## Friday, May 30, 2014

### 1897

1897 = 7 x 271.

1897 is a Padovan number (A000931).

1897 plus the product of its digits produce a square (A066567).

1897 divides 296 - 1.

## Thursday, May 29, 2014

### 3700

3700 = 2 x 2 x 5 x 5 x 37.

3700 is the sum of the squares of four consecutive primes (A133524).

3700 is divisible by the sum of the cubes of its digits (A034088).

3700 and the sum of its digits are both multiples of 10 (A218292).

3700 is 12002001 in base 3.

3700 has three representations as a sum of two squares (A025286 and A025304 and A000443): 3700 = 102 + 602 = 282 + 542 = 422 + 442.

3700 divides 434 - 1.

## Wednesday, May 28, 2014

### 8763

8763 = 3 x 23 x 127.

8763 and its successor have the same digits in their prime factorization (A061665).

8763 is the number of partitions of 38 having not more odd than even parts (A171966).

8763 is a number n such that 4n + 1 is a palindromic prime (A192261).

8763 divides 2218 - 1.

## Tuesday, May 27, 2014

### 6384

6384 = 2 x 2 x 2 x 2 x 3 x 7 x 19.

6384 is a number divisible by each of its digits (A187238).

6384 is an icosahedral number (A006564).

6384 is 4884 in base 11.

6384 divides 316 - 1.

## Friday, May 23, 2014

### 9985

9985 = 5 x 1997.

9985 is the number of hyperbolic knots with 13 crossings (A052408).

9985 is 23401 in base 8.

9985 is a number n such that n, n + 2, n + 4, n + 6, n + 8, n + 10, and n + 12 are all semiprimes (A092129).

9985 is the number of composite numbers between the largest 29-digit prime and the smallest 30-digit prime (A109936).

9985 has two representations as a sum of two squares: 9985 = 242 + 972 = 392 + 922.

9985 is the hypotenuse of two primitive Pythagorean triples: 99852 = 46562 + 88332 = 69432 + 71762.

## Thursday, May 22, 2014

### 2603

2603 = 19 x 137.

2603 divides 374 - 1.

The 2603rd prime minus 2603 gives a square and a fourth power (A064370 and A114067).

2603 is the smallest product of two distinct primes that is greater than 512 (A099610).

2603 is the sum of nine distinct positive pentatope numbers (A104399).

Source: OEIS

### 7990

7990 = 2 x 5 x 17 x 47.

7990 is the number of Young tableaux of height less than or equal to 5, for n = 10 (A049401).

7990 is the number of nondecreasing arrangements of 5 nonzero numbers in -(n + 3)...(n + 3) with sum zero, for n = 14 (A188335).

7990 divides 938 - 1.

Source: OEIS

## Wednesday, May 21, 2014

### 2122

2122 = 2 x 1061.

2122 is a semiprime with a prime sum of factors (A108605).

2122 has a representation as a sum of two squares: 2122 = 212 + 412.

2122 divides 2920 - 1.

2122 is the index of a prime Euclid number (A014545).

2122 is the concatenation of two consecutive numbers (A001704 and A127421).

2122 is the barcode for 2 in the Universal Product Code.

Source: Number Gossip

## Tuesday, May 20, 2014

### 8839

8839 is a prime number.

8837 and 8839 form a twin prime pair.

8839 is a prime whose sum of digits is the perfect number 28 (A048517).

8839 is a prime using only the digits 0, 3, 6, 8, and 9 (A079652).

8839 is a prime that is the arithmetic mean of four successive primes (A126096).

8839 is a prime that can be expressed as a sum of distinct powers of 3 (A077717).

8839 is a number that cannot be written as a sum of three squares.

Source: OEIS

## Monday, May 19, 2014

### 1856

1856 = 2 x 2 x 2 x 2 x 2 x 2 x 29.

The product of the digits of 1856 is 12 times their sum (A062045).

1856 is a number n for which 12n + 1, 12n + 5, and 12n + 7 are primes (A123979).

1856 is the sum of four nonzero squares in exactly two ways (A025358).

1856 has a representation as a sum of two squares: 1856 = 162 + 402.

1856 divides 174 - 1.

1856 is a year in which there were five Fridays in the month of February (A141287).

Source: OEIS

## Friday, May 16, 2014

### 8377

8377 is a prime number.

8377 is a prime that is the sum of eight but no fewer squared primes (A183216).

8377 has a representation as a sum of two squares: 8377 = 512 + 762.

8377 is the hypotenuse of a primitive Pythagorean triple: 83772 = 31752 + 77522.

Source: OEIS

## Thursday, May 15, 2014

### 3225

3225 = 3 x 5 x 5 x 43.

3225 is 100400 in base 5. It is 22533 in base 6.

3225 is the number of primes less than 105 having at least one digit 6 (A091707).

3225 is the sum of the first 41 primes, minus 41 (A101301).

3225 is the number of symmetric 3 x 3 matrices in base 5 with determinant 0.

3225 divides 496 - 1.

## Wednesday, May 14, 2014

### 3917

3917 is a prime number.

3917 and 3919 form a twin prime pair.

3917 has a representation as a sum of two squares: 3917 = 142 + 612.

3917 is the hypotenuse of a primitive Pythagorean triple: 39172 = 17082 + 35252.

3917 divides 6611 - 1.

Source: Prime Curios!

## Tuesday, May 13, 2014

### 5235

5235 = 3 x 5 x 349.

The product of the digits of 5235 is ten times their sum (A062043).

The sum of the cubes of the digits of the cube of 5235 is a perfect cube (A164882).

5235 is a lucky number with only prime digits (A118718).

5235 is the smaller of two consecutive lucky numbers with the same digital sum (A118566).

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

5235 divides 3129 - 1.

Source: OEIS

## Monday, May 12, 2014

### 1835

1835 = 5 x 367.

1835 is a number n such that n, n + 2, + 4, n + 6, and n + 8 are semiprimes (A092127).

1835 is a member of the Fibonacci-like sequence beginning with 1 and 20 (A022110).

1835 is the least sum of 23 distinct pairs of consecutive primes (A102724).

1835 divides 846 - 1.

1835 is the number of Pyramorphix puzzle positions that require exactly four moves to solve.

## Friday, May 9, 2014

### 3750

3750 = 2 x 3 x 5 x 5 x 5 x 5 (A143207).

3750 is a concentric hexagonal number (A032528).

3750 is the first of four consecutive squareful numbers (A070284).

3750 is 110000 in base 5 (A033042).

3750 is the sum of two powers of 5 (A055237).

3750 is a number n such that n and the square of n are sums of two successive primes (A213739).

## Thursday, May 8, 2014

### 6868

6868 = 2 x 2 x 17 x 101.

6868 is the larger number in a Ruth-Aaron pair.

6868 is 100102101 in base 3. It is 15234 in base 8 (uses each of the digits from 1 to 5 once).

6868 has two representations as a sum of two squares: 6868 = 122 + 822 = 282 + 782.

6868 divides 9116 - 1.

## Wednesday, May 7, 2014

### 9767

9767 is a prime number.

9767 is the largest four-digit prime formed by the concatenation of two two-digit primes.

9767 and 9769 form a twin prime pair.

9767 is 14352 in base 9 (using each of the digits from 1 to 5 once).

9767 is the upper prime of a difference of 18 between consecutive primes (A031937).

9767 cannot be written as a sum of three squares.

Source: Number Gossip

## Tuesday, May 6, 2014

### 5735

5735 = 5 x 31 x 37.

5735 is a pentagonal number (A049452 and A014632).

5735 is a number divisible by 5 that is the difference between two different positive cubes in at least one way (A038853).

5735 is a number whose set of base 11 digits is {3, 4} (A032835): 4344.

5735 is a number n such that 2n + 1, 3n + 2, and 4n + 3 are primes (A126995).

5735 divides 266 - 1.

5735 is a number that cannot be written as a sum of three squares.

Source: Number Gossip

## Monday, May 5, 2014

### 6673

6673 is a prime number.

6673 is a prime whose base 3 representation (100011011) also is the base 2 representation of a prime (A235265).

6673 is a prime that is 3 greater than a triangular number (A159047).

6673 is a prime such that the sum of the predecessor and successor primes is divisible by 29 (A112859). It is also divisible by 23 (A112847).

6673 is a prime that can be expressed as a sum of distinct powers of 3 (A077717).

6673 has a representation as a sum of two squares: 6673 = 522 + 632.

6673 is the hypotenuse of a primitive Pythagorean triple: 66732 = 12652 + 65522.

Source: OEIS

## Friday, May 2, 2014

### 8818

8818 = 2 x 4409.

8818 is the smallest semiprime containing exactly three 8s (A104761).

8818 is a number n such that n concatenated with n + 3 gives the product of two numbers that differ by 7 (A116180).

8818 has a representation as a sum of two squares: 8818 = 132 + 932.

Source: OEIS

## Thursday, May 1, 2014

### 7556

7556 = 2 x 2 x 1889.

7556 is 31013 in base 7 (A043017).

7556 is the smallest of four consecutive integers such that their product plus or minus 5 are primes (A174244).

7556 is the number of 9-step walks on a hexagonal lattice (A005549).

7556 is the number of 6-step mappings with five inputs (A005946).

7556 is the number of 5 x 3 binary arrays with a path of adjacent 1s from the upper left corner to anywhere in the right hand column (A069294).

7556 is the number of 6-level rooted trees with 5 leaves (A000405).

7556 has a representation as a sum of two squares: 7556 = 342 + 802.

7556 divides 858 - 1.

Source: OEIS