Thursday, June 9, 2011

644

644 = 22 x 7 x 23.

644 is a Perrin number.

644 is 212212 in base 3 and 2552 in base 6.

644 is a number made up of only semiprime digits (4, 6, and 9).

644 is the sum of five fourth powers: 644 = 54 + 24 + 14 + 14 + 14.

The USS Lewis and Clark (SSBN-644) was a ballistic missile submarine in the U.S. Navy.

Wednesday, June 8, 2011

2098

2098 = 2 x 1049. It is a semiprime with a prime sum of factors: 2 + 1049 = 1051, a prime. It is also a semiprime one less than a prime: 2098 + 1 = 2099, a prime. The sum of its digits is a prime: 2 + 0 + 9 + 8 = 19, a prime.

2098 has a representation as a sum of two squares: 2098 = 272 + 372.

2098 is 747 in base 17.

2098 is the sum of 12 sixth powers.

A transit of Mercury (its passage across the sun) is expected to occur in the year 2098.

Tuesday, June 7, 2011

1100

1100 = 22 x 52 x 11.

1100 has a base 2 (binary) representation that ends in the digits 1100: 10001001100. 1100 is 3131 in base 7. It is 778 in base 12, 668 in base 13, and 588 in base 14.

1100 is the sum of two palindromic primes in three ways: 1100 = 181 + 919 = 313 + 787 = 373 + 727.

1100 is the sum of a square and a cube: 1100 = 103 + 102. It is the sum of two distinct powers of 10.

1100 is the sum of eight positive fifth powers: 1100 = 35 + 35 + 35 + 35 + 25 + 25 + 25 + 25.

1100 AD is an online multiplayer strategy games set in medieval times.

Monday, June 6, 2011

757

757 is a prime number.

757 has a representation as a sum of two squares: 757 = 92 + 262.

757 is the hypotenuse of a primitive Pythagorean triple: 7572 = 4682 + 5952.

757 is the smallest palindromic prime that remains prime when its leading digit is replaced by any nonzero digit that is a power of 2: 157, 257, 457, 857.

757 is the largest of three three-digit palindromic primes that are not the sum of consecutive composite numbers. The others are 313 and 383.

The Boeing 757 is a mid-size, narrow-body, twin-engine jetliner.

Friday, June 3, 2011

879

879 = 3 x 293.

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

The fifth root of 879 has a decimal part that begins with the digits 879: 3.879696696. . .

The sum of the digits of 879 is 8 times the number of digits: 8 + 7 + 9 = 24 = 8 x 3.

879 is a number n such that n - 2 and n + 2 are primes: 877 and 881.

NGC 879 is a galaxy in the constellation Cetus, discovered in 1886.

Thursday, June 2, 2011

536

536 = 23 x 67.

536 starts with the same four digits in base 3 and base 4: 201212 and 20120. It has double digits in base 6 (2252), base 9 (655), base 11 (448), and base 12 (388). It is 323 in base 13.

536 is the lowest happy number beginning with the digit 5.

536 is the solution to the Dancing School Problem with 3 girls and 12 boys.

The stomachion of Archimedes (a 14-piece dissection puzzle) has 536 solutions.

Wednesday, June 1, 2011

450

450 = 2 x 32 x 52.

450 has two representations as a sum of two squares: 450 = 32 + 212 = 152 + 152.

450 is 3300 in base 5, 1212 in base 7, 550 in base 9, 242 in base 14, and 200 in base 15.

450 is the sum of two consecutive primes: 450 = 223 + 227.

450 and 4502 = 202,500 have the same digit sum: 4 + 5 + 0 = 2 + 0 + 2 + 5 + 0 + 0 = 9.

450 is a perfect score in Canadian five-pin bowling.

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