773

773 is a prime number.

773 has a representation as a sum of two squares: 773 = 17² + 22².

773 is the hypotenuse of a primitive Pythagorean triple: 773² = 195² + 748².

773 is the largest three-digit unholey prime; its digits have no holes.

773 is the smallest prime such that adding a preceding or trailing digit will always result in a composite if we omit the case where the leading digit is zero.

773 is a telephone area code for Chicago.

Source: Prime Curios!

1145

1145 = 5 x 229.

1145 has two representations as a sum of two squares: 1145 = 11² + 32² = 19² + 28².

1145 is the hypotenuse of two Pythagorean triples: 1145² = 423² + 1064² = 704² + 903².

1145, 1147 (31 x 37), and 1149 (3 x 383) are each semiprimes, the product of two primes.

Halley's Comet appeared in the skies in the year 1145.

Source: WolframAlpha

137

137 is a prime number.

137 has a representation as a sum of two squares: 137 = 4² + 11².

137 and 139 form a twin prime pair.

137 is the hypotenuse of a primitive Pythagorean triple: 137² = 88² + 105².

137 is a divisor of 37⁴ - 1.

137 = 128 + 8 + 1 = 2⁷ + 2³ + 2⁰.

A molecule of chlorophyll a (C₅₅H₇₂O₅N₄Mg) consists of 137 atoms.

Source: Prime Curios!

272

272 = 2⁴ x 17.

272 has a representation as a sum of two squares: 272 = 4² + 16².

272 is the number of hyperspheres in 9 dimensions that can touch an equivalent hypersphere without any intersections (Kissing Number).

272 is a pronic number, the product of two consecutive numbers: 272 = 16 x 17.

All the digits of 272 are prime, and the sum of the digits of this palindromic composite is 11, a palindromic prime. The product of the digits is 28, a perfect number.

272 is the sum of four consecutive primes: 272 = 61 + 67 + 71 + 73.

A Calorie Counter offers a list of the 272 fast food items highest in calories.

Source: Number Gossip

441

441 = 3² x 7².

441 = 21², a square.

441 is the smallest square that is the sum of six consecutive cubes: 441 = 1³ + 2³ + 3³ + 4³ + 5³ + 6³.

441 = 21² and 144 = 12². Also, 441 x 144 = 252².

441 is the telephone area code for the island of Bermuda.

Source: What's Special About This Number?

344

344 = 2³ x 43.

344 is an octahedral number.

344 is the maximum number of regions into which 19 circles divide the plane.

The sum of the squares and the sum of the cubes of the factors of 344 are both primes: 2² + 2² + 2² + 43² = 1861 and 2³ + 2³ + 2³ + 43³ = 79531.

In the year 344 B.C., the Greek philosopher Aristotle traveled from the town of Assos to the island of Lesbos to study natural history.

Source: Prime Curios!

528

528 = 2⁴ x 3 x 11.

528 is 1000010000 in base 2 (binary).

528 is the 32nd triangular number.

528 concatenated with its successor is a square: 528529 = 727².

528 is 646 in base 9.

Florida State Road 528 (SR 528) connects Orlando with Cape Canaveral.

Source: What's Special About This Number?

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?