2009

2009 = 7² x 41.

2009 has a representation as a sum of two squares: 2009 = 28² + 35².

2009 is an apocalyptic power because 2²⁰⁰⁹ contains the decimal digit string 666.

2009 has been designated the International Year of Astronomy, coinciding with the 400th anniversary of the first recorded astronomical observations with a telescope (Galileo Galilei) and the publication of Astronomia Nova (Johannes Kepler). The United Nations has also designated 2009 the International Year of Natural Fibres.

In the United States, 2009 is the Year of Science, presented by the Coalition on the Public Understanding of Science (COPUS).

Source: Number Gossip

17

17 is a prime number. It is the third Fermat prime: 17 = 2^{2^2} + 1.

17 has a representation as a sum of two squares: 17 = 1² + 4².

17 is the smallest number with four representations as a sum of three primes: 17 = 2 + 2 + 13 = 3 + 3 + 11 = 3 + 7 + 7 = 5 + 5 + 7.

17 and 19 form a twin prime pair.

17 is the hypotenuse of a primitive Pythagorean triple: 17² = 8² + 15².

17 is the first sum of two distinct fourth powers: 17 = 1⁴ + 2⁴.

There are 17 ways to express 17 as the sum of one or more primes; 17 is the only integer that is equal to the number of prime partitions of itself.

Carl Friedrich Gauss proved at the age of 18 that one can construct a regular polygon with a prime number of sides with the use of only straight edge and compasses only if the number of sides is of the form 2²^n. Hence, one can construct a regular 17-gon with rule and compasses only.

Source: Number Gossip

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

1233

1233 = 3² x 137.

1233 has a representation as a sum of two squares: 1233 = 12² + 33². 1233 is the smallest 2n-digit number that is the sum of the squares of its n-digit halves.

1233 is a value of n such that n² - 2 and n² + 2 are both prime: 1,520,287 and 1,520,291.

1233 is a Happy-Go-Lucky number (both Happy and Lucky).


Southern Pacific steam locomotive 1233 was built in 1918 by the Baldwin Locomotive Works in Pennsylvania.

Source: Number Gossip

6141

6141 = 3 x 23 x 89. It is the product of three distinct primes whose binary expansion is palindromic: 1011111111101.

6141 is a Kaprekar constant in base 2.

6141 is the sum of 11 distinct powers of 2.

6141 is a divisor of 2²² - 1.

6141 Durda is a Mars-crossing asteroid discovered in 1992.

Source: JPL

1223

1223 is a prime number. It is a Sophie Germain prime because 2 x 1223 + 1 = 2447, which is also prime.

1223 is a number that cannot be written as a sum of three squares.

1223 is a prime p such that p + 3 is a semiprime: 1223 + 3 = 1226 = 2 x 613.

1223 is a number n such that n and n + 8 are both primes: 1223 and 1231.

1223 is the smallest number with complexity 24. The complexity of an integer is the least number of 1s needed to represent it using only additions, multiplications, and parantheses.


1223 Neckar is an asteroid discovered in 1931.

Source: Wolfram MathWorld

866

866 = 2 x 433.

866 is the smallest number n such that the sum of the proper divisors of n², excluding 1, is a square.

866 has a representation as a sum of two squares: 866 = 5² + 29².

866 is the difference of two positive cubes.


866 is one of the telephone area codes for toll-free calls.

Source: Number Gossip

738

738 = 2 x 3² x 41.

738 = 6 + 66 + 666.

738 has a representation as a sum of two squares: 738 = 3² + 27².

738 is a 13-gonal number.



The SVI 738 - Xpress was a home computer manufactured by Spectravideo in 1986.

Source: What Special About This Number?

495

495 = 3² x 5 x 11.

495 is the Kaprekar constant for three-digit numbers. Arrange the digits of any three-digit number whose digits are not all the same in descending and ascending order, compute the difference, then repeat the process. For example: 311 - 113 = 198; 981 - 189 = 792; 972 - 279 = 693; 963 - 369 = 594; 954 - 459 = 495.

495 is the ninth pentatope number.

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

Interstate 495 (Capital Beltway) is a highway that surrounds Washington, D.C.

Source: Wolfram MathWorld

443

443 is a prime number. It is the 24th Sophie Germain prime: 443 x 2 + 1 = 887, which is also prime.

443 is the first three-digit non-palindromic prime number whose binary equivalent (110111011) is a palindromic prime in base 10.

The sum of the digits of 443 is a prime: 4 + 4 + 3 = 11. Hence, 443 is an additive prime

443 is the smallest prime containing exactly two 4s.

Telephone area code 443 includes Baltimore, Md.

Source: Prime Curios!

300

300 = 2² x 3 x 5².

300 is a triangular number, the sum of all positive integers up to 24: 1 + 2 + 3 + . . . + 22 + 23 + 24 = 300.

300 is the sum of twin primes: 149 + 151 = 300.

300 is a number n such that n² (90000) contains exactly two different digits.

In bowling, 300 is the largest possible score.

Source: Wolfram MathWorld

255

255 = 3 x 5 x 17.

255 = 11111111 in base 2.

255 is the largest value representable as an 8-bit binary number. Eight bits, otherwise known as a byte, is a very common size for storing "small" values in computer memories. Consequently, 255 appears as a bound or an otherwise magic number in many computer-related tasks. For example, 255 is the maximum amount of red, green, or blue that goes into an RGB color, as well as the maximum content of any of the four octets of an IP address.

255 is the least odd integer greater than 3 that is not the sum of two distinct powers of two and a prime.

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

255 is 3333 in base 4.

255 is a Mersenne number: 255 = 2⁸ - 1.


Source: Number Gossip

249

249 = 3 x 83.

The sum of the digits of 249 equals five times the number of digits: 2 + 4 + 9 = 15 = 3 x 5.

249 is a number not divisible by any of its digits.

249 is a Blum number. A natural number n is a Blum integer if n = pq is a semiprime (the product of two prime numbers) for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t.

249 Ilse is an asteroid with an unusually slow rotation period, discovered in 1885.

Source: The On-Line Encyclopedia of Integer Sequences

146

146 = 2 x 73.

The absolute difference between any two digits of 146 is a prime number (2, 3, 5).

146 is 222 in base 8.

146 is an octahedral number, which has the form (2n³ + n)/3.

146 is an untouchable number: No integer's proper divisors add up to 146.

146 has a representation as a sum of two squares: 146 = 5² + 11².


The Grand Union Canal Race is a 146-mile ultramarathon from Birmingham to London.

Source: Prime Curios!

91

91 = 7 x 13.

91 is the first non-trivial odd composite number. Every smaller composite is either even, a familiar square, ends in 5, has a digit sum that is a multiple of 3, or is obviously divisible by 11.

91 is the sum of the squares of the first six integers: 1² + 2² + 3² + 4² + 5² + 6² = 91. It is the 13th triangular number.

91 is the sum of the first 13 positive integers: 1 + 2 + 3 + . . . + 11 + 12 + 13 = 91.

91 has a unique representation as a sum of three squares: 91 = 1² + 3² + 9².

91 is 111 in base 9.

91 cents is the total amount of money one has, given one each of a penny, nickel, dime, quarter, and half dollar.
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!

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?