243

243 = 3⁵, a perfect fifth power.

243 is the first number of the form p^q where p and q are a twin prime pair (3, 5).

243 is the sum of the first three palindromic primes: 243 = 11 + 101 + 131.

243 is 3303 in base 4, 1433 in base 5, 1043 in base 6, 363 in base 8, 300 in base 9, 183 in base 12, and 113 in base 15.

243 Ida is a large, irregularly shaped asteroid. It was the second asteroid to be visited by a spacecraft and the first to be found to possess a satellite.

Source: Number Gossip

821

821 is a prime number.

821 has a representation as a sum of two squares: 821 = 14² + 25².

821 and 823 form a twin prime pair.

821 is the hypotenuse of a primitive Pythagorean triple: 821² = 429² + 700².

821 is the maximum number of regions into which 40 lines divide the plane.

821 is the smallest prime whose reversal is a seventh power: 128 = 2⁷.

821 = 6! + 5! - 4! + 3! - 2! + 1!

Aeroflot Flight 821 crashed on approach to Perm airport on Sept. 14, 2008.

Source: Prime Curios!

16 777 216

16777216 = 2²⁴, a perfect 24th power.

16777216 = 8⁸. 1¹, 8⁸, and 9⁹ are the only powers that have the same number of decimal digits as the power.

16777216 (8⁸) is the number of labeled mappings from n points to themselves, for n = 8.

16777216 is the smallest number beginning with 1 and having exactly n prime divisors (counted with multiplicity), for n = 24.

Computer bug report: Fatal error: Allowed memory size of 16777216 bytes exhausted.

In the RGB color model, the Truecolor scheme defines 256 shades of red, blue, and green, which results in 16,777,216 color variations for each pixel (256 x 256 x 256).

Source: Wikipedia

12

12 = 2² x 3.

12 is the sum of the first three even integers and the sum of thee consecutive odd integers: 12 = 2 + 4 + 6 = 3 + 4 + 5.

A regular dodecahedron has a regular pentagon on each of its 12 faces.

12 has a unique representation as a sum of three squares: 12 = 2² + 2² + 2².

12 is the number of integer partitions of 11 into distinct parts.

12 is 22 in base 5.

There are 12 ways to arrange eight queens on a chessboard so that no queen can capture any other queen (not counting rotations and reflections as being different). Can you find one of these chessboard arrangements?

12 is a dozen. There are 12 months in a year and 12 inches in a foot; 12 o'clock is midday or midnight. There are 12 signs of the Zodiac, 12 apostles, and typically 12 people in a jury.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

844

844 = 2² x 211.

844 is the smallest number so that it and the next four numbers are squareful numbers; that is, they each contain a square in their prime factorization.

844 is the sum of six positive cubes in exactly three ways.

Both 844 and 845 have six divisors.

844 is 444 in base 14.

Steam Locomotive No. 844 was the last steam locomotive built for the Union Pacific Railroad, delivered in 1944.

Source: What's Special About This Number?

439

439 is a prime number.

439 is the sum of three consecutive primes (439 = 139 + 149 + 151) and the sum of nine consecutive primes (439 = 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).

439 is a number that can be expressed as the signed sum of cubes in at least three ways: 439 = 264488³ + 331574³ - 380193³ = 2322404³ - 869418³ - 2281057³ = 402906³ - 211402³ - 382489³.

439 is the smallest prime such that another prime is never produced by inserting the same digit between each pair of its digits: 40309, 41319, 42329, . . . 49399 are all composite.

439 is a number that cannot be written as a sum of three squares.

439 Ohio is a main-belt asteroid discovered in 1898.

Source: Prime Curios!

683

683 is a prime number. It is a Sophie Germain prime because 2 x 683 + 1 is also a prime number.

683 is also a Wagstaff prime because it has the form (2^q + 1)/3, where q is another prime, 11.

683 is a divisor of 4¹¹ - 1.

683 is 838 in base 9.

The submarine USS Parche (SSN-683) was named for a small, coral-reef butterflyfish.

Source: What's Special About This Number?