247

247 = 13 x 19. Its digits sum to the smallest prime factor: 2 + 4 + 7 = 13.

247 is a pentagonal number.

247 is the smallest possible difference between two integers that together contain each digit exactly once: 247 = 50,123 - 49876.

247² is one of six square numbers that use the same digits: 247² = 61,009; 130² = 16.900; 140² = 19,600; 310² = 96,100; 103² = 10,609; and 301² = 90,601.

247 Eukrate is a large, dark asteroid discovered in 1885.

Source: Prime Curios!

477

477 = 3² x 53,

477 has a representation as a sum of two squares: 477 = 6² + 21².

477 is a pentagonal number.

477 is the smallest number that is the sum of different primes by using twice all the digits greater than 0: 477 = 89 + 83 + 67 + 61 + 53 + 47 + 41 + 29 + 5 + 2.

477 is the smallest number whose cube contains four 3s: 477³ = 108,531,333.

Masonic Funeral Music in C by Wolfgang Amadeus Mozart is cataloged as KV 477.

Source: Number Gossip

287

287 = 7 x 41.

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

287 is a pentagonal number.

287 is the sum of consecutive primes in three different ways: 287 = 89 + 97 + 101 = 47 + 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

287 is the sum of the first three NSW primes: 287 = 7 + 41 + 239.

287 Nephthys is a large asteroid discovered in 1889.

Source: Prime Curios!

532

532 = 2² x 7 x 19.

532 has a unique representation as a sum of three squares: 532 = 8² + 12² + 18².

532 is 444 in base 11.

532 is a divisor of 11⁶ - 1.

532 is a pentagonal number.

532 is the smallest even number differing by a composite number from both of its prime neighbors.

532 was the first year in which the Anno Domini calendar was used for numbering the years.

Source: Number Gossip

590

590 = 2 x 5 x 59.

590 is a pentagonal number.

590 plus 590 ones is a prime. This is the only three-digit number with this property.

590 is a number n such that n concatenated with n + 2 gives the product of two numbers that differ by 1: 590592 = 768 x 769.

590 Tomyris is an asteroid discovered in 1906.

Source: Prime Curios!

852

852 = 2² x 3 x 71.

852 is a pentagonal number.

852 is the number of 6-colorable connected graphs with seven vertices.

852 is a Smith number.

NGC 852 is a galaxy in the constellation Eridanus.

Source: What's Special About This Number?

925

925 = 5² x 37.

925 has three representations as a sum of two squares: 925 = 5² + 30² = 14² + 27² = 21² + 22².

925 is the hypotenuse of two primitive Pythagorean triples: 925² = 43² + 924² = 533² + 756².

925 is 1021021 in base 3 and 4141 in base 6.

925 is a pentagonal number.

Asteroid 925 Alphonsina was discovered in 1920.

Source: Wolfram MathWorld

425

425 = 5² x 17.

425 has three representations as a sum of two squares: 425 = 5² + 20² = 8² + 19² = 13² + 16².

425 is the hypotenuse of two primitive Pythagorean triples: 425² = 87² + 416² = 297² + 304².

425 is a pentagonal number, a number of the form n(3n - 1)/2, where n = 17.

425 is the number of subsets of {1, 2, 3, . . . 11} that have an integer average.

425 is the telephone area code for suburbs to the north and east of Seattle, Washington.

Source: What's Special About This Number?

2501

2501 = 41 x 61.

2501 is the product of the only two primes (41 and 61) that can be the last two digits of a perfect fourth power. If you replace the 5 by a 4, you get a fourth power: 2401 = 7⁴.

2501 is a pentagonal number, having the form n(3n – 1)/2. In this case, n = 41.

2501 has two representations as a sum of two squares: 2501 = 1² + 50² = 10² + 49².

2501 is the hypotenuse of two primitive Pythagorean triples: 2501² = 100² + 2499² = 980² + 2301².


Project 2501, from the film and manga Ghost in the Shell, is an artificial intelligence program that develops sapience.

Source: Prime Curios!

92

92 = 2² x 23.

92 is a pentagonal number.

92 is the maximum number of regions into which 13 lines divide a plane.

92 is the maximum number of regions into which 10 circles divide a plane.

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


The snub dodecahedron is an Archimedean solid with 92 faces.
Source: Wolfram MathWorld

1717

1717 = 17 x 101.

1717 is a pentagonal number.

1717 has two representations as a sum of two squares: 1717 = 6² + 41² = 14² + 39².

1717 is the hypotenuse of two primitive Pythagorean triples: 1717² = 492² + 1645² = 1092² + 1325².

1717 is a divisor of 100⁸ - 1.

French mathematician and encylopaedist Jean le Rond d'Alembert was born on Nov. 16, 1717.

Photo credit: MathDL Portrait Gallery

Source: Number Gossip

51

51 = 3 x 17.

51 is the smallest number that can be written with all the digits from 1 to 5 (without repetition) as a sum of prime numbers: 2 + 3 + 5 + 41 = 51. Note that the highest digit (5) and the lowest digit (1) are the digits of 51.

51 is a pentagonal number, a number of the form n(3n - 1)/2, and a centered pentagonal number (one of the few numbers to be both).

51 is 110011 in base 2 (binary) and 33 in base 16.

51 is the sixth Motzkin number.

Area 51 is a nickname for a secret military base located in the southern portion of Nevada in the western United States.

Source: Prime Curios!