## Thursday, January 31, 2013

### 9000

9000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5.

9000 has two representations as a sum of two squares: 9000 = 302 + 902 = 542 + 782.

9000 is the index of a triangular number containing only three different digits.

9000 is a centered cube number.

9000 is the number of palindromes of length 8 (A050683).

The BFG-9000 is the most powerful weapon in the video game series Doom.

## Wednesday, January 30, 2013

### 992

992 = 2 x 2 x 2 x 2 x 2 x 31. It is the product of two consecutive numbers (a pronic number): 992 = 32 x 31.

992 is 1111100000 in base 2 (binary). It is 212 in base 22.

992 is the number of differential structures on the 11-dimensional hypersphere.

992 is the largest known even number that is expressible as the sum of two primes in only 13 ways.

Source: Number Gossip

## Tuesday, January 29, 2013

### 1687

1687 = 7 x 241.

1687, 1689, and 1691 are all semiprimes (A092125), the product of two primes.

1687 is 777 in base 15.

The last 1687 digits of 16871687 form a prime number.

1687 and its reversal 7861 are both multiples of 7 (A062901).

1687 is the sum of three consecutive hexagonal numbers (A129109): 1687 = 496 + 561 + 630.

Source: Prime Curios!

## Monday, January 28, 2013

### 1509

1509 = 3 x 503.

1509 is the number of disconnected 2-regular graphs on 39 vertices (A165652).

1509 is a number n such that 2n + 1, 4n + 1, and 8n + 1 are all primes (A124041).

1509 is a pinwheel number, satisfying the equation 2n2 + 6n + 1 for n = 26 (A059993).

1509 is a number n such that 1 + n + n3 + n5 + n7 + . . . + n33 + n35 is prime (A124187).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, January 25, 2013

### 2225

2225 = 5 x 5 x 89.

2225 has three representations as a sum of two squares (A025313 and A000443): 2225 = 42 + 472 = 172 + 442 = 252 + 402.

2225 is the hypotenuse of two primitive Pythagorean triples: 22252 = 3762 + 21932 = 14962 + 16472.

2225 is a value of n where the sum of the nth powers of its digits are prime for n = 1 to 10: 21 + 21 + 21 + 51 = 11, 22 + 22 + 22 + 52 = 37, and so on.

Source: Prime Curios!

## Thursday, January 24, 2013

### 491

491 is a prime number. It is a Sophie Germain prime (A005384) because 2 x 491 + 1 = 983 is also prime.

491 is a prime number with distinct, nonprime digits (A034844) in English consecutive order: four, nine, one. Each digit is also a square.

It is conjectured that 491 is the smallest prime not of the form x3 + y3 + 2z3.

491 is the smallest number n such that the largest prime factors of the numbers n through n + 4 decrease.

Source: Prime Curios!

## Wednesday, January 23, 2013

### 547

547 is a prime number.

547 is a centered hexagonal number (or hex number) and a centered heptagonal number.

The number of primes between 6! and 7! is itself prime. 547 is the smallest odd prime to enumerate the primes between n! and (n + 1)! for any n.

547 is the smallest number that cannot be written using 11 copies of 11 and the operations +, -, x, /.

547 is 202021 in base 3 and 20203 in base 4. It is 4142 in base 4.

Source: Prime Curios!

## Tuesday, January 22, 2013

### 343

343 = 7 x 7 x 7.

343 = (3 + 4)3.

342343 + 343342 is prime.

343 is the sum of the first five odd Fibonacci primes: 343 = 3 + 5 + 13 + 89 + 233.

343 can be expressed using the first six odd primes: 7(3 + 5 + 11 + 13 + 17).

343 + 656 = 999 = 323 + 676.

343 is 1331 in base 6 and 292 in base 11.

343 = 180 + 181 + 182.

The Willow Grove exit on the Pennsylvania Turnpike started out as exit 27 (the cube of an odd prime). With a change in exit numbers, Willow Grove is now exit 343, another cube of an odd prime.

Source: Prime Curios!

## Friday, January 18, 2013

### 2413

2413 = 19 x 127.

2413 is a divisor of 206 - 1.

2413 is a hexadecagonal number (A051868).

2413 is a semiprime that is the sum of two positive cubes (A085366).

The difference between 2413 and its reversal, 3142, is a nonzero cube (A061923): 3142 - 2413 = 729 = 93.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, January 17, 2013

### 918

918 = 2 x 3 x 3 x 3 x 17.

918 is a number that does not have any digits in common with its cube (773620632).

918 is 646 in base 12.

The sum of the digits of 918 (18) is a substring of 918 (A052018).

918 is the smallest number that is 51 times the sum of its digits (A003634).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, January 16, 2013

### 871

871 = 13 x 67.

871 = 4! + 5! + 3! + 6! + 1! and 45,361 = 8! + 7! + 1!

871 is 31213 in base 4.

871 is a central, polygonal number (A002061). It is also a tridecagonal number (A051865).

871 has the representation 2533 + 7.

871 is a divisor of 662 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, January 15, 2013

### 587

587 is a prime number.

587 is the smallest number whose sum of digits (20) is larger than that of its cube (5873 = 202262003; 17).

587 is the number of 10-smooth numbers up to 105. An integer is 10-smooth if all its prime factors are less than or equal to 10.

Add 587 zeros between the 9 and the 7 in the prime number 97 to obtain a 589-digit prime.

587 is the sum of five consecutive primes: 587 = 107 + 109 + 113 + 127 + 131.

Nickel Plate Road No. 587 (at the Indiana Transportation Museum) is an example of a United States Railroad Administration light Mikado steam locomotive.

Source: Number Gossip

## Monday, January 14, 2013

### 2351

2351 is a prime number. It is a Sophie Germain prime because 2 x 2351 + 1 = 4703 is also prime.

23512351 ends in the digits 2351.

There are 6907 digits in 2351! Note that 6907 is prime.

2351 is in the middle of a sequence of 17 consecutive primes whose sum is also prime: 2293 + 2297 + . . . + 2351 + 2393 + 2399 = 39971 is prime and 17 is prime.

2351 is the sum of all three-digit Fibonacci numbers.

Source: Prime Curios!

## Friday, January 11, 2013

### 988

988 = 2 x 2 x 13 x 19.

988 is the maximum number of pieces into which 18 cuts can divide a cube (A000125).

988 is the sum of four consecutive primes (A034963): 988 = 239 + 241 + 251 + 257.

988 is the number of walks of length 6 on a square lattice, starting at the origin, staying on points x greater than or equal to 0 and y less than or equal to x (A060900).

988 and the 988th prime (7817) have only one digit in common (A107939): 8.

## Thursday, January 10, 2013

### 853

853 is a prime number.

853 is formed from three consecutive Fibonacci numbers, in reverse order.

853 divides the sum of the first 853 prime numbers (2615298).

853 is the number of connected graphs with seven vertices.

853 has a representation as a sum of two squares: 853 = 182 + 232.

853 is the hypotenuse of a primitive Pythagorean triple: 8532 = 2052 + 8282.

853 is the start of the smallest string of five consecutive cousin prime pairs.

The Transamerica Pyramid, the tallest skyscraper in San Francisco, has a structural height of 853 feet.

Source: Prime Curios!

## Wednesday, January 9, 2013

### 670

670 = 2 x 5 x 67.

670 is an octahedral number (A005900).

670 is a sum of composite numbers between successive primes (A054265).

670 is the number of ways of making change for 57 cents using coins of 1, 2, 5, 10, 20, and 50 cents (A001313).

670 is the sum of 15 but no fewer nonzero fourth powers (A046046).

## Tuesday, January 8, 2013

### 972

972 = 2 x 2 x 3 x 3 x 3 x 3 x 3.

972 is the largest number for which the absolute difference between any two digits of the number is always prime.

972 is an Achilles number, which is powerful in the sense that each prime factor occurs with exponent greater than one but imperfect in the sense that the number is not a perfect power.

972 is the sum of four positive fifth powers (A003349): 972 = 35 + 35 + 35 + 35.

Source: Number Gossip

## Monday, January 7, 2013

### 747

747 = 3 x 3 x 83.

747 is 456 in base 13.

747 is the sum of distinct factorials (A059590): 747 = 6! + 4! + 2! + 1!

747 is the number of ways to tile a 4 x 7 region with 1 x 1 and 2 x 2 tiles (A054854).

The Boeing 747 is a larger commercial airliner.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, January 4, 2013

### 2153

2153 is a prime number.

2153 is the sum of five consecutive composite numbers (A060330): 2153 = 428 + 429 + 430 + 432 + 434.

2153 has a representation as a sum of two squares: 2153 = 282 + 372.

2153 is the hypotenuse of a primitive Pythagorean triple: 21532 = 5852 + 20722.

In 1977, Akio Suzuki used primes ranging from 53 to 2153 to construct the magic cube with the smallest possible magic sum (for cubes with side three and distinct prime entries). Source: Prime Curios!

## Thursday, January 3, 2013

### 2040

2040 = 2 x 2 x 2 x 3 x 5 x 17.

2040 is a number that can be expressed as the difference of the squares of primes in exactly four distinct ways (A092000).

2040 is the sum of a twin prime pair (A054735): 2040 = 1019 + 1021.

2040 is the number of ways of writing 13 as a sum of six squares (A000141).

2040 is the sum of 12 consecutive primes (A127339): 2040 = 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197.

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, January 2, 2013

### 936

936 = 2 x 2 x 2 x 3 x 3 x 13.

936 is an octagonal number (A000567) and a pentagonal pyramidal number (A002411).

936 is 12221 in base 5.

9363 = 820,025,856 = (820 + 02 + 58 + 56)3.

936 has a representation as a sum of two squares: 936 = 62 + 302.

936 is a number that can be expressed as the difference of the squares of primes in just one distinct way (A090781).