## Thursday, July 31, 2014

### 7289

7289 = 37 x 197.

7289 and each of its two divisors include the digit 7 (A062676).

7289 is 2929 in base 14.

7289 has two representations as a sum of two squares: 7289 = 82 + 852 = 202 + 832.

7289 is the hypotenuse of two primitive Pythagorean triples: 72892 = 13602 + 71612 = 33202 + 64892.

7289 divides 1412 - 1.

Source: OEIS

## Wednesday, July 30, 2014

### 7368

7368 = 2 x 2 x 2 x 3 x 307.

7368 is a multiple of 24 whose digits also sum to 24 (A066270).

7368 is 5599 in base 11.

7368 minus the sum of its unique prime factors is a square (A216894): 7368 - (2 + 3 + 307) = 7056 = 842.

7368 divides 176 - 1.

7368 is the number of partitions of 52 such that the sum of the square of the parts is a square (A240127).

Source: OEIS

## Tuesday, July 29, 2014

### 1847

1847 is a prime number.

1847 is the number of 2 x 2 x 2 Rubik's cube positions that require exactly four moves to solve.

1847 is 24342 (palindromic) in base 5. It is 737 in base 16 (A029732).

1847 is the sum of the first 50 nonprimes (A051349).

1847 is the lower prime of a difference of 14 between consecutive primes (A031932).

The first adhesive U.S. postage stamp went on sale in the year 1847. Thomas Edison was born in the year 1847 and died in the prime year 1931.

Source: Prime Curios!

## Monday, July 28, 2014

### 2579

2579 is a prime number. It is a safe prime (A005385).

2579 is the smallest prime number that can be expressed as the sum of 13 consecutive Fibonacci numbers (the fourth to the sixteenth). It is also a prime that is the difference of two Fibonacci numbers (A113188).

2579 is the smallest prime that is equal to the sum of 35 consecutive primes (A070934).

2579 is 40304 in base 5 (A029973).

Source: Prime Curios!

## Friday, July 25, 2014

### 7777

7777 = 7 x 11 x 101. It is a palindrome with exactly three distinct palindromic prime factors (A046409).

7777 has the representation 65 + 1 (A062394). It is 100001 (palindromic) in base 6 (A029963 and A033043).

7777 divides 365 - 1.

7777 is a number that is the sum of two positive fifth powers (A003347 and A004842).

7777 is a Kaprekar number (A006886).

Source: OEIS

## Thursday, July 24, 2014

### 1809

1809 = 3 x 3 x 3 x 67.

1809 is the sum of the first 26 palindromes (A046489).

1809 is the sum of the first 17 primes whose indices are primes (A083186).

1809 is a non-palindromic balanced number; the first and last half of its digits have the same sum (A145808).

1809 is a multiple of 9 that contains 9 in its decimal representation (A121029).

1809 is 3421 in base 8. It is 809 in base 15.

1809 divides 373 - 1.

Source: OEIS

## Wednesday, July 23, 2014

### 4391

4391 is a prime number. It is a Sophie Germain prime because 2 x 4391 + 1 = 8783 is also a prime.

4391 is the smaller of two consecutive Sophie Germain primes with the same digital sum (A118506).

4391 is the sum of the first 47 primes minus 47 (A101301).

4391 is a number that cannot be written as a sum of three squares.

4391 is 3332 in base 11 (A032811).

Source: OEIS

## Tuesday, July 22, 2014

### 2504

2504 = 2 x 2 x 2 x 313.

2504 is 40004 in base 5 (A097251).

2504 is a Friedman number (A036057).

2504 is the number of forests of ordered trees on 9 total nodes (A052854).

2504 has a representation as a sum of two squares: 2504 = 22 + 502.

2504 divides 254 - 1.

## Monday, July 21, 2014

### 1623

1623 = 3 x 541.

1623 is a number for which the sum of the reciprocals of its digits is an integer (A034708).

1623 is a number whose product of digits is three times the sum of its digits (A062035).

1623 is a semiprime that is the sum of three consecutive semiprimes (A131610).

1623 is a number that is not the sum of two triangular numbers and a fourth power (A115160).

1623 cannot be written as the sum of three squares.

1623 divides 524 - 1.

Source: OEIS

## Friday, July 18, 2014

### 9668

9668 = 2 x 2 x 2417.

9668 is the number of Sophie Germain primes among the first 105 primes (A04940).

9668 is 112432 in base 6 and 14232 in base 9.

9668 has a representation as a sum of two squares: 9668 = 82 + 982.

9668 divides 6716 - 1.

Source: OEIS

## Thursday, July 17, 2014

### 8420

8420 = 2 x 2 x 5 x 421.

8420 is the number of symmetric ways to fold a strip of 20 stamps (A001010).

8420 = 203 + 202 + 20 (A027444 and A063012).

8420 has two representations as a sum of two squares: 8420 = 262 + 882 = 322 + 862.

8420 divides 294 - 1.

## Wednesday, July 16, 2014

### 3260

3260 = 2 x 2 x 5 x 163.

3260 is 23032 in base 6. It is 4422 in base 9 (A033007).

3260 is the number of inequivalent ways to cut an 11 x 11 square into squares with integer sides, such that the dissection has 90-degree rotational symmetry and no reflective symmetry (A240122).

3260 is a number that is not the sum of a triangular number, a cube, and a Fibonacci number (A115177).

3260 cannot be written as the sum of three squares.

3260 divides 596 - 1.

Source: OEIS

## Tuesday, July 15, 2014

### 1379

1379 = 7 x 197.

Dropping any digit of 1379 gives a prime number (A034895).

1379 is the maximum number of regions into which 52 lines divide the plane. It is a central polygonal numbers (A000124).

1379 is a heptadecagonal number (A051869).

1379 is the magic constant of a 24 x 24 normal magic square.

1379 is 4010 in base 7 and 1044 in base 11. It is 2543 in base 8 and 707 in base 14.

1379 divides 367 - 1.

## Monday, July 14, 2014

### 4126

4126 = 2 x 2063.

4126 is 113001 in base 5 and 3111 in base 11 (A032918).

4126 is a number that contains the product of any two adjacent digits as a substring, and has at least one pair of adjacent digits (A203566).

4126 is the number of positions that are exactly 16 moves from the starting position in the "hockey puck" puzzle (A079735).

4126 is the number of primes between 34 and 343 (A117491).

Source: OEIS

## Friday, July 11, 2014

### 9703

9703 = 31 x 313.

9703 is 302303 in base 5. It is 40201 in base 7.

9703 is a number of the form n3 + n2 + 1 for n = 21 (A098547).

9703 is a number that cannot be written as a sum of three squares.

9703 divides 983 - 1.

Source: OEIS

## Thursday, July 10, 2014

### 5303

5303 is a prime number. It is a Sophie Germain prime because 2 x 5303 + 1 = 10607 is also a prime. The sum of the digits of 5303 (11) is also a Sophie Germain prime (A118504).

5303 is a balanced prime (the average of the previous prime and the following prime) (A006562). 5297, 5303, and 5309 are three consecutive primes (A053070).

5303 is a prime that is the sum of five consecutive composite numbers (A060330).

Source: OEIS

## Wednesday, July 9, 2014

### 2017

2017 is a prime number.

2011 and 2017 are a sexy prime pair (differing by 6).

2017 is an odd central polygonal number (A193867).

2017 is the sum of four consecutive composite numbers (A060329).

2017 is a prime that remains a prime when a single "7" digit is inserted between any two adjacent digits (A217065).

2017 is a prime with digit sum 10 (A107579).

2017 has a representation as a sum of two squares: 2017 = 92 + 442.

2017 is the hypotenuse of a primitive Pythagorean triple: 20172 = 7922 + 18552.

2017 divides 797 - 1.

Source: OEIS

## Tuesday, July 8, 2014

### 2003

2003 is a prime number. It is a Sophie Germain prime because 2 x 2003 + 1 = 4007 is also a prime.

2003 is formed from the first two primes (2 and 3) separated by two zeroes. Add 23, then 2 x 3 to get the next two primes: 2011 and 2017.

The concatenation of numbers from 2000 to 2003 (2000200120022003) is a prime.

2003 is the only known prime of the form 2 x 10p + p, where p and p + 4 are primes (with p = 3).

2003 is 133103 in base 4 and 31003 in base 5.

2003 divides 2213 - 1.

2003 was the first prime year of the current millennium. The next two are 2011 and 2017.

Source: Number Gossip and Prime Curios!

## Monday, July 7, 2014

### 6661

6661 is a prime number.

6659 and 6661 form a twin prime pair.

6661 is the smallest beastly (containing the string 666) prime number.

6661 and its inversion, 1999, are both primes.

6661 uses only the digits 0, 1, and 5 in bases 6 (50501) and 8 (15005).

6661 has a representation as a sum of two squares: 6661 = 102 + 812.

6661 is the hypotenuse of a primitive Pythagorean triple: 66612 = 16202 + 64612.

Source: Number Gossip

## Thursday, July 3, 2014

### 3666

3666 = 2 x 3 x 13 x 47.

3666 is the number of ways to tile a 4 x 46 room with 1 x 2 Tatami mats, with at most three Tatami mats meeting at a point (A068923).

3666 is the number of partitions of the 33rd decimal palindrome into distinct decimal palindromes (A091585).

3666 divides 956 - 1.

Source: OEIS

## Wednesday, July 2, 2014

### 7070

7070 = 2 x 5 x 7 x 101.

7070 is the number of lines through at least two points of an 8 x 22 grid of points (A160848).

7070 divides 4120 - 1.

7070 is a number n such that n and the square of n use only the digits 0, 4, 7, 8, and 9 (A136959).

Source: OEIS

## Tuesday, July 1, 2014

### 7837

7837 = 17 x 461.

7837 is the number of primes less than 80000 (A038813).

7837 is a number n such that there are 17 primes between 100n and 100n + 99 (A186509).

7837 is a number n such that 27n + 1 is a square (A219258).

7837 is the smaller of two consecutive lucky numbers with the same digital sum (A118566).

7837 has two representations as a sum of two squares: 7837 = 212 + 862 = 592 + 662.

7837 is the hypotenuse of two primitive Pythagorean triples: 78372 = 8752 + 77882 = 36122 + 69552.

7837 divides 4816 - 1.

Source: OEIS