## Friday, April 30, 2010

### 980

980 = 22 x 5 x 72.

980 has a representation as a sum of two squares: 980 = 142 + 282.

980 is a divisor of 992 - 1.

980 is 1100022 in base 3 and 500 in base 14. NGC 980 is a galaxy in the constellation Andromeda.

Source: WolframAlpha

## Thursday, April 29, 2010

### 648

648 = 23 x 34 = 12 x 23 x 34.

648 has a representation as a sum of two squares: 648 = 182 + 182.

648 is the smallest number whose decimal part of its 6th root begins with the digits 1 to 9 in some order: 2.941682753. . . .

6483 = 272,097,792 = (-27 - 20 - 97 + 792)3.

648 is 220000 in base 3, 22020 in base 4, 3000 in base 6, 800 in base 9, and 200 in base 18. EgyptAir Flight 648 was a Boeing 737-200 airliner hijacked in 1985 by the terrorist Abu Nadal Organization.

## Wednesday, April 28, 2010

### 119

119 = 7 x 17. It is the product of the first two primes ending with 7.

119 = 14 + 15 + 16 + 17 + 18 + 19 + 20.

119 is 1110111 in base 2 (binary) and 77 in base 16.

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

119 is the smallest three-digit number having two prime digit permutations: 191 and 911. In the United States, the largest amount of money one can have in coins without being able to make change for a dollar is 119 cents. The combination is three quarters, four dimes, and four pennies.

## Tuesday, April 27, 2010

### 764

764 = 22 x 191.

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

764 is the number of 8 x 8 symmetric permutation matrices.

764 is the sum of three distinct positive cubes: 93 + 33 + 23 = 764.

764 is the sum of seven positive fifth powers: 764 = 35 + 35 + 35 + 25 + 15 + 15 + 15. 764-HERO was a rock band from Seattle, Washington.

## Monday, April 26, 2010

### 962

962 = 2 x 13 x 37.

962 has two representations as a sum of two squares: 962 = 12 + 312 = 112 + 292.

962 is 4242 in base 6 and 282 in base 20.

962 is the sum of three non-zero fourth powers: 962 = 34 + 44 + 54.

962 is a centered square number: 4n2 + 4n + 2, for n = 15. The Porsche 962 was a sports-prototype racing car, first built in 1984.

## Friday, April 23, 2010

### 104

104 = 23 x 13.

104 has a representation as a sum of two squares: 104 = 22 + 102.

104 is the number of integer partitions of 23 into distinct parts.

104 is a divisor of 252 - 1.

104 is 88 in base 12. 104 is the atomic number of the element rutherfordium.

Source: Wikipedia

## Thursday, April 22, 2010

### 412

412 = 22 x 103.

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

412 is the number of subsets of {1, 2, 3, . . . , 11} that have a sum divisible by 5.

412 is 120021 in base 3 and 345 in base 11. A Neptune-Pluto conjunction occurred in Taurus in the year 412.

## Wednesday, April 21, 2010

### 800

800 = 25 x 52.

800 has two representations as a sum of two squares: 800 = 42 + 282 = 202 + 202.

800 is 2222 in base 7 and 200 in base 20.

8008 + 1 is a prime number.

800 is the sum of four consecutive prime numbers: 800 = 193 + 197 + 199 + 211. T-800 was the robot in the film The Terminator.

## Tuesday, April 20, 2010

### 8518

8518 = 2 x 4259.

8518 is 6444 in base 11.

It takes 11 steps of the "reverse and add" algorithm to reach a palindrome: 8518; 8518 + 8158 = 16676;16676 + 67661 = 84337; . . . 1771331771.

183 x 28518 - 1 is a prime number. LEGO product 8518 is the Ben 10 Alien Force Jet Ray.

## Monday, April 19, 2010

### 2096

2096 = 24 x 131.

2096 is 2212122 in base 3, 200300 in base 4, and 4060 in base 8.

2096 is a number such that n2 + 1 and n2 + 3 are both primes.

2096 is the sum of four nonzero squares in exactly nine ways. 2096 is a year in which there will be five Wednesdays in the month of February. This last occurred in the year 1984 and will happen again in 2012.

## Friday, April 16, 2010

### 596

596 = 22 x 149.

596 has a representation as a sum of two squares: 596 = 142 + 202.

596 is the maximum number of regions into which 34 lines divide the plane.

596 is the number of Hamiltonian cycles of a 4 x 9 rectangle graph. 596 was the code name for China's first nuclear weapons test, detonated Oct. 16, 1964.

## Thursday, April 15, 2010

### 961

961 = 312. It is a perfect square.

961 is the largest square with strictly decreasing digits. It is also the largest prime power of a prime with strictly decreasing digits.

The digits of 961 can be rearranged to give two other squares: 169 = 132 and 196 = 142.

961 is 12321 in base 5 and 4241 in base 6. 961 beer is brewed in Beirut, Lebanon.

## Wednesday, April 14, 2010

### 705

705 = 3 x 5 x 47.

705 is the smallest Lucas psuedoprime.

705 is a rhombic matchstick number: n(3n + 2) for n = 15.

705 is an odd interprime because it lies at the midpoint between two consecutive odd primes, 701 and 709. The IBM 705 was one of the most powerful data processing systems available in the mid-1950s.

## Tuesday, April 13, 2010

### 208

208 = 24 x 13.

208 has a representation as a sum of two squares: 208 = 82 + 122.

208 = 28 - 48.

208 is a divisor of 252 - 1.

208 = 22 + 32 + 52 + 72 + 112. 208 is the telephone area code for the state of Idaho.

## Monday, April 12, 2010

### 3892

3892 = 22 x 7 x 139.

3892 has the representation 24 x 35 + 4.

3892 is a divisor of 436 - 1.

3892 is 30004 in base 6 and 7464 in base 8.

The 3892nd triangular number contains only the digits 5, 7, and 8: 7575778. The asteroid 3892 Dezsö was discovered in 1941.

## Friday, April 9, 2010

### 863

863 is a prime number.

863 is the largest three-digit prime that can be written as the sum of fifteen consecutive primes: 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 = 863.

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

863 = (11 + 71) + (11 x 71), where 11, 71, and 863 are all primes.

863 is a value of n so that n(n + 6) is a palindrome: 863(869) = 749947. 863 is a telephone area code for central Florida.

Source: Prime Curios!

## Thursday, April 8, 2010

### 372

372 = 22 x 3 x 31.

372 has a unique representation as a sum of three squares: 372 = 42 + 102 + 162.

372 is a hexagonal pyramidal number, having the form n(n + 1)(4n - 1)/6 for n = 8.

372/(3 + 7 + 2) is a prime number, 31.

101,556 = 273 x 372 = 651 x 156. NGC 372 is a triple star in the constellation Pisces.

## Wednesday, April 7, 2010

### 446

446 = 2 x 223.

446 is the smallest number that can be written as the sum of three distinct squares in eight different ways: 446 = 212 + 22 + 12 = 192 + 92 + 22 = 192 + 72 + 62 = 182 + 112 + 12 = 172 + 112 + 62 = 152 + 142 + 52 = 152 + 112 + 102 = 142 + 132 + 92.

446 is 676 in base 8 and 545 in base 9.

446 is a self number. A self number is an integer that cannot be generated by any other integer added to that other integer's digits. 446 Aeternitas is an asteroid discovered in 1899.