47

47 is a safe prime number. A safe prime has the form 2p + 1, where p is also a prime.

There are 47 occurrences of 47 in the first thousand prime numbers.

4³ + 7³ = 407.

47 is the smallest number n for which 666ⁿ has a digit sum of 666.

The atomic number of silver is 47.

Sources: Number Gossip; Prime Curios!

711

711 = 3² x 79.

711 is the concatenation of the fourth and fifth primes.

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

711 is a divisor of 80² - 1.

711 is the sum of ten positive fifth powers: 711 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

711 is the phone number of the Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.

The logo for a chain of convenience stores.

#711 was a comics superhero created by George Brenner and published by Quality Comics from 1941 to 1943.

In the 1950 movie 711 Ocean Drive, a telephone repairman in Los Angeles uses his knowledge of electronics to help a bookie set up a betting operation.

Source: WolframAlpha

692

692 = 2² x 173.

692 is a number that has no digits in common with its cube (331373888).

692 has a representation as a sum of two squares: 692 = 4² + 16².

692 is a member of the sequence generated when you start with 1, then repeatedly multiply by 5 and reverse the digits: 1, 5, 52, 62, 13, . . . , 592, 692, 643, . . .


In Microsoft Windows, error 692 signals a "hardware failure in port or attached device."

The U.S.S. Allen M. Sumner (DD-692), a destroyer, served in the U.S. Navy from 1943 to 1973.

1225

1225 is the product of the square of 5 and the square of 7 and hence is the square of 35. It is the product of the squares of two consecutive primes, 5 and 7.

1225 has a representation as a sum of two squares: 1225 = 21² + 28².

1225 is the smallest number with three representations as a sum of four positive cubes: 1225 = 1³ + 2³ + 6³ + 10³ = 3³ + 7³ + 7³ + 8³ = 4³ + 6³ + 6³ + 9³.

1225 is a triangular square number; it is both a perfect square and a triangular number. 1225 is also a hexagonal number.

A representation of consecutive hexagonal numbers.

Pere Marquette 1225 is a steam locomotive.

Source: Wolfram MathWorld

105

"Every number is built by multiplying prime numbers—105, for example, is three times five times seven. They are like the atoms of arithmetic—the hydrogen and oxygen of the world of numbers."—Marcus du Sautoy, The Guardian, Nov. 1, 2008.

105 is the 14th triangular number. It is the sum of consecutive integers: 1 + 2 + 3 + . . . + 13 + 14 = 105.

105 is the sum of consecutive integers in four other ways: 12 + 13 + . . . + 17 + 18 = 15 + 16 + 17 + 18 + 19 + 20 = 19 + 20 + 21 + 22 + 23 = 34 + 35 + 36 = 52 + 53.

Paul Erdös conjectured that 105 is the largest number n such that the positive values of n - 2^k are all prime: 105 - 2 = 103, 105 - 4 = 101, 105 - 8 = 97; 105 - 16 = 89; 105 - 32 = 73; 105 - 64 = 41.

105 is 77 in base 14.

Space Shuttle Mission STS-105 was launched into space on Aug. 10, 2001.

Source: Wolfram MathWorld

2929

2929 = 29 x 101.

2929 has two representations as a sum of two squares: 2929 = 15² + 52² = 25² + 48².

2929 is the hypotenuse of two primitive Pythagorean triples: 2929² = 1560² + 2479² = 1679² + 2400².

2929 is a square-free number because its prime decomposition contains no repeated factors.

2929 is a divisor of 100¹⁴ - 1.

2929 Entertainment is a media company with interests ranging from movie production to video games.

Source: Number Gossip

1875

1875 = 3 x 5⁴

1875 is an economical number.

1875 is the smallest order for which there are 21 groups.

The product of the prime factors of 1875 plus one is a perfect square: 3 x 5 + 1 = 16 = 4².

1875 is a number n such that n - 4, n - 2, n + 2, and n + 4 are prime: 1871, 1873, 1877, and 1879 are all prime.


French mathematician Henri Lebesgue was born June 28, 1875.

Source: What's Special About This Number?