## Wednesday, June 30, 2010

### 437

437 = 19 x 23. It is the product of two successive primes.

437 is a brilliant number. It is a semiprime (product of two primes) whose prime factors have the same number of decimal digits.

437 has a cube with the last three digits the same as the three digits before that: 83453453.

437 is 3222 in base 5 and 233 in base 14.

The digit 1 can be found at the 437th position in the decimal expansion of pi. Cosmonaut Valeri Polyakov spent 437 days aboard the space station Mir in 1994-5, the longest time spent by a human in outer space.

## Tuesday, June 29, 2010

### 348

348 = 22 x 3 x 29.

348 is the sum of four consecutive primes: 348 = 79 + 83 + 89 + 97.

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

348 is the smallest number whose 5th power contains exactly the same digits as another 5th power: 3485 = 5103830227968.

348 is 110220 in base 3 and 250 in base 12. The Ferrari 348 is a two-seat sports car.

## Monday, June 28, 2010

### 32

32 = 25, a perfect fifth power.

32 is the sum of four consecutive odd numbers: 32 = 5 + 7 + 9 + 11.

A truncated icosahedron has 32 sides, consisting of 12 regular pentagons and 20 regular hexagons. It has 60 vertices.
32 has a representation as a sum of two squares: 32 = 42 + 42.

32 is the number of integer partitions of 16 into distinct parts.

32 is 44 in base 7, 22 in base 15, and 11 in base 31. 32 degrees Fahrenheit is the melting point of ice.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

## Friday, June 25, 2010

### 818

818 = 2 x 409.

818 is the smallest palindrome that can be expressed as the sum of the squares of two primes: 818 = 172 + 232.

818 is the only three-digit tetradic integer such that the sum of the differences of the number and each digit raised to the digit is prime: (818 - 8)8 + (818 - 1)1 + (818 - 8)8 = 370604037770368200000817, a prime.

818 is the number of ways to dissect a 12-gon using non-crossing diagonals into polygons with an even number of sides. 818 is the telephone area code for the San Fernando Valley, California.

## Thursday, June 24, 2010

### 209

209 = 11 x 19.

209 is the smallest number with six representations as a sum of three squares: 209 = 12 + 82 + 122 = 22 + 32 + 142 = 22 + 62 + 132 = 32 + 102 + 102 = 42 + 72 + 122 = 82 + 82 + 92.

209 is the smallest composite number that is 1 less than a primorial.

209 is the number of consecutive composite numbers that follow the prime 20831323, the first prime gap exceeding 200. The chemical element bismuth has one stable isotope, which contains 209 neutrons.

## Wednesday, June 23, 2010

### 658

658 = 2 x 7 x 47.

658 is the number of triangles of any size contained in the triangle of side 13 on a triangular grid.

A zero is located at the 658th position in the decimal expansion of pi.

658 is the sum of six positive cubes in exactly three ways. PT-658, built in 1945, is a historic naval ship now being restored, in Portland, Ore.

## Tuesday, June 22, 2010

### 824

824 is the sum of ten consecutive primes: 824 = 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103.

824 is 11244 in base 5 and 2255 in base 7. 824 Anastasia, discovered in 1916, is a main-belt minor planet orbiting the sun. On April 6, 2010, 824 Anastasia had the distinction of causing the brightest asteroid occultation ever predicted for North America for an asteroid of its size.

Source: Wikipedia

## Monday, June 21, 2010

### 9852

9852 = 22 x 3 x 821.

9852 is a number that cannot be written as a sum of three squares.

9852 is 7447 in base 11. The Alpine CDE-9852 is a car CD player.

Source: WolframAlpha

## Friday, June 18, 2010

### 977

977 is a prime number. It is a Stern prime.

977 has a representation as a sum of two squares: 977 = 42 + 312.

977 is the hypotenuse of a primitive Pythagorean triple: 9772 = 2482 + 9452.

977 is the first prime that results in a cube if added to the sum of its digits: 977 + 9 + 7 + 7 = 1000. In the 1950 movie Harvey, Dr. Sanderson prescribes "Formula 977" to Elwood P. Dowd (James Stewart).

## Thursday, June 17, 2010

### 809

809 is a prime number. It is a Sophie Germain prime because 2 x 809 + 1 = 1619 is also a prime.

809 has a representation as a sum of two squares: 809 = 52 + 282.

809 and 811 form a twin prime pair.

809 is the hypotenuse of a primitive Pythagorean triple: 8092 = 2802 + 7592.

809 is a divisor of 448 - 1.

809 is the only three-digit pime. Pimes are primes whose digits contain circles (that is, use only 0, 6, 8, and 9). 809 was the hotel room number in the 1952 film Don't Bother to Knock, starring Richard Widmark and Marilyn Monroe.

## Wednesday, June 16, 2010

### 3

3 is a prime number. 3 is also a Sophie Germain prime because 2 x 3 + 1 = 7, which is a prime.

3 is the second triangular number, or the sum of the first two positive integers: 3 = 1 + 2.

3 is the fourth Fibonacci number: 1, 1, 2, 3, 5, 8, 13, 21, . . .

3 is the second Lucas number: 1, 3, 4, 7, 11, 18, 29, . . .

3 has a unique representation as a sum of three squares: 3 = 12 + 12 + 12.

3 is the number of integer partitions of 3.

3 is the number of integer partitions of 5 into distinct parts.

3 and 5 form a twin prime pair. Tri- means three. So triangles have three sides, a tripod has three legs, and the dinosaur triceratops had three horns. The French flag is a tricolore because it has three colors.

Three-dimensional means that something has length, width, and depth.

The letters A F H K N Y Z are all made up of three lines.
The trillium, Ontario's provincial flower, has three petals.

Source: R. Phillips. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

## Tuesday, June 15, 2010

### 246

246 = 2 x 3 x 41. It is a sphenic number: the product of three distinct primes.

246 is the lowest number (and the only one with three factors) whose unique prime factorization contains exactly the first four digits.

246 is 1441 in base 5 and 303 in base 9.

246 is the sum of four positive fifth powers: 246 = 35 + 15 + 15 + 15. Charles de Gaulle (1890-1970), President of France, once complained: "How can you govern a country that has 246 varieties of cheese."

## Monday, June 14, 2010

### 699

699 = 3 x 233.

699 has the representation 699 = 36 - 30.

699 is a number n such that n2 + 2 is a prime: 6992 + 2 = 488603.

699 is the smallest number whose sum of digits is 24. The submarine USS Jacksonville (SSN-699) is nicknamed "The Bold One."

## Friday, June 11, 2010

### 878

878 = 2 x 439.

878 is the number of 3 x 3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on one side.

878 is a canyon number. Discovered in 1916, 878 Mildred is a minor planet in the main belt orbiting the sun.

## Thursday, June 10, 2010

### 214

214 = 2 x 107.

The number 214 x 412 + 1 is a prime number, 88169.

214 is a value of n for which n!! - 1 is a prime number; in this case, a 205-digit prime.

214 is 424 in base 7. 214 is the number of bones in a normal human skeleton, according to Sarah in Terminator 2: Judgment Day.

Source: Wikipedia

## Wednesday, June 9, 2010

### 1137

1137 = 3 x 379.

1137 is the product of two primes, as are 1136 (24 x 71) and 1138 (2 x 569).

1137 is a semiprime (product of two distinct primes), as are 1139 (17 x 67) and 1141 (7 x 163).

1137 is the maximum value of n so that there exist seven denominations of stamps so that every postage from 1 to n can be paid for with at most seven stamps (postage stamp problem). It is also the solution to the postage stamp problem for n denominations and seven stamps, for n = 7.

1137 in base 2 (binary) is palindromic: 10001110001.

1137 is 696 in base 13 and 393 in base 18. Atlantic Records 1957 release 45-1137 featured "Rakin and Scrapin" by Dean Beard and the Crew Cats.