## Wednesday, February 29, 2012

### 1315

1315 = 5 x 263.

1315 is the middle semiprime of a semiprime triple n - 2, n, n + 2: 1313, 1315, 1317.

1315 is the concatenation of the sixth prime number (13) and the sixth lucky number (15).

The sum of the factorials of the digits of 1315 is a power of 2: 1! + 3! + 1! + 5! = 128 = 27.

1315 is the sum of three consecutive primes: 1315 = 433 + 439 + 443.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, February 28, 2012

### 940

940 = 2 x 2 x 5 x 47.

940 has a unique representation as a sum of three squares: 940 = 22 + 62 + 302.

940 is the sum of the squares for four consecutive primes: 940 = 112 + 132 + 172 + 192.

The sum of the divisors of 940 is a triangular number: 1 + 2 + 4 + 5 + 10 + 20 + 47 + 94 + 188 + 235 + 470 + 940 = 2016, the 63rd triangular number.

940 is the maximum number of regions into which 15 spheres can divide space.

## Friday, February 24, 2012

### 847

847 = 7 x 11 x 11.

847 is a divisor of 2710 - 1.

847 is the sum of the digits of the 14th Mersenne prime.

847 is 1011101 in base 3.

847 is the sum of distinct factorials: 847 = 6! + 5! + 3! + 1!

## Thursday, February 23, 2012

### 453

453 = 3 x 151.

453 is the only number n such that n, 2n, and 6n together contain every digit exactly once: 453, 906, and 2718.

453 is 381 in base 11 and 318 in base 12. It is 202 in base 15.

453 is the sum of distinct double factorials: 453 = 8!! + 6!! + 5!! + 3!! + 2!! + 1!!

## Wednesday, February 22, 2012

### 285

285 = 3 x 5 x 19.

285 is the smallest number whose sum of distinct prime factors is an odd prime to the power of an odd prime: 3 + 5 + 19 = 27 = 33.

285 is 555 in base 7.

285 is a square pyramidal number (the sum of all squares of integers from 1 to 9): 285 = 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92.

2852 = 81225 uses the same digits as 1352 (18225) and 1592 (25281).

285 is the number of binary rooted trees with 13 vertices.

Source: Prime Curios!

## Tuesday, February 21, 2012

### 733

733 is a prime number.

733 is the smallest multidigit number that can be represented in the following way: 733 = 7 + 3! + (3!)!

733 = 17 + 26 + 35 + 44 + 53 + 62 + 71 + 80.

733 has a representation as a sum of two squares: 733 = 22 + 272.

733 is the hypotenuse of a primitive Pythagorean triple: 7332 = 1082 + 7252.

Hank Aaron hit a total of 733 home runs during the years that he played in the National League.

Source: Number Gossip

## Friday, February 17, 2012

### 275

275 = 5 x 5 x 11.

275 is 101012 in base 3 and 10103 in base 4.

275 is the total number of parts in all partitions of 11. It is also the sum of the largest parts of all partitions of 11. And it is the number of partitions of 28 in which no part occurs only once.

275 is the sum of two distinct positive fifth powers: 275 = 35 + 25.

275 is the lesser of two consecutive numbers (275 and 276), each divisible by a square.

The Ferrari 275 was a 2-seat car produced between 1964 and 1968.

## Thursday, February 16, 2012

### 554

554 = 2 x 277.

554 has a representation as a sum of two squares: 554 = 52 + 232.

554 is the maximum number of regions into which 24 circles can divide a plane.

554 is the number of self-dual planar graphs with 20 edges.

554 is 202112 in base 3 and 20222 in base 4. It is 464 in base 11.

## Wednesday, February 15, 2012

### 728

728 = 2 x 2 x 2 x 7 x 13. It is the smallest number n where n and n + 1 are both products of five or more primes.

728 is 222222 in base 3 and 888 in base 9.

Consecutive Smith numbers are called Smith brothers: 728 is the smaller brother of the smallest pair (728 and 729) of Smith brothers. The sum of its digits is equal to the sum of the digits of its prime factors: 7 + 2 + 8 = 2 + 2 + 2 + 7 + 1 + 3 = 17.

728 is the sum of two distinct positive cubes: 728 = 83 + 63.

728 is the number of nodes in a regular 13-gon with all diagonals drawn.

Source: Number Gossip

## Tuesday, February 14, 2012

### 549

549 = 3 x 3 x 61.

549 has a representation as a sum of two squares: 549 = 152 + 182.

549 is 333 in base 13. It is 202100 in base 3 and 20211 in base 4.

The sum of the digits of 549 is six times the number of digits: 5 + 4 + 9 = 6 x 3 = 18.

549 is the number of primes less than 104 having at least one digit 7.

549 is a number n such that n2 contains no digit greater than 4: 5492 = 301401.

Source: On-Line Encyclopedia of Integer Sequences

## Monday, February 13, 2012

### 8331

8331 = 3 x 2777.

The base 2, 3, 4, 5, 6, 7, and 8 representations of 8331 use no digit greater than 3.

8331 is a centered 14-gonal number.

8331 is the sum of the primes in an ordered 3 x 3 prime square, which consists of nine consecutive primes arranged in a square.

UGC 8331 is an irregular galaxy in the constellation Canes Venatici.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, February 10, 2012

### 822

822 = 2 x 3 x 137.

822 is the smallest nonpalindromic composite number located between twin primes (821 and 823), whose reversal, which is less than it (288), is also located between twin primes (287 and 289).

822 is the number of planar graphs with 7 vertices.

822 is the sum of 12 consecutive primes: 822 = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

822 Lalage is an asteroid discovered in 1916.

Source: Prime Curios!

## Thursday, February 9, 2012

### 534

534 = 2 x 3 x 89. It is the product of three distinct Sophie Germain primes.

534 is 4114 in base 5. It is 321 in base 13.

534 is a divisor of 554 - 1.

534 is the sum of four consecutive primes: 534 = 127 + 131 + 137 + 139.

534 is the sum of thirteen positive fifth powers.

534 was the fourth studio album produced by the rapper Memphis Bleek, released in 2005.

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, February 8, 2012

### 135

135 = 3 x 3 x 3 x 5.

135 is the smallest number with exactly seven representations as a sum of four positive squares: 135 = 12 + 22 + 32 + 112 = 12 + 22 + 72 + 92 = 12 + 32 + 52 + 102 = 12 + 62 + 72 + 72 = 22 + 52 + 52 + 92 = 32 + 32 + 62 + 92 = 52 + 52 + 62 + 72.

135 is the number of integer partitions of 14.

135 is 99 in base 14.

135 = (1 + 3 + 5)(1 x 3 x 5).

135 is the smallest three digit number that is the sum of its first digit and the square of its second digit and the cube of its third digit: 135 = 11 + 32 + 53.

The term 135 (ISO 2007) was introduced by Kodak in 1934 as a designation for cartridge film 35 millimeters wide, specifically for still photography.

Source: Number Gossip

## Tuesday, February 7, 2012

### 312

312 = 2 x 2 x 2 x 3 x 13.

312 has a unique representation as a sum of three squares: 312 = 42 + 102 + 142.

312 is 2222 in base 5. Its is 624 in base 7 and 264 in base 11.

3122 = 143 + 153 + 163 + 173 + 183 + 193 + 203 + 213 + 223 + 233 + 243 + 253 = 97344.

312 x 221 = 68952 and (backwards) 25986 = 213 x 122.

312 Urban Wheat Ale is produced by the Goose Island Beer Company in Chicago.

Source: Numeropedia

## Monday, February 6, 2012

### 710

710 = 2 x 5 x 71.

710 is a divisor of 917 - 1.

710 is 222022 in base 3. It is 868 in base 9.

The sum of the divisors of 710 is a square: 1 + 2 + 5 + 10 + 71 + 142 + 355 + 710 = 1296 = 362.

710 is the sum of nine positive fifth powers: 710 = 35 + 35 + 25 + 25 + 25 + 25 + 25 + 25 + 25.

710 is the number of connected graphs with 9 edges.

## Friday, February 3, 2012

### 607

607 is a prime number.

607 is the smallest prime resulting from the concatenation of two consecutive numbers separated by 0.

607 is the exponent of the Mersenne prime 2607 - 1.

607 is the smallest prime that can be expressed as the sum of 11 consecutive Fibonacci numbers: 607 = 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233.

1650/607 is the closest fraction to e with a prime denominator less than 1000.

Halley's Comet was visible from Earth in the year 607.

Source: Prime Curios!

## Thursday, February 2, 2012

### 507

507 = 3 x 13 x 13.

507 is a divisor of 223 - 1.

507 is 13323 in base 4 and 1323 in base 7.

507 is the lesser of two consecutive numbers (507 and 508) each divisible by a square.

The square of 507 contains exactly six different digits: 5072 = 257049.

507 is the number of rooted ternary trees with 10 vertices.

## Wednesday, February 1, 2012

### 960

960 = 26 x 3 x 5.

960 is equal to the sum of its digits plus the sum of the cubes of its digits: 960 = 9 + 6 + 0 + 93 + 63 + 03.

960 is 1111000000 in base 2 (binary), 33000 in base 4, and 1700 in base 8. The representations of 960 in bases 2, 3, 4, 5, 6, 8, and 10 all end in 0.

960 is the sum of six consecutive primes: 960 = 149 + 151 + 157 + 163 + 167 + 173.

960 is a hendecagonal number.