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

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