## Monday, October 31, 2011

### 1393

1393 = 7 x 199.

1393 is a divisor of 923 - 1.

1393 is an NSW number.

1393 is 4030 in base 7 and 717 in base 14.

1393 is the number of nodes in a regular 16-sided polygon with all diagonals drawn. International Brotherhood of Electrical Workers Local Union 1393 in based in Indianapolis, Indiana.

## Friday, October 28, 2011

### 768

768 = 28 x 3.

768 has a unique representation as a sum of three squares: 768 = 162 + 162 + 162.

768 is a divisor of 654 - 1.

768 is the number of subsets of {1, 2, 3, . . . , 12} that have an integer average.

416,768 = 7682 - 4162. RSA-768 was a member of set of large semiprimes (RSA Numbers) that were part of the RSA Factoring Challenge.

## Thursday, October 27, 2011

### 273

273 = 3 x 7 x 13.

273 is 100010001 in base 2 (binary), 333 in base 9, and 111 in base 16.

The 273rd prime minus the sum of gaps between the first 273 consecutive primes minus 1 equals 273.

273 is the sum of each of two consecutive sums of consecutive numbers: 273 = 36 + 37 + 38 + 39 + 40 + 41 + 42 = 43 + 44 + 45 + 46 + 47 + 48. The zero on the Celsius temperature is 273 (to the nearest whole number) on the Kelvin temperature scale.

## Wednesday, October 26, 2011

### 762

762 = 2 x 3 x 127.

It is a Smith number because the sum its digits is equal to the sum of the digits of its prime factors: 7 + 6 + 2 = 2 + 3 + 1 + 2 + 7 = 15.

762 is the starting location of the string 999999 in the decimal expansion of pi. This is known as the Feynman point.

762 is the sum of four consecutive primes: 762 = 181 + 191 + 193 + 197.

762 is a divisor of 193 - 1. USS Columbus (SSN-762) was a submarine in the U.S. Navy, launched in 1992.

## Tuesday, October 25, 2011

### 540

540 = 22 x 33 x 5. All prime divisors are consecutive primes starting at 2.

540 is divisible by its reverse, 45.

540 is the sum of three distinct positive cubes: 540 = 83 + 33 + 13. 540 is the sum of the internal angles of a five-sided convex polygon (or a pentagon).

## Monday, October 24, 2011

### 1179

1179 = 32 x 131.

1179 is the sum of the squares of three consecutive primes: 1179 = 172 + 192 + 232.

1179 and 11792 (1390041) have the same digit sum: 1 + 1 + 7 + 9 = 1 + 3 + 9 + 0 + 0 + 4 + 1 = 18.

1179 is a divisor of 5310 - 1.

1179 is 2233 in base 8. NGC 1179 is a barred spiral galaxy in the constellation Eridanus.

## Friday, October 21, 2011

### 3278

3278 = 2 x 11 x 149. The three prime factors are distinct in length.

327824 + 1 is a prime number.

The decimal expansion of pi has a string of two 7s starting in the 3278th position.

In base 6, the digits of 3278 are, in order, the first five digits of the periodic sequence with initial period 2, 3, 1, 0: 23102. The IBM 3278 was a member of a class of video terminals (display devices) manufactured in the 1970s.

## Thursday, October 20, 2011

### 324

324 = 22 x 34.

324 is a perfect square: 324 = 182.

324 is the smallest untouchable square. Untouchable numbers are those that are not the sum of the proper divisors of any number.

324 is the largest possible product of positive integers with sum 16. 324 Bamberga, discovered in 1892, is one of the largest asteroids in the main belt.

## Wednesday, October 19, 2011

### 418

418 = 2 x 11 x 19.

418 has the property that the sum of its prime factors is equal to the product of its digits: 2 + 11 + 19 = 4 x 1 x 8 = 32.

418 is the sum of three nonzero fourth powers: 418 = 44 + 34 + 34.

418 is 262 in base 13. 418 is a telephone area code in the province of Quebec, Canada.

## Tuesday, October 18, 2011

### 924

924 = 22 x 3 x 7 x 11.

924 is the smallest value of n such that 2n choose n is divisible by n2: 1848 choose 924 is divisible by 9242.

924 is 1110011100 in base 2 (binary).

924 is a divisor of 432 - 1. The Porsche 924 was an automobile produced from 1976 t0 1988.

## Monday, October 17, 2011

### 1136

1136 = 24 x 71.

1136 is a divisor of 1710 - 1.

1136 is a member of the toothpick sequence starting from a cross formed from four toothpicks.

1136 is the number of ways of writing 4 as a sum of eight squares.

1136 is the smallest number whose sum of squares of digits is 47: 12 + 12 + 32 + 62 = 47. Spanish mathematician and astronomer Abraham bar Hiyya Ha-Nasi (Savasorda) died in the year 1136.

## Friday, October 14, 2011

### 613

613 is a prime number.

613 is the smallest prime such that bringing the first digit to the back produces a triangular number (136) and repeating this operation produces a square (361).

613 is the smallest number n such that the numbers of divisors of n, n + 1, n + 2, and n + 3 are k, 2k, 4k, and 8k for k = 2.

613 has a representation as a sum of two squares: 613 = 172 + 182.

613 is the hypotenuse of a primitive Pythagorean triple: 6132 = 352 + 6122. The 613 commandments (613 Mitzvot) is a numbering of the statements and principles of law, ethics, and spiritual practice contained in the Torah (the Five Books of Moses).

## Thursday, October 13, 2011

### 1029

1029 = 3 x 73.

1029 is the smallest order for which there are 19 groups.

1029 is 4433 in base 6, 3000 in base 7, and 333 in base 18. It can be written from base 2 to base 18 using only the digits from 0 to 9.

The sum of the base 2 digits (10000000101) of 1029 equals the sum of the base 4 digits (100011) of 1029.

1029 is the sum of distinct powers of 4: 1029 = 45 + 41 + 40. The Atari 1029 printer was one of Atari's final printers for the XL series computers in 1984.

## Wednesday, October 12, 2011

### 108

108 = 22 x 33. It is the product of the first three numbers raised to themselves: 108 = 11 x 22 x 33.

108 is the smallest number whose divisors contain every digit at least once. The divisors are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.

108 is 99 in base 11.

The interior angles of a regular (equilateral) pentagon measure 108 degrees each.

There are 108 different types of heptomino, a shape made by fitting together seven squares. For an article on the symbolism of 108, see the webpage "Why 108."

## Tuesday, October 11, 2011

### 505

505 = 5 x 101.

505 has two representations as a sum of two squares: 505 = 82 + 212 = 122 + 192.

505 is the hypotenuse of two primitive Pythagorean triples: 5052 = 2172 + 4562 = 3362 + 3772.

5053 = 593 + 1633 + 4993, where 59, 163, and 499 are primes.

505 is the magic constant for a 10 x 10 normal magic square. 505 is the model number of a type of denim jeans produced by Levi Strauss & Co.

## Friday, October 7, 2011

### 196

196 = 22 x 72.

196 is the smallest square that contains a multidigit prime number as a substring.

196 = 142 is a perfect square.

196 is the difference of two square numbers: 196 = 502 - 482.

The consecutive squares 132 = 169 and 142 = 196 use the same digits; 312 = 961 also uses the same digits.

196 has a unique representation as a sum of three squares: 196 = 42 + 62 + 122.

It is conjectured that 196 is the lowest Lychrel number. It is the lowest number not known to produce a palindrome by repeated reversal and addition. The algorithm has been tested to more than 246 million digits without finding a palindrome, but no one has ever proved that it will never produce one. The Mercedes-Benz W196 was an entry in the 1954 and 1955 Formula One car racing series, winning 9 of 12 races.

## Thursday, October 6, 2011

### 482

482 = 2 x 241.

482 has a representation as a sum of two squares: 482 = 112 + 192.

482 is 222 in base 15. It is 585 in base 9.

482 is a number whose square (232,324) and cube (111,980,168) use different digits. 482 Music is an independent record label featuring international jazz.

## Wednesday, October 5, 2011

### 981

981 = 32 x 109.

981 has a representation as a sum of two squares: 981 = 92 + 302.

327 + 654 = 981 uses each of the digits 1-9 once.

981 and 9812 = 962,361 have the same initial digit and final digit. Turkish Airlines Flight 981 was a McDonnell Douglas DC-10 that crashed in France in 1974, killing all 346 people on board.

Source: Numeropedia

## Tuesday, October 4, 2011

### 186

186 = 2 x 3 x 31.

186 is the maximum number of regions into which 9 spheres divide space.

7 x 5 x 3 x 2 - 4 x 3 x 2 x 1 = 186.

186 x 39 = 7254 uses each of the nine digits 1-9 once.

186 is 1221 in base 5 and 272 in base 8. 186 is the number of odd days in a year that is not a leap year.

## Monday, October 3, 2011

### 594

594 = 2 x 33 x 11.

594 is 1001010010 in base 2 (binary). It is 4334 in base 5 and 1122 in base 8.

594 is the smallest number that has 10 representations as a sum of three positive squares: 594 = 12 + 82 + 232 = 32 + 32 + 242 = 32 + 122 + 212 = 42 + 72 + 232 = 42 + 172 + 172 = 52 + 132 + 202 = 72 + 162 + 172 = 82 + 132 + 192 = 122 + 152 + 152 = 132 + 132 + 162.

594 = 15 + 29 + 34.

594 is the sum of 10 consecutive primes: 594 = 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79. USS Permit (SSN-594) was a nuclear submarine that was launched in 1961 and decommissioned in 1991.