## Friday, August 29, 2014

### 4236

4236 = 2 x 2 x 3 x 353.

4236 is a number divisible by each of its digits (A187238).

4236 has a fourth power that is the sum of 4 distinct fourth powers (A003294 and A096739).

4236 is the number of ways to color the edges of a tetrahedron using 6 or fewer colors (A046023).

4236 is 1002030 in base 4 (A045034).

4236 is a number n such that n and 2n end with the same two digits (A067865).

4236 divides 4916 - 1.

## Thursday, August 28, 2014

### 2457

2457 = 3 x 3 x 3 x 7 x 13.

2457 = 169 + 170 + . . . + 182 = 183 + 184 + . . . + 195 (A059270).

2457 is 999 in base 16 (A033029). It is 212121 in base 4. 2457 is 100110011001 (palindromic) in base 2 (A048701), 10101000 in base 3, and 10110 in base 7 (A033044).

2457 is the sum of two cubes and the sum is divisible by 13 (A094447).

2457 is both a sum and a difference of two positive cubes (A225908).

2457 divides 1003 - 1 (A027892).

2457 x 2458 = 6039306 (a palindrome) (A028336).

## Wednesday, August 27, 2014

### 7602

7602 = 2 x 3 x 7 x 181. It is a number with exactly 4 distinct palindromic prime factors (A046402).

7602 is the product of 42 and the 42nd prime (A033286).

7602 is the sum of composite numbers less than the 34th prime (A079725).

7602 is a positive integer n such that n11 + 1 is semiprime (A105122).

7602 divides 439 - 1.

Source: OEIS

## Tuesday, August 26, 2014

### 5558

5558 = 2 x 7 x 397.

5558 is the smallest number whose digital product is equal to 103 (A089386).

5558 is 1010110110110 in base 2 (binary) and 21121212 in base 3. It is 12666 in base 8 (A043447) and 7555 in base 9 (A043475). 5558 is 2050 in base 14.

5558 is a number n such that 1 + n + n3 + n5 + n7 + n9 + . . . + n41 is prime (A244386).

5558 is a value n such that 90n + 11, 90n + 13, 90n + 17, 90n + 19 are all primes (A051897).

5558 is an integer n such that 6n -/+ 1 and 30n -/+ 1 are all primes (A216847).

5558 divides 799 - 1.

Source: OEIS

## Monday, August 25, 2014

### 8751

8751 = 3 x 2917.

The cube of 8751 ends with 8751 (A033819).

The square of 8751 and the cube of 8751 have the same set of digits (A029797).

8751 is a perfect totient number (A082897).

8751 is the total height of trees with 11 nodes (A001853).

8751 is the sum of seven positive 7th powers (A003374).

8751 is a number that cannot be written as a sum of three squares.

## Friday, August 22, 2014

### 4770

4770 = 2 x 3 x 3 x 5 x 53.

4770 is a number n such that 2n - 1, 4n - 1, and 6n - 1 are primes (A124486).

4770 is the number of planar partitions of 19 with exactly two rows (A091356).

4770 has two representations as a sum of two squares: 4770 = 32 + 692 = 392 + 572.

4770 divides 2312 - 1.

Source: OEIS

## Thursday, August 21, 2014

### 7808

7808 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 61.

7808 is the number of 4 x 4 sliding-block puzzle positions that require exactly 12 moves to solve starting with the hole in a corner (A089484).

7808 is 101201012 in base 3 (A043589). Reversing the base-3 representation of 7808 produces twice the original number (A173951).

7808 is the sum of two positive fifth powers (A003347). It is the sum of the fifth powers of the digits of 26 (A055014).

7808 has a representation as a sum of two squares: 7808 = 82 + 882.

7808 divides 3320 - 1.

## Wednesday, August 20, 2014

### 5909

5909 = 19 x 311.

5909 is 13425 in base 8. It is 3505 in base 12.

5909 is the largest number whose base 8 representation does not contain any digit more than once and that is not divisible by any of its base 8 digits (A114342).

5909 is the number of symmetric plane partitions of 32 (A005987).

Source: OEIS

## Tuesday, August 19, 2014

### 5236

5236 = 2 x 2 x 7 x 11 x 17.

5236 divides 676 - 1.

5236 is a multiple of 17 such that its reversal - 1 is also a multiple of 17 (A166398).

5236 is a number n such that n and n + 2 are both divisible by exactly five primes (counted with multiplicity) (A180151).

5236 is the number of disconnected 2-regular graphs on 47 vertices (A165652).

Source: OEIS

## Monday, August 18, 2014

### 1776

1776 = 2 x 2 x 2 x 2 x 3 x 37.

1776 is a number that can be expressed as the product of numbers made of only fours (A161142): 1776 =  4 x 444.

1776 is 5115 in base 7.

1776 is a rhombic matchstick number (A045944).

1776 is a number with 20 divisors (A030638).

1776 is the difference of two positive fourth powers (A147857).

1776 divides 732 - 1.

Source: OEIS

## Friday, August 15, 2014

### 5861

5861 is a prime number.

5861 is 1123211 in base 4 (A029972). It is 141421 in base 5.

5861 is the mean of five successive primes (A219478).

5861 is a number such that the product of its digits is 12 times their sum (A062045).

5861 is the first prime in a sequence produced from a prime-generating cubic polynomial of the form 82n3 - 1288n2 + 6130n - 5861 (A076808).

5861 has a representation as a sum of two squares: 5861 = 312 + 702.

5861 is the hypotenuse of a primitive Pythagorean triple: 58612 = 39392 + 43402.

Source: Prime Curios!

## Thursday, August 14, 2014

### 1736

1736 = 2 x 2 x 2 x 7 x 31.

1736 is the number of ways to place two non-attacking bishops on an 8 x 8 chessboard (A172123).

1736 is the number of ways of writing 65 as the sum of eight nonnegative cubes (A173681).

1736 is a number that is the sum of two positive cubes and divisible by 7 (A101421).

1736 is 12012 in base 6.

1736 divides 253 - 1.

## Wednesday, August 13, 2014

### 3798

3798 = 2 x 3 x 3 x 211.

3798 is a value of n for which 2n and 9n together use each of the digits 1 to 9 exactly once.

3798 is the number of ways of writing 64 as a sum of nine nonnegative cubes (A173682).

3798 divides 555 - 1.

## Tuesday, August 12, 2014

### 1599

1599 = 3 x 13 x 41.

1599 is 22344 in base 5 and 11223 in base 6. It is 4443 in base 7 (A032831).

1599 is a number n such that the square of n is the sum of two or more consecutive squares (A097812).

1599 is the sum of three consecutive pentagonal numbers (A129863).

1599 is a happy-go-lucky number; it is both happy and lucky (A091431).

Source: OEIS

## Monday, August 11, 2014

### 1559

1559 is a prime number. It is a Sophie Germain prime because 2 x 1559 + 1 = 3119 is also prime (A005384).

Reversing the digits of 1559 produces the prime 9551. 1559 is the smallest such prime that becomes a semiprime when any single digit is removed.

1559 is the smallest prime p with 16 consecutive quadratic residues mod p.

1559 is the number of different ways to divide an 11 x 11 square into sub-squares, considering only the list of parts (A034295).

1559 is 2010202 in base 3. It is 2122 in base 9.

Source: Prime Curios!

## Friday, August 8, 2014

### 7296

7296 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 19.

7296 is a multiple of 24 whose digits also sum to 24 (A066270). The sum of the digits of 7296 equals the sum of the unique prime divisors of 7296 (A070275).

7296 is 5533 in base 11 and 2266 in base 15 (A033013).

7296 is the number of rooted polyhedral graphs with 15 edges (A000287).

7296 divides 656 - 1.

Source: OEIS

## Thursday, August 7, 2014

### 4500

4500 = 2 x 2 x 3 x 3 x 5 x 5 x 5. It has exactly three distinct prime factors, none of which is greater than 5 (A143207).

4500 is the smallest base in which KJIHGFEDCBA987654321 is a prime. All shorter such strings achieve prime status in mch smaller bases (192 is the maximum required). Not until the string (110)(109)(108) . . . 321 is a higher base required.

4500 is the number of regions formed when all diagonals are drawn in a regular 20-gon (A007678).

4500 is a concentric icosagonal number (A195148).

4500 can be represented in bases 2, 3, 4, and 5 using only the digits 0, 1, and 2. It is 3421 in base 11.

4500 has two representations as a sum of two squares: 4500 = 122 + 662 = 302 + 602.

Source: Prime Curios!

## Wednesday, August 6, 2014

### 3701

3701 is a prime number.

3701 is a prime that is the sum of seven consecutive primes (A082246).

3701 is the smallest prime with exactly 22 representations as a sum of three distinct positive squares (A242675).

3701 has a representation as a sum of two squares (A108655): 3701 = 262 + 552.

3701 is the hypotenuse of a primitive Pythagorean triple: 37012 = 23492 + 28602.

Source: OEIS

## Tuesday, August 5, 2014

### 8111

8111 is a prime number. It is a Sophie Germain prime because 2 x 8111 = 16223 is also prime. Every digit of 8111 is a perfect cube (A061247 and A066592).

8111 is a prime that results from merging four successive digits in the decimal expansion of pi (A104824).

8111 is the concatenation of the first two digits and the last two digits of the 35th Mersenne prime (A138863).

8111 is 102010102 in base 3. It is 12112 in base 9 (A032930).

Source: OEIS

## Monday, August 4, 2014

### 2004

2004 = 2 x 2 x 3 x 167.

2004 has a square with the last three digits the same as the three digits before them: 20042 = 4016016.

22004 + 823 is a prime. It is the smallest prime of the form 22004 + k. The reversal of 22004 is a prime (A057708).

(2004 x 4002) - 1 is a prime.

2004 was a year in which there were five Sundays in the month of February (A119406).

Source: Prime Curios!

## Friday, August 1, 2014

### 5325

5325 = 3 x 5 x 5 x 71.

5325 is a lucky number of only prime digits (A118718).

5325 and its reversal (5235) are both multiples of 15 (A062905).

The product of the digits of 5325 is 10 times the sum of the digits (A062043).

5325 is 21345 in base 7. It is 4001 in base 11.

5325 is the sum of the remainders when the 40th prime is divided by all preceding integers (A050482).

5325 divides 765 - 1.

Source: OEIS