## Tuesday, January 31, 2012

### 476

476 = 2 x 2 x 7 x 17.

476 is the number of different products of subsets of the set {1, 2, 3, . . . 11}.

476 is 122122 in base 3 and 2112 in base 6. It is 13130 in base 4.

476 is the sum of three distinct positive cubes: 476 = 73 + 53 + 23.

476 is the lesser of two consecutive numbers (476 and 477) divisible by squares.

## Monday, January 30, 2012

### 748

748 = 22 x 11 x 17.

7484 = 313,044,726,016 = (3 + 1 + 3 + 0 + 4 + 4 + 726 + 0 + 1 + 6)4.

The sum of the base 3 digits (1000201) of 748 equals the sum of the base 9 digits (1021) of 748.

748 is the sum of factorials of distinct integers: 748 = 6! + 4! + 2! + 1! + 0!.

748 is the number of 3 x 3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

## Friday, January 27, 2012

### 206

206 = 2 x 103.

206 is the smallest number m such that 111111 + m is prime.

The squares of 206 and 208, two consecutive even numbers, use the same digits: 2062 = 42436 and 2082 = 43264.

206 = 13 + 23 + 23 + 43 + 53.

206 is 248 in base 9.

206 is the smallest number whose English name (two hundred and six) contains all five vowels exactly once.

Source: Number Gossip

## Thursday, January 26, 2012

### 652

652 = 22 x 163. It is a power of 2 written backwards.

652 has a unique representation as a sum of three squares: 652 = 22 + 182 + 182.

652 is the maximum number of regions into which 26 circles can divide the plane.

652 is the only known non-perfect number whose number of divisors and sum of smaller divisors are perfect.

652 is 220011 in base 3. It is 543 in base 11, 464 in base 12, and 246 in base 18.

## Wednesday, January 25, 2012

### 9797

9797 = 97 x 101. It is the product of two consecutive primes.

The square root of 9797 includes the digits 9797 immediately to the right of the decimal point: 98.979795918 . . .

9797 has two representations as a sum of two squares: 9797 = 312 + 942 = 492 + 862.

9797 is the hypotenuse of two primitive Pythagorean triples: 97972 = 49952 + 84282 = 58282 + 78752.

9797 is a divisor of 9112 - 1.

The sum of the digits of 9797 is eight times the number of digits: 9 + 7 + 9 + 7 = 8 x 4 = 32.

9797 is IBM in base 23.

## Tuesday, January 24, 2012

### 941

941 is a prime number.

941 has a representation as a sum of two squares: 941 = 102 + 292.

941 is the hypotenuse of a primitive Pythagorean triple: 9412 = 5802 + 7412.

941 is the smallest prime formed by the reverse concatenation of three consecutive squares.

941 is the smallest number whose proper substrings sum to its reversal: 9 + 4 + 1 + 94 + 41 = 149.

941 is the smallest prime resulting from the nine-digit fraction equation (A + B)C + (D + E)F + (G + H)I,  where the letters A through I represent any combination of the nine digits 1 through 9. Note that (4 + 5)3 + (6 + 8)2 + (7 + 9)1 is the only distinct solution for 941.

Source: Prime Curios!

## Monday, January 23, 2012

### 737

737 = 11 x 67.

737 is the smallest multidigit number m such that m+ 2 is prime.

737 is 515 in base 12 and 191 in base 21.

737 is the sum of two positive cubes: 737 = 93 + 23.

The Boeing 737 is a twin-engine, narrow-body jet airliner that first flew in 1967.

Source: Prime Curios!

## Friday, January 20, 2012

### 358

358 = 2 x 179.

358 is the smallest number whose first two digits are distinct odd primes such that their sum equals the third digit.

The sum of the digit splits of 358 is equal to the product of the digits of 358: (3 + 58) + (35 + 8) + (3 + 5 + 8) = 120 = 3 x 5 x 8.

358 has a base 3 representation (111021) that ends with its base 7 representation (1021).

358 is the sum of six consecutive primes: 358 = 47 + 53 + 59 + 61 + 67 + 71.

The Jaguar XJ X358 is a luxury car that debuted in 2007.

Source: Prime Curios!

## Thursday, January 19, 2012

### 278

278 = 2 x 139.

278 is the sum of the first 18 nonprimes.

278 has the representation 28 + 22.

278 is the closest integer to 6π.

278 is 545 in base 7.

Telephone area code 278 serves Ann Arbor, Michigan, and the surrounding area.

## Wednesday, January 18, 2012

### 636

636 = 22 x 3 x 53.

The decimal part of the fifth root of 636 begins with the digits 636.

636 is 336 in base 14.

636 is the sum of 10 consecutive primes: 636 = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83.

Telephone area code 636 serves the east-central portion of the state of Missouri.

## Tuesday, January 17, 2012

### 4393

4393 = 23 x 191.

4393 is 1000100101001 in base 2 (binary).

4393 is a number such that each digit leaves the same nonzero remainder when each is divided into the number.

4393 is a multiple of 23 such that reversing the digits and subtracting 1 gives a result that is also a multiple of 23.

4393 is the sum of distinct 5th powers: 4393 = 55 + 45 + 35 + 15.

Parlophone recording R. 4393 featured the song "No Other Baby" by The Vipers, later recorded by Paul McCartney.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, January 13, 2012

### 438

438 = 2 x 3 x 73.

438 is a Smith number because the sum of its digits is equal to the sum of the digits of its prime factors: 4 + 3 + 8 = 2 + 3 + 7 + 3 = 15.

438 is 110110110 in base 2 (binary) and 666 in base 8. It is 3223 in base 5 and 141 in base 19.

438 divides 656 - 1.

438 is the sum of 10 positive 5th powers: 438 = 35 + 25 + 25 + 25 + 25 + 25 + 25 + 15 + 15 + 15.

The term "438 match" or "438 game" has been used by cricket news media to describe the famous 2006 One Day International in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.

## Thursday, January 12, 2012

### 724

724 = 22 x 181.

724 has a representation as a sum of two squares: 724 = 182 + 202.

724 divides 194 - 1.

724 is the number of perfect connected undirected simple graphs on seven nodes.

724 is the number of different arrangements of 10 non-attacking queens on a 10 x 10 chessboard.

724 Hapag is an asteroid discovered in 1911, lost, then rediscovered in 1988.

## Wednesday, January 11, 2012

### 1293

1293 = 3 x 431.

The sum of the divisors of 1293 is a cube: 1 + 3 + 431 + 1293 = 1728 = 123.

1293 is a divisor of 2610 - 1.

1293 is a structured truncated tetrahedral number.

12933 = 2161700757 is the sum of three consecutive primes: 2161700757 = 720566909 + 720566921 + 720566927.

Southern Pacific 1293 is a retired switch engine built in 1924 and now on display in Tracy, California.

## Tuesday, January 10, 2012

### 1126

1126 = 2 x 563.

1126 is the number of 3 x 4 checkerboards in which the set of red squares is edge-connected.

1126 is the sum of the first 15 Sophie Germain primes.

11263 (1427628376) includes the digits of 11262 (1267876).

In the year 1126, Adelard of Bath translated Muhammad ibn-Musa al-Kwarizmi's arithmetic and astronomical tables into Latin.

Source: On-Line Encyclopedia of Integer Sequences

## Monday, January 9, 2012

### 826

826 = 2 x 7 x 59.

826 is the sum of seven positive 5th powers: 826 = 35 + 35 + 35 + 25 + 25 + 25 + 15.

The sum of the digits of the 826th prime (6343) equals the sum of the digits of 826: 6 + 3 + 4 + 3 = 8 + 2 + 6 = 16.

The digits of 8262 (68276) contain the digits of 826 as a subsequence.

826 National is a nonprofit organization that manages a network of writing and tutoring centers.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, January 6, 2012

### 423

423 = 32 x 47.

423 is a number that does not have any digits in common with its cube (75686967).

423 is the sum of 13 consecutive primes: 423 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59.

Inserting the digit 1 between adjacent digits of 423 produces a prime: 41213.

423 Diotima is one of the largest main-belt asteroids.

## Thursday, January 5, 2012

### 537

537 = 3 x 179.

537 divides the sum of the cubes of the first 537 primes.

537 is 656 in base 9.

The sum of the digits of 537 is 5 times the number of digits: 5 + 3 + 7 = 5 x 3 = 15.

537 is the average of three successive primes: 537 = (523 + 541 + 547)/3.

In the final official count in the 2000 U.S. presidential election, George W. Bush defeated Al Gore by 537 votes in the state of Florida.

## Wednesday, January 4, 2012

### 816

816 = 24 x 3 x 17.

816 is the 16th tetrahedral number.

816/(8 x 1 x 6) = 816/48 = 17, a prime. 816 is the largest three-digit integer that has this property.

816 is 30300 in base 4 and 330 in base 16. It is 2244 in base 7 and 424 in base 14.

816 is a telephone area code that covers the Kansas City area in Missouri.

Source: Prime Curios!

## Tuesday, January 3, 2012

### 124

124 = 22 x 31.

124 is 444 in base 5.

124 is the smallest number whose sum of digits (1 + 2 + 4 = 7) as well as the number itself are one less than the cube of a prime.

124 is the smallest number with the property that its first three multiples contain the digit 2: 124, 248, and 372.

124 is the sum of eight consecutive primes: 124 = 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

124 = 27 - 22.

124 = 52 + 52 + 52 + 72. The Fiat 124 was a family car produced in Italy from 1966 to 1974.