## Tuesday, November 30, 2010

### 2133

2133 = 33 x 79.

2133 is a 2-hyperperfect number.

2133 is an octagonal number.

2133 is a lucky number that is divisible by the sum of its digits (9).

The HP 2133 Mini-Note is a small laptop computer.

## Monday, November 29, 2010

### 228

228 = 22 x 3 x 19.

228 is 444 in base 7.

228 can be represented as 28 - 28.

228 + 1, 228 - 1, 822 + 1, 822 - 1, (228 + 882) + 1, and (228 + 882) - 1 are all primes.

228 is the sum of six consecutive primes (29 + 31 + 37 + 41 + 43 + 47) and the sum of ten consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41).

The 228 incident was an anti-government uprising in Taiwan. The number refers to the day the massacre began: February 28, 1947.

## Wednesday, November 24, 2010

### 627

627 = 3 x 11 x 19.

627 is the number of integer partitions of 20.

124,367,958 = 627 x 198354 = 9 x 26 x 531487. Note that the numbers in each expression use each digit from 1 to 9 once.

627 is 393 in base 13.

627 is a Smith number: the sum its digits is equal to the sum of its digits in its prime factorization: 6 + 2 + 7 = 15 = 3 + 1 + 1 + 1 + 9.

A pill with the imprint AN 627 is the drug Tramadol hydrochloride (50 mg), which is used in the treatment of pain.

## Tuesday, November 23, 2010

### 4258

4258 = 2 x 2129.

4258 has a representation as a sum of two squares: 4258 = 172 + 632.

4258 is a divisor of 2319 - 1.

4258 is the sum of the digits of the 18th Mersenne prime.

4528 Berg is an asteroid discovered in 1983 and named after Austrian composer Alban Berg.

## Monday, November 22, 2010

### 424

424 = 23 x 53.

424 has a representation as a sum of two squares: 424 = 102 + 182.

424 is 1144 in base 7 and 224 in base 14.

424 is the sum of ten consecutive primes: 424 = 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

On April 10, 1941, USS Niblack (DD 424) used depth charges against a German U-boat while conducing rescue operations of a torpedoed Dutch freighter. This was the first action taken by a U.S. naval vessel against the Axis Powers.

Source: Wikipedia

## Friday, November 19, 2010

### 602

602 = 2 x 7 x 43.

602 is the maximum number of regions into which 25 circles divide the plane.

602 is the smallest number starting a block of five consecutive numbers with the same number of prime divisors (including multiplicity): 602 = 2 x 7 x 43; 603 = 3 x 3 x 67; 604 = 2 x 2 x 51; 605 = 5 x 11 x 11; 606 = 2 x 3 x 101.

602 are the first three digits of 5602.

Telephone area code 602 covers most of the city of Phoenix, Arizona.

## Thursday, November 18, 2010

### 901

901 = 17 x 53.

901 has two representations as a sum of two squares: 901 = 12 + 302 = 152 + 262.

901 is the hypotenuse of two primitive Pythagorean triples: 9012 = 602 + 8992 = 4512 + 7802.

901 is the sum of the digits of the first 100 positive integers.

901 is a telephone area code in the state of Tennessee.

## Wednesday, November 17, 2010

### 5327

5327 = 7 x 761.

5327 is a multiple of 7 that uses only prime digits (2, 3, 5, and 7).

5327 is a number that cannot be written as a sum of three squares.

5327 is a value of n for which 2n and 7n together use each digit exactly once: 10654 and 37289.

Playmobil set #5327 is living room furniture for the Victorian doll house.

## Tuesday, November 16, 2010

### 590

590 = 2 x 5 x 59.

590 plus 590 ones is a prime. This is the only three-digit number with this property.

590 is a number n such that n concatenated with n + 2 gives the product of two numbers that differ by 1: 590592 = 768 x 769.

590 Tomyris is an asteroid discovered in 1906.

## Monday, November 15, 2010

### 70

70 = 2 x 5 x 7.

The sum of its divisors, including 70 itself, is a square (144): 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 = 144 = 122.

70 has a unique representation as a sum of three squares: 70 = 32 + 52 + 62.

70 is the 5th pentatope number.

70 is 77 in base 9.

Three score years and ten (70) is traditionally considered the natural human life span.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.

## Friday, November 12, 2010

### 1271

1271 = 31 x 41.

1271 is a number that cannot be written as a sum of three squares.

1271 has a sixth power whose last few digits are: . . . 21211121.

1271 is the sum of six positive fifth powers: 1271 = 45 + 35 + 15 + 15 + 15 + 15.

Marco Polo left Venice in the year 1271 on his travels to Asia.

## Thursday, November 11, 2010

### 168

168 = 23 x 3 x 7.

168 has a unique representation as a sum of three squares: 168 = 22 + 82 + 102.

168 is the number of primes less than 1,000.

144,648 = 861 x 168 = 492 x 294.

168 is the total number of spots on a standard (double-6) set of dominoes.

168 is the number of hours in a week.

## Wednesday, November 10, 2010

### 202

202 = 2 x 101.

202 has a representation as a sum of two squares: 202 = 92 + 112.

202 is the sum of four consecutive primes: 202 = 43 + 47 + 53 + 59.

202 is a semiprime palindrome equal to (2 + 3 + 5 + 7)2 - (22 + 32 + 52 + 72).

202293 begins with the digits 293 (a prime). Note that 293202 begins with the digits 202.

202 is the telephone area code for Washington, D.C.

## Tuesday, November 9, 2010

### 580

580 = 22 x 5 x 29.

580 has two representations as a sum of two squares: 580 = 22 + 242 = 162 + 182.

580 is a divisor of 592 - 1.

580 is 2404 in base 6, 404 in base 12, and 202 in base 17.

Interstate 580 in northern California connects the San Francisco Bay area with Interstate 5 through California's Central Valley.

## Monday, November 8, 2010

### 812

812 = 22 x 7 x 29. It is the product of a prime and the previous number (two consecutive integers): 812 = 28 x 29.

812 is a pronic number.

812 is the number of triangles of any size contained in a triangle of side 14 on a triangular grid.

The sum of the base 3 digits of 812 equals the sum of the base 9 digits of 812: (1 + 0 + 1 + 0 + 0 + 0 + 2) = (1 + 1 + 0 + 2) = 4.

Telephone area code 812 covers the southern part of Indiana.

## Friday, November 5, 2010

### 369

369 = 32 x 41.

369 has a representation as a sum of two squares: 369 = 122 + 152.

369 is the magic constant of an 9-by-9 magic square.

369 is the number of octominoes.

369 Aeria is a large asteroid discovered in 1893.

## Thursday, November 4, 2010

### 949

949 = 13 x 73.

949 has two representations as a sum of two squares: 949 = 72 + 302 = 182 + 252.

949 is the hypotenuse of two primitive Pythagorean triples: 9492 = 3012 + 9002 = 4202 + 8512.

949 is the larger number in a Ruth-Aaron pair.

NGC 949 is a galaxy in the constellation Triangulum.

## Wednesday, November 3, 2010

### 154

154 = 2 x 7 x 11.

154 is the maximum number of regions into which 17 lines divide the plane.

154 is the smallest number that is palindromic in bases 6 (414), 8 (232), and 9 (181).

William Shakespeare wrote 154 sonnets.

## Tuesday, November 2, 2010

### 78

78 = 2 x 3 x 13.

78 has a unique representation as a sum of three squares: 78 = 22 + 52 + 72.

78 is the smallest number with seven representations as a sum of two primes: 78 = 5 + 73 = 7 + 71, 11 + 67 = 17 + 61 = 19 + 59 = 31 + 47 = 37 + 41.

78 is the twelfth triangular number. According to the song "The Twelve Days of Christmas," 78 gifts were sent on the twelfth day.

78 is 66 in base 12.

A 78 is an old type of gramophone record playing at 78 revolutions per minute.

Source: Phillips, R. 2004. Numbers: Facts, Figures and Fiction. Badsey Publications.

## Monday, November 1, 2010

### 750

750 = 2 x 3 x 53. It is the product of exactly five primes, three of which are distinct (the first three primes).

750 is a number with 16 divisors: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750.

The customary size of a wine bottle in the United States is 750 milliliters