## Friday, January 30, 2009

### 12032

12032 = 28 x 47.

12032 is a number that cannot be written as a sum of three squares.

12032 is a number evenly divisible by twice the sum of the products of each of its digits.

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.

## Thursday, January 29, 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.

## Wednesday, January 28, 2009

### 362

362 = 2 x 181.

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

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

362 has a representation as a sum of two squares: 362 = 12 + 192.

The 2003 movie
Dallas 362 featured Scott Caan as writer, director, and actor.

## Tuesday, January 27, 2009

### 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: 662 + 1 = 4357, a 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!

## Monday, January 26, 2009

### 2519

2519 = 11 x 229.

2519 is a number that cannot be written as a sum of three squares.

2519 is the sum of the first 41 semiprimes.

2519 is a number n such that 2n + 1, 3n + 2, and 4n + 3 are all primes.

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

2519 Annagerman is an asteroid discovered in 1975 and named for the Polish singer Anna German.

## Friday, January 23, 2009

### 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.

875 is the difference of two positive cubes.

875 is a number that can't be expressed as a sum of a prime and a Fibonacci number.

Asteroid 875 Nymphe was discovered in 1917.

## Thursday, January 22, 2009

### 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.

171 is 333 in base 7.

171 Ophelia is a large, dark asteroid discovered in 1877.

Source: Number Gossip

## Wednesday, January 21, 2009

### 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 has a representation as a sum of two squares: 26 = 52 + 12.

26 is the smallest number with three representations as a sum of three distinct primes: 26 = 2 + 5 + 19 = 2 + 7 + 17 = 2 + 11 + 13.

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

Source:
Number Gossip

## Friday, January 16, 2009

### 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.

1056 is a pronic number.

1056 is the sum of two distinct powers of 2: 1056 = 210 + 25.

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

Source:
Number Gossip

## Thursday, January 15, 2009

### 233

233 is a prime number. It is a Sophie Germain prime because 2 x 233 + 1 = 467 is also a prime.

233 is the 13th Fibonacci number.

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

233 has a representation as a sum of two squares: 233 = 82 + 132.

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: 2332 = 1052 + 2082.

2
233 - 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

## Wednesday, January 14, 2009

### 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.

59 and 61 are twin primes.

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

Source: Number Gossip

## Tuesday, January 13, 2009

### 1920

1920= 27 x 3 x 5.

1920 has a unique representation as a sum of three squares: 1920 = 82 + 162 + 402.

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

1920 is a 12-gonal number.

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

Source: Number Gossip

## Monday, January 12, 2009

### 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.

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

Telephone area code 519 is in Ontario, Canada.

## Friday, January 9, 2009

### 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.

33 is the smallest number with nine representations as a sum of three primes: 33 = 2 + 2 + 29 = 3 + 7 + 23 = 3 + 11 + 19 = 3 + 13 + 17 = 5 + 5 + 23 = 5 + 11 + 17 = 7 + 7 + 19 = 7 + 13 + 13 = 11 + 11 + 11.

A normal human spine has 33 vertebrae.

Source: 33 Mysteries

## Thursday, January 8, 2009

### 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 a prime of the form n2 + n + 1, for n = 17.

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

## Wednesday, January 7, 2009

### 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 is 222 in base 6.

86 arises in the sequence generated by starting with 1, then adding 4 and reversing the digits to get the next term: 1, 5, 9, 13, 35, 57, . . . , 28, 86, 72, . . .

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.

## Tuesday, January 6, 2009

### 122

122 = 2 x 61.

122 has a representation as a sum of two squares: 122 = 12 + 112.

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.

122 is the number of integer partitions of 22 into distinct parts.

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

## Monday, January 5, 2009

### 18

18 = 2 x 32

18 has a representation as a sum of two squares: 18 = 32 + 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 smallest number with two representations as a sum of three primes: 18 = 2 + 3 + 13 = 2 + 5 + 11.

18 is the sixth Lucas number.

18 is the number of integer partitions of 13 into distinct parts.

18 is 33 in base 5.

18 is the voting age in many countries.

## Friday, January 2, 2009

### 1726

1726 = 2 x 863.

1726 is 23401 in base 5, with each digit from 0 to 4 represented once.

The 1726th prime is 14741, which is palindromic.

Six distinct permutations of the digits of 1726 give primes: 1627, 2617, 2671, 6217, 6271, and 7621.

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