284

284 = 2² x 71.

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

284 = 2⁸ + 28.

284 and 220 form a pair of amicable numbers, the smallest amicable pair. Two numbers n and m are called an amicable pair if the sum of all positive divisors of n is equal to the sum of all positive divisors of m and both are equal to n + m.

The Greek mathematician Diophantus died in the year 284.

Source: Number Gossip

792

792 = 2³ x 3² x 11.

792 is 1100011000 in base 2 (binary) and 2211 in base 7.

792 is the number of integer partitions of 21.

792 is a number that can be expressed as the difference of the squares of primes in exactly four distinct ways.

792 is the number of inches in a chain, a unit used in surveying.1 mile = 8 furlongs = 80 chains = 5280 feet = 8000 links = 63,360 inches.

Source: Numeropedia

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

199

199 is a prime number.

199 is the 11th Lucas number.

197 and 199 form a twin prime pair.

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

199 is the smallest number with an additive persistence of 3: 1 + 9 + 9 = 19; 1 + 9 = 10; 1 + 0 = 1.

The Cape May Lighthouse in New Jersey has 199 steps in the tower's cast-iron spiral staircase.

Source: Number Gossip

481

481 = 13 x 37.

481 has two representations as a sum of two squares: 481 = 9² + 20² = 15² + 16².

481 is the hypotenuse of two primitive Pythagorean triples: 481² = 31² + 480² = 319² + 360².

481 is an octagonal number.

The Great Pyramid of Giza in Egypt is 481 feet high.

Source: WolframAlpha

604

604 = 2² x 151.

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

604 and the two numbers before it and after it are all products of exactly three primes: 602 = 2 x 7 x 43; 603 = 3 x 3 x 67; 604 = 2 x 2 x 151; 605 = 5 x 11 x 11; 606 = 2 x 3 x 101.

604 is 2444 in base 6 and 424 in base 12.

Nebula NGC 604 was discovered by William Herschel in 1784. It is 3 million light years away. Note that 604 x 1784 + 3 is prime.

Source: Prime Curios!

67

67 is a prime number.

67 has a unique representation as a sum of three squares: 67 = 3² + 3² + 7².

67 is the largest prime that is not the sum of distinct squares.

67 is the maximum number of regions into which 11 lines divide a plane.

67 is the only number such that the common alphabetical value of its Roman representation (LXVII) is equal to its reversal: 12 + 24 + 22 + 9 + 9 = 76.

67 is the smallest prime that contains all 10 digits when raised to the 10th power: 67¹⁰ = 1,822,837,804,551,761,449.

The chemical element holmliun has the atomic number 67.

Source: Number Gossip