## Friday, November 30, 2012

### 499

499 is a prime number.

499 is the smallest prime that is the sum of a prime number of first odd primes: 499 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

499499 ends with the digits 499499. In general, its odd powers end with 499 and its even powers end with 001.

Separate 499 into two (49, 9) and three (4, 9, 9) groups and get two primes after replacing each subset with each subset with its square root, namely 73 and 233. Replacing each digit of these latter two primes with their cubes results in two new primes: 34327 and 82727.

499 is the number of ways to place 26 points on a 13 x 13 grid so that no three points are on a line.

499 is the smallest number with the property that its first 12 multiples contain the digit 9.

499 seconds is the average time interval for sunlight from the sun to reach Earth.

Source: Prime Curios!

## Thursday, November 29, 2012

### 1507

1507 = 11 x 137.

1507 is a divisor of 1004 - 1 (A027890). It is also a divisor of 1016 - 1 (A111211).

1507 is the number of partitions of 32 that do not contain 1 as a part (A002865).

1507 is the sum of exactly three sets of Fibonacci numbers (A122195).

The sums of the digits of 1507 in base 2 (10111100011), base 3 (2001211), and base 5 (22012) are equal (A135121).

The word "America" was first used on a map published in the year 1507.

## Wednesday, November 28, 2012

### 1422

1422 = 2 x 3 x 3 x 79.

1422 is the number of ways to stack 27 boxes in a line so that each box lies on the table or on a box next to two boxes (A001522).

1422 is a divisor of 553 - 1.

14222 = 2022084 has only even digits (A030097).

The sum of the digits of 1422 and 14222 are both squares (A197125): 1 + 4 + 2 + 2 = 9 = 32 and 2 + 0 + 2 + 0 + 8 + 4 = 16 = 42.

## Tuesday, November 27, 2012

### 394

394 = 2 x 197.

394 has a representation as a sum of two squares: 394 = 132 + 152.

394 is a Schroeder number (A006318).

394 is 202 in base 14.

The sum of the digits of 394 equals the sum of the digits of the 394th prime (2707) (A033549).

394 is the middle semiprime of three consecutive semiprimes: 393, 394, 395.

## Monday, November 26, 2012

### 487

487 is a prime number.

487 is the smallest prime p such that p and p3 (115501303) have the same digit sum: 4 + 8 + 7 = 19 = 1 + 1 + 5 + 5 + 0 + 1 + 3 + 0 + 3.

487 is the number of Hadamard matrices of order 28.

487 is 200001 in base 3. It is 13213 in base 4 and 2131 in base 6. It is 747 in base 8 and 191 in base 18.

487 is the sum of three consecutive primes: 487 = 157 + 163 + 167.

Source: Number Gossip

## Wednesday, November 21, 2012

### 371

371 = 7 x 53.

371 is a narcissistic number (Armstrong number): 371 = 33 + 73 + 13.

371 is the largest known semiprime that is also the sum of consecutive prime numbers from 7 (smallest prime factor) to 53 (largest prime factor): 371 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53.

371 is the sum of three consecutive primes and seven consecutive primes: 371 = 113 + 117 + 131 = 41 + 43 + 47 + 53 + 59 + 61 + 67.

371 is the sum of five positive fifth powers: 371 = 35 + 25 + 25 + 25 + 25.

Source: Number Gossip

## Tuesday, November 20, 2012

### 561

561 = 3 x 11 x 17.

561 is 1000110001 in base 2 (binary) (A006995).

561 is the 33rd triangular number (A000217), the sum of the first 33 integers. It is also a hexagonal number (A000384) and a dodecagonal number (A051624).

561 is the smallest Carmichael number (A002997).

561 is a centered icosahedral number (cuboctahedral number) (A005902).

Source: Number Gossip

## Monday, November 19, 2012

### 952

952 = 2 x 2 x 2 x 7 x 17.

952 = 93 + 53 + 23 + (9 x 5 x 2).

952 is 4224 in base 6.

952 is the number of regions in an 14-gon with all diagonals drawn (A007678).

952 is a number that can be expressed as the difference of squares of primes in just one distinct way (A090781).

952 is the number of possible queen moves on a 7 x 7 chessboard (A035005).

952 Caia is an asteroid orbiting the sun.

## Friday, November 16, 2012

### 454

454 = 2 x 227.

454 is the largest number known that cannot be written as a sum of seven or fewer cubes (A018889).

454 is a Smith number (A006753). The sum of its digits (4 + 5 + 4 = 13) is equal to the sum of the digits of its prime factors (2 + 2 + 2 + 7 = 13).

1 + 8 + 10 + 17 = 36 = 2 + 5 + 13 + 16
12 + 82 + 102 + 172 = 454 = 22 + 52 + 132 + 162
13 + 83 + 103 + 173 = 6426 = 23 + 53 + 133 + 163

454 is 383 in base 11 (A029966) and 246 in base 14.

## Thursday, November 15, 2012

### 2034

2034 = 2 x 3 x 3 x 113.

2034 is the number of self-avoiding walks of length 9.

2034 is the number of ways of writing 4 as a sum of nine squares (A008452).

2034 has a representation as a sum of two squares: 2034 = 32 + 452.

2034 is a divisor of 3516 - 1.

2034 is 909 in base 15. It is 369 in base 25.

## Wednesday, November 14, 2012

### 2006

2006 = 2 x 17 x 59.

2006 is 2202022 in base 3. It is 434 in base 22.

2006 is a term in the sequence starting with 1, then adding 35, then repeatedly reversing the digits and adding 35 (A118632).

2006 is a multiple of 17 such that its reversal minus 1 (6001) is also a multiple of 17 (A166398).

2006 is the number of line segments connecting exactly 10 points in a 26 x 26 grid (A177726).

A transit of Mercury as seen from Earth took place in the year 2006 (A171466).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, November 13, 2012

### 1203

1203 = 3 x 401.

1203 is a divisor of 204 - 1.

1203 is the smallest number n for which the concatenation n, (n + 1), (n + 2), . . . . (n + 34) is prime (A052079).

1203 is 102303 in base 4, 14303 in base 5, and 303 in base 20. It is 717 in base 13.

12032 = 1447209 and 12033 = 1740992427 have the same set of digits (A029797 and A045620).

## Monday, November 12, 2012

### 1010

1010 = 2 x 5 x 101.

1010 has two representations as a sum of two squares: 1010 = 72 + 312 = 132 + 292.

1010 is the sum of two distinct powers of 10 (A052216 and A038444): 1010 = 103 + 101.

1010 is the number of ways to tile a 5 x 12 rectangle with pentominoes.

1010 is 2642 in base 7 and 1342 in base 9. It is 262 in base 21.

1010 is the number of primes less than 104 that do not contain the digit 0 (A091634).

## Friday, November 9, 2012

### 902

902 = 2 x 11 x41. It is the smallest number beginning with 9 that is the product of exactly three primes (A106419).

902 is a value of n such that n(n + 7) is palindromic: 902(909) = 819918.

902 is 1020102 in base 3, 12102 in base 5, and 4102 in base 6. It is 1212 in base 9 and 321 in base 17. It is 545 in base 13 and 252 in base 20.

902, 903, and 904 have the same number of divisors (A005238).

902 is a multiple of 11 such that sum of its digits is also a multiple of 11 (A216995).

## Thursday, November 8, 2012

### 1483

1483 is a prime number.

1481 and 1483 form a twin prime pair.

1483 is the smallest prime that is the sum of three prime cubes: 1483 = 33 + 53 + 113.

1483 has the representation 2 x 36 + 25.

1483 is a divisor of 383 - 1.

The Petronas Towers in Kuala Lumpur, Malaysia, are 1483 feet tall.

Source: Prime Curios!

## Wednesday, November 7, 2012

### 4656

4656 = 2 x 2 x 2 x 2 x 3 x 97.

4656 is the 96th triangular number, with digit sum 21 (A068131).

4656 is 1020300 in base 4 and 1230 in base 16.

4656 is a structured pentagonal hexacontahedral number (A100169).

4656 is the number of 3 x 3 arrays of squares on integers summing to 18 (A159401).

Source: Numeropedia

## Tuesday, November 6, 2012

### 442

442 = 2 x 13 x 17.

442 has two representations as a sum of two squares: 442 = 12 + 212 = 92 + 192.

442 is the smallest composite number n that divides F(n - 1) where F(k) are the Fibonacci numbers.

442 is the number of planar partitions of 13.

442 is the sum of eight consecutive primes: 442 = 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71.

442 is 3232 in base 5 and 101 in base 21.

Source: Number Gossip

## Monday, November 5, 2012

### 693

693 = 3 x 3 x 7 x 11.

693 is 1010110101 in base 2 (binary). It is 3113 in base 6, 414 in base 13, and 313 in base 15.

693 has the representation 693 = 36 - 36.

A primitive Pythagorean triangles of sides (693, 1924, 2045) has area 666,666.

693 is the number of sections in Ludwig Wittgenstein's Philosophical Investigations.

Source: Numeropedia

## Friday, November 2, 2012

### 884

884 = 2 x 2 x 13 x 17.

884 has two representations as a sum of two squares: 884 = 102 + 282 = 202 + 222.

The fifth root of 884 has a decimal part that begins with the digits 884.

884 is 202 in base 21.

The sum of the divisors of 884 is a square (A006532): 1 + 2 + 4 + 13 + 17 + 26 + 34 + 52 + 68 + 221 + 442 + 884 = 1764 = 422.

## Thursday, November 1, 2012

### 407

407 = 11 x 37.

407 is a divisor of 1003 - 1.

407 is the maximum number of regions into which 28 lines divide the plane.

407 is the largest number that is the sum of the cubes of its digits: 407 = 43 + 03 + 73. It is a narcissistic number.

407 = (7 - 3)3 + 73.

407 is 1515 in base 6.

407 is the sum of three consecutive primes: 407 = 131 + 137 + 139.

Source: Number Gossip