824

824 = 2³ x 103; the product of the cube of a prime and a different prime.

824 is the sum of ten consecutive primes: 824 = 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103.

824 is 11244 in base 5 and 2255 in base 7.

824 is the number of 3 x 3 magic squares with the sum 3n, where n = 23.

824 Anastasia, discovered in 1916, is a main-belt minor planet orbiting the sun. On April 6, 2010, 824 Anastasia had the distinction of causing the brightest asteroid occultation ever predicted for North America for an asteroid of its size.

Source: Wikipedia

9852

9852 = 2² x 3 x 821.

9852 is a number that cannot be written as a sum of three squares.

9852 is 7447 in base 11.

The Alpine CDE-9852 is a car CD player.

Source: WolframAlpha

977

977 is a prime number. It is a Stern prime.

977 has a representation as a sum of two squares: 977 = 4² + 31².

977 is the hypotenuse of a primitive Pythagorean triple: 977² = 248² + 945².

977 is the first prime that results in a cube if added to the sum of its digits: 977 + 9 + 7 + 7 = 1000.

In the 1950 movie Harvey, Dr. Sanderson prescribes "Formula 977" to Elwood P. Dowd (James Stewart).

Source: Prime Curios!

809

809 is a prime number. It is a Sophie Germain prime because 2 x 809 + 1 = 1619 is also a prime.

809 has a representation as a sum of two squares: 809 = 5² + 28².

809 and 811 form a twin prime pair.

809 is the hypotenuse of a primitive Pythagorean triple: 809² = 280² + 759².

809 is a divisor of 44⁸ - 1.

809 is the only three-digit pime. Pimes are primes whose digits contain circles (that is, use only 0, 6, 8, and 9).

809 was the hotel room number in the 1952 film Don't Bother to Knock, starring Richard Widmark and Marilyn Monroe.

Source: Number Gossip

3

3 is a prime number. 3 is also a Sophie Germain prime because 2 x 3 + 1 = 7, which is a prime.

3 is the second triangular number, or the sum of the first two positive integers: 3 = 1 + 2.

3 is the fourth Fibonacci number: 1, 1, 2, 3, 5, 8, 13, 21, . . .

3 is the second Lucas number: 1, 3, 4, 7, 11, 18, 29, . . .

3 has a unique representation as a sum of three squares: 3 = 1² + 1² + 1².

3 is the number of integer partitions of 3.

3 is the number of integer partitions of 5 into distinct parts.

3 and 5 form a twin prime pair.

Tri- means three. So triangles have three sides, a tripod has three legs, and the dinosaur triceratops had three horns. The French flag is a tricolore because it has three colors.

Three-dimensional means that something has length, width, and depth.

The letters A F H K N Y Z are all made up of three lines.

The trillium, Ontario's provincial flower, has three petals.

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

246

246 = 2 x 3 x 41. It is a sphenic number: the product of three distinct primes.

246 is the lowest number (and the only one with three factors) whose unique prime factorization contains exactly the first four digits.

246 is 1441 in base 5 and 303 in base 9.

The digit 1 occurs in the 246th position in the decimal expansion of pi.

246 is the sum of four positive fifth powers: 246 = 3⁵ + 1⁵ + 1⁵ + 1⁵.

Charles de Gaulle (1890-1970), President of France, once complained: "How can you govern a country that has 246 varieties of cheese."

Source: Prime Curios!

699

699 = 3 x 233.

699 has the representation 699 = 3⁶ - 30.

699 is a number n such that n² + 2 is a prime: 699² + 2 = 488603.

For 699, the sum of the digits is eight times the number of digits: 6 + 9 + 9 = 8 x 3.

699 is the smallest number whose sum of digits is 24.

The submarine USS Jacksonville (SSN-699) is nicknamed "The Bold One."

Source: On-Line Encyclopedia of Integer Sequences

878

878 = 2 x 439.

878 is a palindrome with exactly two prime factors.

878 is the number of 3 x 3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on one side.

878 is a canyon number.

Discovered in 1916, 878 Mildred is a minor planet in the main belt orbiting the sun.

Source: What's Special About This Number?

214

214 = 2 x 107.

The number 214 x 412 + 1 is a prime number, 88169.

214 is a value of n for which n!! - 1 is a prime number; in this case, a 205-digit prime.

214 is 424 in base 7.

214 is the number of bones in a normal human skeleton, according to Sarah in Terminator 2: Judgment Day.

Source: Wikipedia

1137

1137 = 3 x 379.

1137 is the product of two primes, as are 1136 (2⁴ x 71) and 1138 (2 x 569).

1137 is a semiprime (product of two distinct primes), as are 1139 (17 x 67) and 1141 (7 x 163).

1137 is the maximum value of n so that there exist seven denominations of stamps so that every postage from 1 to n can be paid for with at most seven stamps (postage stamp problem). It is also the solution to the postage stamp problem for n denominations and seven stamps, for n = 7.

1137 in base 2 (binary) is palindromic: 10001110001.

1137 is 696 in base 13 and 393 in base 18.

Atlantic Records 1957 release 45-1137 featured "Rakin and Scrapin" by Dean Beard and the Crew Cats.

Source: What's Special About This Number?

72

72 = 2³ x 3².

72 is the sum of the first eight even numbers: 72 = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16.

72 is the sum of nine consecutive integers: 72 = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12.

72 has a representation as a sum of two squares: 72 = 6² + 6².

72 is 2200 in base 3, 200 in base 6, 110 in base 8, 66 in base 11, 44 in base 17, 33 in base 23, and 22 in base 35.

The normal human pulse rate is about 72 beats per second at rest.

The Cambodian alphabet, with 72 letters, is the longest in the world.

Source: Phillips, R. 2004. Numbers: Facts, Figures and Fiction. Badsey Publications.

469

469 = 7 x 67.

469 is a heptagonal number. 469 is also a centered hexagonal number.

469 is a value of n for which n! - 1 is a prime number.

469 is the sum of three distinct positive cubes: 469 = 7³ + 5³ + 1³.

Inserting a zero between adjacent digits makes 469 a prime number: 40609.

469 Argentina is a main-belt asteroid discovered in 1901.

Source: What's Special About This Number?

663

663 = 3 x 13 x 17.

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

663 has the representation 663 = 3⁶ - 66.

663 is the generalized Catalan number C(15,3).

663 is the numerical equivalent of ONE on a touch-tone telephone.

Source: Number Gossip

144

144 = 2⁴ x 3².

144² = 12², a perfect square. If you reverse the digits, 21² = 441.

144 has a unique representation as a sum of three squares: 144 = 4² + 8² + 8².

144 is a square number. Divide it by 4 and you get 36, which is also square. Does this happen with any other square numbers?

144 is the 12th Fibonacci number.

144 is 99 in base 15.

The interior angles in a regular decagon measure 144 degrees. In counting objects, 144 is called a gross (a dozen dozens).

Source: WolframAlpha

843

843 = 3 x 281.

843 is the 14th Lucas number.

843 is a divisor of 53⁴ - 1.

843 is 31023 in base 4, 11333 in base 5, 3523 in base 6, 2313 in base 7, and 1513 in base 8, all ending in 3. 843 is 443 in base 14, 223 in base 20, and 123 in base 28.

843 is palindromic in base 2: 1101001011.

Telephone area code 843 covers coastal South Carolina, including Charleston, Myrtle Beach, and Hilton Head Island.

Source: WolframAlpha

700

700 = 2² x 5² x 7.

700 is the sum of four consecutive primes: 700 = 167 + 173 + 179 + 181.

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

700 is 221221 in base 3 and 2020 in base 7.

700 is the number of n-bead necklaces with four colors, for n = 7.

The first known recorded use of the zero in Europe occurred in the year 700.

Source: Wikipedia