## Wednesday, November 26, 2014

### 2445

2445 = 3 x 5 x 163.

2445 is a truncated tetrahedral number (A005906).

2445 is a number n such that n! has a square number of digits (A006488).

2445 is the sum of nine nonzero 6th powers (A003365).

2445 is a lucky number that is divisible by the sum of its digits (A118564).

2445 divides 596 - 1.

## Tuesday, November 25, 2014

### 1795

1795 = 5 x 359.

1795, 1797, and 1799 are consecutive semiprimes (A133609).

1795 is the product of two distinct safe primes (A157352).

1795 has a base 5 representation (24140) that begins with its base 9 representation (2414).

1795 is the sum of 10 nonzero 8th powers (A003388).

1795 is a Smith semiprime (A098837).

## Monday, November 24, 2014

### 1792

1792 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

1792 is a Friedman number (A036057).

1792 is the maximum number of pieces obtained by slicing a bagel (torus) with 21 cuts (A003600).

1792 is a composite number such that the square root of the sum of squares of its prime factors is an integer (A134605).

1792 is the number of simple graphs with 9 vertices and two cycles (A112410).

1792 divides 978 - 1.

Source: OEIS

## Friday, November 21, 2014

### 5101

5101 is a prime number.

5099 and 5101 form a twin prime pair.

5101 is the initial prime in a set of four consecutive primes with common difference 6 (A033451).

5101 is a prime formed from merging four successive digits in the decimal expansion of e (A104845).

5101 is a prime whose sum of digits is 7 (A062337).

5101 is a centered 17-gonal number (A069130).

5101 has a representation as a sum of two squares: 5101 = 502 + 512. 5101 is a prime that is the sum of at least two consecutive squares (A163251).

5101 is the hypotenuse of a primitive Pythagorean triple: 51012 = 1012 + 51002.

5101 divides 4620 - 1.

Source: OEIS

## Thursday, November 20, 2014

### 3001

3001 is a prime number.

2999 and 3001 form a twin prime pair.

3001 is a prime whose digit sum is 4 (A062339). It is the largest 4-digit prime with minimum digit sum (A069664).

3001 is a centered decagonal number (A062786).

3001 is a prime that can be expressed as the sum of distinct powers of 3 (A077717).

3001 is 1/24 of the 24th Fibonacci number.

3001 has a representation as a sum of two squares: 3001 = 202 + 512.

3001 is the hypotenuse of a primitive Pythagorean triple: 30012 = 20402 + 22012.

3001 divides 2015 - 1.

Arthur C. Clarke wrote a book titled 3001: The Final Odyssey.

Source: Prime Curios!

## Wednesday, November 19, 2014

### 1785

1785 = 3 x 5 x 7 x 17.

1785 is a multiple of 7 such that its digit sum is divisible by 7 (A216994).

1785 is a square pyramidal number (A000330). It is also a pentadecagonal number (A051867).

1785 is palindromic in base 5: 123321.

1785 is the sum of five positive fifth powers (A003350).

1785 divides 134 - 1.

Source: OEIS

## Tuesday, November 18, 2014

### 3900

3900 = 2 x 2 x 3 x 5 x 5 x 13.

3900 has a base 2 representation (111100111100) that is two copies of its base 5 representation (111100) concatenated (A175514). It is 330330 in base 4 (A045075) and 7474 in base 8 (A033079). It is 14241 in base 7 (palindromic).

3900 is the number of rooted trees with 15 nodes and 4 leaves (A055279).

3900 is the sum of four distinct powers of 5 (A038476).

3900 divides 496 - 1.

## Monday, November 17, 2014

### 3640

3640 = 2 x 2 x 2 x 5 x 7 x 13.

The sum of the digits of 3640 (13) is the largest prime factor of 3640 (A052021).

3640 is 111000111000111 in base 2 (binary) and 7070 in base 8. It is 11222211 in base 3, 320320 in base 4, and 4884 in base 9. It uses each of the digits 0, 1, 2, 3, 4 once in base 7 (13420).

3640 is a triple factorial number (A007661).

3640 is the number of regions in a regular 35-gon that are hexagons (A067153).

3640 divides 813 - 1.

Source: OEIS

## Friday, November 14, 2014

### 4699

4699 = 37 x 127.  4699 is a semiprime and each of its digits is a semiprime (A107342).

The sum of the digits of 4699 is 7 times the number of digits (A061424).

4699 is a nonagonal number (A001106).

4699 is 11133 in base 8 (A032915).

4699 is the number of 8-digit squares such that there is at least one permutation that is also a square (no initial zeros) (A177952).

4699 divides 2818 - 1.

Source: OEIS

## Thursday, November 13, 2014

### 1767

1767 = 3 x 19 x 31. The sum 3 + 19 + 31 = 53 is a prime number (A176877).

1767 is 123213 in base 4.

1767 is the sum of the digit reversals of the first 47 natural numbers (A062918).

1767 is a number n such that n, n + 1, and the sum of these two numbers each have three distinct prime factors (A168629).

1767 divides 942 - 1.

Source: OEIS

## Wednesday, November 12, 2014

### 8866

8866 = 2 x 11 x 13 x 31.

8866 is 2022202 in base 4. 8866 is 3334 in base 14 (A032838).

8866 is the number of necklaces with 6 black beads and 20 white beads (A032191).

8866 is the number of tilings of a 5 x 6 rectangle using pentominoes of any but the L shape (A247768).

8866 is a truncated triangular pyramid number (A051941).

8866 divides 876 - 1.

Source: OEIS

## Tuesday, November 11, 2014

### 6662

6662 = 2 x 3331.

The sum of the reciprocals of the digits of 6662 is 1 (A037268).

6662 is a beastly (or hateful) number because it contains the string 666 (A051003).

6662 is the number of 3-dimensional polyominoes (or polycubes) with 8 cells and trivial symmetry group (A066453).

6662 and the square of 6662 use only the digits 2, 3, 4, 6, and 8 (A137072).

6662 has the same set of digits in base 4 (1220012) and base 9 (10112) (A037427).

Source: OEIS

## Monday, November 10, 2014

### 5356

5356 = 2 x 2 x 13 x 103.

5356 is the 103rd triangular number. It is also a centered nonagonal number (A060544). It is a triangular number whose digit reversal is a semiprime (A115742). It is also a triangular number for which the sum of digits is a prime number (A117512).

5356 is the number of inequivalent ways to place a pair of checkers on a 17 x 17 board (A014409).

5356 is the number of complete squares that fit inside a circle with radius 42, drawn on squared paper (A119677).

5356 divides 4712 - 1.

5356 is 40444 in base 6 (A043388). It is 12354 in base 8.

Source: OEIS

## Friday, November 7, 2014

### 5377

5377 = 19 x 283.

5377 is the sum of four distinct powers of 4 (A038472).

5377 is a lucky number for which the product of the digits is also a lucky number (A118556).

5377 * 5379 = 28922883 (A116226).

5377 is a semiprime n such that 3 x n - 2 is a square (A112393): 3 x 5377 - 2 = 16129 = 1272.

5377 divides 456 - 1.

Source: OEIS

## Thursday, November 6, 2014

### 1669

1669 is a prime number.

1667 and 1669 form a twin prime pair.

1669 is the smallest prime that appears in the same position as its own value when the Roman numerals (from 1 to 3999) are placed in lexicographic order. The other primes with this property are 3623 and 3631.

1669 is the smallest number whose 9th power has 29 digits.

16692 = 2785561, and 278 * (5/5) * 6 + 1 = 1669.

1669 has a representation as the sum of two squares: 1669 = 152 + 382.

1669 is the hypotenuse of a primitive Pythagorean triple: 16692 = 11402 + 12192.

Source: Prime Curios!

## Wednesday, November 5, 2014

### 3600

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5.

3600 is a perfect square (A159991). It is both the sum and the difference of two primes (A106575).

3600 has a representation as a sum of two squares: 3600 = 362 + 482.

3600 is the order of a perfect group.

3600 is 11221100 in base 3 (A033001). It is 2100 in base 12 and 1100 in base 15.

3600 is a concentric hexadecagonal number (A195146).

3600 is the number of seconds in an hour.

Source: Number Gossip

## Tuesday, November 4, 2014

### 1160

1160 = 2 x 2 x 2 x 5 x 29.

1160 is divisible by the sum of its prime factors (40) (A046346).

1160 is an octagonal number (A000567).

1160 is a cake number (A000125). It is the maximum number of pieces into which a cylindrical cake can be cut with 19 straight-plane cuts.

The sum of the squares of the first 1160 primes is prime (A098561).

1160 is the smaller of two consecutive numbers each divisible by a cube (A068140).

1160 is 1120222 in base 3, 102020 in base 4, and 2210 in base 8. It is 3245 in base 7. It is 808 in base 12 and 404 in base 17. It is 488 in base 16.

Source: Number Gossip

## Monday, November 3, 2014

### 1130

1130 = 2 x 5 x 113. It is the product of three distinct Sophie Germain primes (A157346).

1130 is a Perrin number (A001608).

1130 is a number whose sum of digits is 5 (A052219). The sum of the digits of 1130 in base 2 (10001101010) is also 5 (A037308). It is a multiple of 5 with a digit sum of 5 (A069540).

Every base 6 digit of 1130 (5122) is a base 8 digit of 1130 (2152) (A037399).

1130 is the first of a pair of consecutive sphenic numbers (the product of three distinct primes) (A215217).

1130 has two representations as a sum of two squares: 1130 = 132 + 312 = 172 + 292.

1130 divides 698 - 1.