12032

12032 = 2⁸ x 47

12032 is the number of different seven-digit combinations (possible phone numbers) that use any of the four digits (0, 2, 5, and 8) down the center of a standard phone keypad, excluding combinations that start with 555 (not available for residential phone use). The first digit of the combination also can't be 0.

12032 is the postal zip code for Fulton County, N.Y.

Source: Wall Street Journal, Jan. 14, 2009.

631

631 is a prime number.

631 is the maximum number of regions into which 35 lines divide a plane.

631 values of n less than or equal to 1000 produce primes for 2n² + 144251.

631 has a base 2 representation (1001110111) that begins with its base 5 representation

 (10011).

Researchers "estimate that there are 631 Asian elephants living in Taman Negara National Park--a 4,343 square kilometer (1,676 square mile) protected area in the center of Peninsular Malaysia . . . . The team counted elephant dung piles to estimate population size—a scientifically proven technique that produces accurate figures."--Wildlife Conservation Society press release, Jan. 14, 2009.

Source: Prime Curios!

362

362 = 2 x 181

362 and its double (724) and triple (1086) all use the same number of digits in when expressed in Romn numerals: CCCLXII, DCCXXIV, and MLXXXVI.

Both numbers 3! + 6! + 2! - 1 and 3!*6!*2! + 1 are primes.


Source: Prime Curios!

66

66 = 2 x 3 x 11

66 is the 11th triangular number, the sum of the integers from 1 to 11.

66 is the smallest palindromic composite number n such that ⁿ2 + 1 is prime.

66 is the smallest number that can be expressed as a sum of two two-digit primes, each ending with the digit 3, in two different ways: 66 = 13 + 53 = 23 + 43.


U.S. Route 66 (also known as the Will Rogers Highway) ran from Chicago to Los Angeles and was the title of a weekly TV series (1960-1964).


Source: Prime Curios!

2519

2519 = 11 x 229.

2519 is the smallest number n where either n or n + 1 is divisible by the numbers from 1 to 12.

2519 mod n means the remainder after dividing 2519 by n:
2519 mod 2 = 1
2519 mod 3 = 2
2519 mod 4 = 3
2519 mod 5 = 4
2519 mod 6 = 5
2519 mod 7 = 6
2519 mod 8 = 7
2519 mod 9 = 8
2519 mod 10 = 9

Source: Easy Calculation

875

875 = 5³ x 7

875 is 3-automorphic. A number k such that nk² has its last digits equal to k is called n-automorphic: 3 x 875² = 2296875.


Source: What's Special About This Number?

171

171 = 3² x 19

171 is a Harshad number, divisible by the sum of its digits (1 + 7 + 1 = 9).

171 is the 18th triangular number, the sum of the integers from 1 to 18.

If you write n consecutive digits starting with 1 and following 9 by 0, the smallest n that will give you a prime number is 171.


Source: Number Gossip

26

26 = 2 x 13

26 is the only integer sandwiched between a square (25) and a cube (27).

26 is the smallest non-palindromic number whose square is palindromic: 26² = 676.

26 is equal to the sum of the digits of its cube: 26³ = 17,576 and 1 + 7 + 5 + 7 + 6 = 26.

26 (together with 11) cannot be represented as the sum of less than six hexagonal numbers from the sequence 1 6 15 28 45 . . . .


26 is the atomic number of iron and the number of letters in the English alphabet.

Source: Number Gossip

1056

1056 = 2⁵ x 3 x 11

1056 = 32 x 33 = 1 x 6 x 11 x 16, one of only two solutions of x(x + 1) = y(y + 5)(y + 10)(y + 15). The other is 207 x 208 = 8 x 13 x 18 x 23 = 43,056.

1056 is the area of the smallest non-square rectangle that can be tiled with distinct integer-sided squares.


A Chinese astronomer observed the creation of the Crab Nebula in the year 1056.

Source: Number Gossip

233

233 is a prime number and a Fibonacci number.

233 is the only known Fibonacci prime whose sum of digits is a Fibonacci number: 2 + 3 + 3 = 8.

233 is the smallest number with the property that it and its neighbors can be written as a sum of two squares and therefore can be the hypotenuse of a Pythagorean triangle.

2²³³ - 3 is a prime.


Had Ray Bradbury used the metric system, he may have called his novel Celsius 233 instead of Fahrenheit 451.

Source: Number Gossip

61

61 is a prime number.

The 61st Fibonacci number (2504730781961) is the smallest Fibonacci number that contains all the digits from 0 to 9.

61 is the smallest prime whose reversal (16) is a square.

There are 61 abstract groups of order 1464. Note that 61 divides 1464.


The official length of an ice hockey rink must be no more than 61 meters.

Source: Number Gossip

1920

1920= 2⁷ x 3 x 5

1920 is the smallest number that contains more different digits than its cube: 1920³ = 7077888000.

Science fiction author Isaac Asimov was born on Jan. 2, 1920.

Source: Number Gossip

519

519 = 3 x 173.

519 is the sum of three consecutive primes: 167 + 173 + 179 = 519.

519 is the number of trees on 15 vertices with diameter 5.

Telephone area code 519 is in Ontario, Canada.

Source: What's Special About This Number?

33

33 = 3 x 11

33 is the smallest integer that cannot be expressed as a sum of different triangular numbers (1, 3, 6, 10, 15, 21, 28, . . . ).

The smallest run of three consecutive integers that are semi-primes (the product of two primes) begins with 33: 33 = 3 x 11, 34 = 2 x 17, 35 = 5 x 7.

A normal human spine has 33 vertebrae.

Source: 33 Mysteries

307

307 is a prime number.

307 is the smallest number that is the sum of any set of primes containing all digits: 2 + 5 + 41 + 67 + 83 + 109 = 307.

307² = 94249, which is a palindromic number.

307 is the telephone area code for the state of Wyoming.

Source: Number Gossip

86

86 = 2 x 43

86 is conjectured to be the largest number n such that 2ⁿ (in decimal) doesn't contain a 0.

86 = 222 in base 6.

86 is the atomic number of radon.

In the TV series and movie Get Smart, the principal character Maxwell Smart was known as Agent 86.

Source: Number Gossip

122

122 = 2 x 61

The square of 122 minus each of 122's prime factors squared is a prime: 122² - 2² - 61² = 11159.

122 is the smallest sum of two non-consecutive factorials of distinct primes: 2! + 5! = 2 + 120 = 122.

In 122 AD, Roman Emperor Hadrian ordered the building of a 72-mile wall across northern Britain.

Source: Prime Curios!

18

18 = 2 x 3²

18 = 9 + 9 and 81 = 9 x 9.

18 is the only number that is twice the sum of its digits: 18 = 2(1 + 8).

The cube together with the 4th power of 18 use all the digits 0 to 9 once each: 18³ = 5832 and 18⁴ = 104,976.

18 is the voting age in many countries.

Source: Number Gossip

1726

1726 = 2 x 863.



Mathematician Nicolaus II Bernoulii, son of Johan and older brother of Daniel, died on July 31, 1726, in St. Petersburg, Russia.

Source: MacTutor History of Mathematics Archive