smallest number that together with its double and triple contain every digit from 1 to 9 exactly once: 192, 384, and 576.

192 has a unique representation as a sum of three squares: 192 = 8² + 8² + 8².

192 is the number of integer partitions of 27 into distinct parts.


192 Nausikaa is a large main belt asteroid.

Source: Number Gossip