## Wednesday, October 31, 2012

### 182

182 = 2 x 7 x 13.

182 is a pronic number; it is the product of two consecutive numbers: 182 = 13 x 14.

182 is 222 in base 9 and 77 in base 25. It is 20202 in base 3 and 1212 in base 5.

182 is the number of connected bipartite graphs with 8 vertices.

182 = 33 + 33 + 43 + 43 = 142 - 14.

The USS Salmon  (SS-182) was a United States Navy submarine during World War II.

Source: Number Gossip

## Tuesday, October 30, 2012

### 777

777 = 3 x 7 x 37.

777 is a divisor of 1003 - 1.

777 is 3333 in base 6.

Surrounding the number 777 with the number 11 forms the prime numbers 11777, 77711, 1177711, and 11117771111.

The Boeing 777 is a long-range, wide-body, twin-engine jet airliner.

Source: Numeropedia

## Monday, October 29, 2012

### 869

869 = 11 x 79.

869 is the number of different resistances that can be created in a circuit of nine equal resistors (A048211).

The sum of the digits of 869 equals the sum of the digits of the 869th prime (6737) (A033549). 869 and the 869th prime (6737) have only the digit 6 in common (A107937).

869 is a number that yields a prime when 0 is inserted anywhere in it (but not added to the end or beginning) (A216169).

## Friday, October 26, 2012

### 2142

2142 = 2 x 3 x 3 x 7 x 17.

2142 is a divisor of 554 - 1.

2142 is 32032 in base 5.

2142 is the sum of the totient function for the first 83 integers.

2142 is the number of ways of writing the number 63 as the sum of nine nonnegative cubes (A173682).

2142 is the sum of 10 consecutive primes (A127337): 2142 = 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, October 25, 2012

### 198

198 = 2 x 3 x 3 x 11.

198 is the smallest number with ten representations as a sum of four positive squares: 198 = 12 + 22 + 72 + 122 = 12 + 42 + 92 + 102 = 22 + 32 + 42 + 132 = 22 + 32 + 82 + 112 = 22 + 52 + 52 + 122 = 22 + 72 + 82 + 92 = 32 + 32 + 62 + 122 = 32 + 52 + 82 + 102 = 42 + 52 + 62 + 112 = 62 + 72 + 72 + 82.

198 is the first number between a twin prime pair such that if multiplied by its reversal (198 x 891 = 176418), the product is also between a twin prime pair.

198 can be formed by concatenating 19 and 8, where 19 is the 8th prime number. 198 is the (19 x 8 = 152)nd composite number.

198 = 11 + 99 + 88 = (100 - 1)(100-98).

198 x 27 = 5346 = 18 x 297. Each equality uses each of the nine digits 1 to 9 once.

Source: Prime Curios!

## Wednesday, October 24, 2012

### 756

756 = 2 x 2 x 3 x 3 x 3 x 7.

756 is a pronic number, the product of two consecutive numbers, 27 and 28.

12 x 63 = 756 = 21 x 36.

756 is the maximum number of regions into which 14 spheres divide space.

756!/657! - 1 is a prime.

756 is 11011 in base 5. It is 3300 in base 6.

756 is the sum of six consecutive primes: 756 = 109 + 113 + 127 + 131 + 137 + 139.

Source: Number Gossip

## Tuesday, October 23, 2012

### 387

387 = 3 x 3 x 43.

387 is the lesser of two consecutive numbers divisible by a square (A068781).

387 is 110000011 in base 2 (binary) (A006995).

387 x 7 - 38 = 2671, the 387th prime.

387 is the smallest number with sort-then-add persistence 10.

Source: Prime Curios!

## Monday, October 22, 2012

### 667

667 = 23 x 29. It is the product of two successive primes (A006094) and two distinct Sophie Germain primes (A157344).

667 is the maximum number of regions into which 36 lines divide the plane (A000124).

667 is the number of asymmetric trees with 16 vertices (A000220).

667, 669, and 671 are all semiprimes (A092125).

667 YCF was on the license plates of the car driven by Meeno Paloma (Lou Diamond Philips) in the 2009 movie The Triangle.

Source: Prime Curios!

## Friday, October 19, 2012

### 355

355 = 5 x 71.

355 divided by the prime number 113 yields a nice approximation of pi: 355/113 = 3.141592. . .

355 is the number of labeled topologies with four elements.

355 = 3 x 5! - 5.

355 is 543 in base 8 and 434 in base 9.

Source: Prime Curios!

## Thursday, October 18, 2012

### 740

740 = 2 x 2 x 5 x 37.

740 has two representations as a sum of two squares: 740 = 82 + 262 = 162 + 222.

740 is the number of self-avoiding walks of length 8.

740 is 3232 in base 8 and 345 in base 15.

740 is a hypotenuse for which there exist four distinct integer triangles (A084648).

## Wednesday, October 17, 2012

### 129

129 = 3 x 43.

129 is 10000001 in base (binary). It is 333 in base 6.

129 is the smallest number with four representations as a sum of three positive squares: 129 = 12 + 82 + 82 = 22 + 22 + 112 = 22 + 52 + 102 = 42 + 72 + 82.

129 is the sum of the first ten primes: 129 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

129 is the smallest sum of distinct seventh powers: 129 = 17 + 27.

Source: Number Gossip

## Tuesday, October 16, 2012

### 930

930 = 2 x 3 x 5 x 31. It is a pronic number, the product of two consecutive integers (A002378): 930 = 30 x 31. It is also the product of a prime and the previous number (A036689).

930 is the number of even permutations of seven elements with no fixed points.

930 is 656 in base 12 and 567 in base 13.

The sum of the divisors of 930 is a square (A006532): 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 31 + 62 + 93 + 155 + 186 + 310 + 465 + 930 = 2304 = 482.

## Monday, October 15, 2012

### 1124

1124 = 2 x 2 x 281.

1124 has a representation as a sum of two squares: 1124 = 102 + 322.

1124 is the maximum number of regions into which 34 circles divide a plane.

1124 is a number whose product of digits is equal to its sum of digits: 1 + 1 + 2 + 4 = 8 = 1 x 1 x 2 x 4.

1124 is 686 in base 13, 464 in base 16, 323 in base 19, and 272 in base 22.

1124 is a Leyland number (A076980).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, October 12, 2012

### 617

617 is a prime number.

617 and 619 form a twin prime pair.

617 = 1!2 + 2!2 + 3!2 + 4!2.

617 is the largest multi-digit prime that is exactly half of a number formed with distinct consecutive digits: 1234.

617 has a representation as a sum of two squares: 617 = 162 + 192.

617 is the hypotenuse of a primitive Pythagorean triple: 6172 = 1052 + 6082.

617 is a divisor of 3111 - 1.

Source: Prime Curios!

## Thursday, October 11, 2012

### 914

914 = 2 x 457.

914 has a representation as a sum of two squares: 914 = 172 + 252.

914 is the number of binary rooted trees with 15 vertices.

914 is 494 in base 14.

The sum of the digits of 914 (9 + 1 + 4 = 14) is a substring of 914 (A052018).

Each of the digits of 914 are squares (A046030).

## Wednesday, October 10, 2012

### 813

813 = 3 x 271.

813 are the first three digits of 813e.

813 is 393 in base 15.

813 is a divisor of 99999 (A027893) and 9999999999 (A027895): 99999/813 = 123 and 9999999999/813 = 12300123.

813 is the concatenation of the sixth Fibonacci number and the sixth prime (A138821).

## Tuesday, October 9, 2012

### 7011

7011 = 3 x 3 x 19 x 41.

7011 yields a prime whenever 1 is inserted anywhere in the number (A068679 and A216165): 17011, 71011, and 70111 are all primes.

7011 is the sum of three cubes of distinct primes (A138853 and A138854): 7011 = 193 + 53 + 33.

7011 is the number of 16-crossing knots with symmetry group Z2 (A052412).

7011 is the number of 5 x 5 arrays of squares of integers, symmetric about the main diagonal, with all rows summing to 36 (A156385).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, October 5, 2012

### 793

793 = 13 x 61.

793 is one less than twice its reversal: 793 = 2(397) - 1.

793 is a dodecagonal number and a centered dodecagonal number (A003154).

793 has two representations as a sum of two squares: 793 = 32 + 282 = 82 + 272.

793 is the hypotenuse of two primitive Pythagorean triples: 7932 = 1682 + 7752 = 4322 + 6652.

## Thursday, October 4, 2012

### 598

598 = 2 x 13 x 23.

598 is the largest number that is the sum of its first digit, the square of its second digit, and the cube of its third digit: 598 = 51 + 92 + 83.

598 is 21112 in base 4. It is 4343 in base 5.

598 is a divisor of 474 - 1.

598 is the maximum number of regions into which 13 spheres divide space.

Source: Number Gossip

## Wednesday, October 3, 2012

### 787

787 is a prime number.

The six integers following 787 are divisible by the first six primes, respectively.

787 is the smallest prime that can be represented as the sum of a prime and its reversal in two different ways.

787 is 30103 in base 4, 656 in base 11, and 313 in base 16.

787 is the sum of five consecutive primes: 787 = 149 + 151 + 157 + 163 + 167.

The Boeing 787 Dreamliner is a long-range, mid-size, twin-engine jet airliner.

Source: Prime Curios!

## Tuesday, October 2, 2012

### 254

254 = 2 x 127.

254 is the maximum number of regions into which 22 lines divide a plane. It is a central polygonal number (A000124).

254 is the smallest multi-digit composite number all of whose proper divisors include the digit 2.

254 is the sum of the first 13 semiprimes (A062198).

The state of Texas has 254 counties, the most of any state of the United States.

## Monday, October 1, 2012

### 403

403 = 13 x 31. It is the smallest semiprime whose factors form a pair of emirps (13 and 31).

403 is 110010011 in base 2.

403 has a unique representation as a sum of three squares: 403 = 32 + 132 + 152.

403 is a heptagonal number.

403 = 23 + 33 + 33 + 53 + 63.

Source: Prime Curios!