## Friday, February 28, 2014

### 7175

7175 = 5 x 5 x 7 x 41.

7175 is 1110000000111 in base 2 (binary) (A222813). It is 1300013 in base 4.

7175 is a centered octahedral number (A001845). It is also a tetradecagonal number (A051866).

7175 divides 6410 - 1.

## Thursday, February 27, 2014

### 2113

2113 is a prime number.

2111 and 2113 form a twin prime pair.

2113 = 15 + 25 + 25 + 45 + 45 = (25)2 + (25 + 1)2.

2113 is the largest prime factor of 222 + 1.

2113 is 100001000001 in base 2 (binary).

2113 has a representation as a sum of two squares: 2113 = 322 + 332. It is the sum of two consecutive squares.

2113 is the hypotenuse of a primitive Pythagorean triple: 21132 = 652 + 21122.

2113 divides 654 - 1.

Source: Prime Curios!

## Wednesday, February 26, 2014

### 9203

9203 is a prime number.

9203 is the sum of no fewer than eight squared primes (A183216).

9203 is the number of 21-node rooted identity trees of height 5 (A038089).

9203 is one of 510 four-digit prime with distinct digits (A074673).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, February 25, 2014

### 1803

1803 = 3 x 601.

1803 is a semiprime that becomes a triangular number when its digits are reversed (3081) (A115741).

1803 divides 256 - 1. It also divides 250 - 1 (A003554).

1803 is 2423 in base 9.

1803 is not a number that is the sum of a triangular number, a cube, and a positive Fibonacci number (A115177).

1803 is a non-leap year beginning and ending on a Saturday (A224994).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, February 24, 2014

### 1800

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5.

1800 is a pentagonal pyramidal number.

1800 is the sum of 10 consecutive primes: 1800 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199.

1800 is 5151 in base 7. It is 800 in base 15.

1800 has two representations as a sum of two squares: 1800 = 62 + 422 = 302 + 302.

1800 divides 496 - 1.

Source: Prime Curios!

## Friday, February 21, 2014

### 3583

3583 is a prime number.

3581 and 3583 form a twin prime pair.

3583 is the smallest number requiring an addition chain of length 16 (A003064).

3583 is the sum of 11 distinct powers of 2 (A038462): 3583 = 211 + 210 + 28 + 27 + 26 + 25 + 24 + 23 + 22 + 21 + 20.

3583 is the smallest prime with exactly nine consecutive ones in the longest run of ones in its binary expansion (A090593).

3583 divides 959 - 1.

The Commodore VIC-20 (an early 8-bit computer from 1980) had "3853 bytes free" once started up under Commodore BASIC V2.

Source: Prime Curios!

## Thursday, February 20, 2014

### 1723

1723 is a prime number.

1721 and 1723 form a twin prime pair.

1723 is a prime with distinct digits that is also a prime when the number is reversed (A046732).

1723 is the smallest of 101 consecutive primes whose sum is prime (A226380).

1723 is a central polygonal number (A002061).

1723 is the number of distinct lines through the origin in a three-dimensional cube of side length 12 (A090025).

1723 is 2324 in base 9.

1723 divides 413 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, February 19, 2014

### 6446

6446 = 2 x 11 x 293. It is a palindrome with exactly three distinct prime factors (A046329 and A046393).

6446 is a sphenic number with semiprime digits (A111494) and with even digits (A062287).

6446 is a palindrome that is the sum of consecutive squares (A180436).

6446 is a palindrome not divisible by any of its digits (A082947) nor by the sum of its digits (A082948).

6446 is a palindrome of length greater than 1 in the decimal expansion of pi (A068046).

6446 is 24536 in base 7.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, February 18, 2014

### 695

695 = 5 x 139.

695, 697, and 699 are all semiprimes (A092125). 694 and 695 are consecutive semiprimes (A109373).

695 is the maximum number of sections into which 15 slices can cut a torus (A033600).

695 uses the same three digits in base 3 (221202) and base 7 (2012).

695!! + 2 is a prime (A076185).

695 divides 963 - 1.

## Friday, February 14, 2014

### 1769

1769 = 29 x 61.

1769 is a semiprime of the special form: the sum of a semiprime k and the kth semiprime (A100467).

1769 is a centered tridecagonal number (A069126).

The square of 1769 is the sum of three consecutive primes (A076304).

The 1769th triangular number (1,565,565) contains only the digits 1, 5, and 6 (A119133).

1769 has two representations as a sum of two squares: 1769 = 132 + 402 = 202 + 372.

1769 is the hypotenuse of two primitive Pythagorean triples: 17692 = 6962 + 14802 = 10402 + 14312.

1769 divides 8810 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, February 13, 2014

### 8371

8371 = 11 x 761.

8371 is a centered 18-gonal number (A069131).

8371 is a number of the form n2 - n - 1 (n = 92) for which the sum of the digits (19) is also a number of the form n2 - n - 1 (n = 5) (A117746).

8371 divides 675 - 1.

Source: On-Line Encyclopedia of Integer Seqences

## Wednesday, February 12, 2014

### 8732

8732 = 2 x 2 x 37 x 59.

8732 is a number that cannot be written as a sum of three squares.

8732 contains exactly the same digits (with the correct multiplicity) in three different, smaller bases (A059828).

8732 is a number of the form n3 - (n + 2)2, for n = 22 (A153258).

8732 is a chain of retail clothing stores inspired by hip-hop.

## Tuesday, February 11, 2014

### 694

694 = 2 x 347.

694 is a centered triangular number (A005448).

694 and 695 are consecutive semiprimes (A070552). 694 is a semiprime with only semiprime digits (A107342).

694 is 1010110110 in base (binary). 694 is the smallest pandigital number in base 5 (10234), containing all possible digits.

694 is the number of different arrangements (up to rotation and reflection) of 7 non-attacking rooks on a 7 x 7 chessboard.

694 is the number of partitions of 34 in which no part occurs only once (A007690).

Source: Number Gossip

## Monday, February 10, 2014

### 2702

2702 = 2 x 7 x 193.

2702 is the maximum number of regions into which space can be divided by 21 spheres (A046127).

2702 is 20302 in base 6.

2702 is the sum of composite numbers between 47 and 94, inclusive (A073839).

The square of 2702 is the sum of 24 consecutive squares (A180274).

2702 is an even central polygonal number (A193868).

2702 is the sum of the totient function for the first 94 integers.

2702 divides 856 - 1.

## Friday, February 7, 2014

### 2580

2580 = 2 x 2 x 3 x 5 x 43.

2580 is a Keith number (A130010).

2580 is 220110 in base 4.

2580 is divisible by the sum of the cubes of its digits (A034088): 2580/(23 + 53 + 83 + 03) = 4.

2580 is the sum of the first 38 primes minus the next prime (A166448).

2580 divides 496 - 1.

2580 is a year in which the month of February has five Tuesdays (A143994).

## Thursday, February 6, 2014

### 7488

7488 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13.

7488 = (12 x 13 x 14 x 15 x 16)/(12 + 13 + 14 + 15 + 16)

7488 is 54400 in base 6 and 4400 in base 12.

7488 is the smallest positive number that can be written as the sum of distinct Fibonacci numbers in 75 ways (A013583).

7488 is the number of 3 x 3 magic squares (with distinct positive entries) having all entries less than 41 (A108576).

7488 is a concentric tridecagonal number (A195045).

7488 can be represented as the sum of two squares: 7488 = 482 + 722.

7488 divides 956 - 1.

## Wednesday, February 5, 2014

### 1551

1551 = 3 x 11 x 47 (A046329). 1551 is the product of three distinct prime numbers, and the sum of its factors is itself a prime (A176877): 3 + 11 + 47 = 61.

1551 is the number of trees on 25 vertices with diameter 4 (A000094).

1551 is the sum of the first 20 perfect powers (A076408).

1551 is the number of sums payable using exactly 19 banknotes of denominations 1, 5, 10, 20, 50, 100 (A135454).

1551 is a number n such that n2 + n - 1 is a prime (A058912).

1551 divides 4610 - 1.

## Tuesday, February 4, 2014

### 2340

2340 = 2 x 2 x 3 x 3 x 5 x 13.

2340 is 100100100100 in base 2 (binary) (A033138 and A020330). It is 4444 in base 8 and 210210 in base 4.

2340 is the number of ways of dissecting a polygon into 7 hexagons (A005038).

2340!!!!! - 1 is a prime number (A085149).

2340 is the sum of the divisors of 103 (A046915).

2340 has two representations as a sum of two squares: 2340 = 62 + 482 = 242 + 422.

2340 divides 613 - 1.

2340 is a year in which there are five Thursdays in the month of February (A143995).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, February 3, 2014

### 3239

3239 = 41 x 79.

3239 is a number of the form n(2n - 3), for n = 41 (A014107).

3239 is the number of colors that can be mixed with 27 units of yellow, blue, red (A048241).

3239 is 11102222 in base 3 and 22555 in base 6.

3239 divides 7810 - 1.

3239 is a number that cannot be written as a sum of three squares.

Source: On-Line Encyclopedia of Integer Sequences