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

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

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!

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.

Source: What's Special About This Number?

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!

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).

Source: What's Special About This Number?

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

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

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!

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

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).

Source: What's Special About This Number?

2013

2013 = 3 x 11 x 61.

2013 is a permutation of the digits 0, 1, 2, and 3  (A203569)

2013, 2014, and 2015 have the same number of divisors (A005238). Each is the product of three distinct primes (A066509 and A113789).

The digital sums of 2013 in base 2 (11111011101), base 3 (2202120), and base 5 (31023) are equal (A135121).

The sum of 2013 and its prime factors equals the sum of 2014 and its prime factors (A020700): 2013 + 3 + 11 + 61 = 2014 + 2 + 19 + 53 = 2088.

2013 is the number of trees with 27 nodes and 4 leaves (A055291).

The year 2013 celebrates the Mathematics of Planet Earth.

2013 is also the International Year of Statistics.

931

931 = 7 x 7 x 19.

931 is the sum of three consecutive prime numbers: 931 = 307 + 311 + 313. It is also the sum of 11 consecutive primes (A127338).

931 is 777 in base 11 and 111 in base 30. It is 2500 in base 7.

931 is a divisor of 30³ - 1.

931 is a central polygonal number (A002061).

931 is a number that is the sum of exactly three sets of Fibonacci numbers (A122195).

Source: On-Line Encyclopedia of Integer Sequences

719

719 is a prime number. It is a Sophie Germain prime because 2 x 719 + 1 = 1439, also a prime.

719 is a number that can be expressed as both a factorial prime (6! - 1) and as an abundant number less 1.

719 is the number of rooted trees with 12 vertices.

719 is a right-truncatable prime number: 719, 71, and 7 are all primes.

719, 197, and 971 are all primes.

The hour and second hands of an analog clock align 719 times every twelve hours.

Source: Prime Curios!

1234

1234 = 2 x 617.


1234 is the smallest four-digit number with increasing digits (A007908).

1234 is the number of digits in the 12th Fermat number (A057755).

1234 is 103102 in base 4. It is 14414 in base 5 and 5414 in base 6.

1234 is the number of ways to place three nonattacking bishops on a 3 x 8 board (A172207).


1234 has a representation as a sum of two squares: 1234 = 3² + 35².

Source: What's Special About This Number?

541

541 is a prime number. It is the 100th prime.

541 is a centered dodecagonal number. It is the 10th hexagonal star number.

5! + 4! + 1 = 145, the reverse of 541. 541 is the only odd number greater than 1 with this property.

541 is the number of orderings of five objects with ties allowed.

541 has a representation as a sum of two squares: 541 = 10² + 21².

541 is the hypotenuse of a primitive Pythagorean triple: 541² = 341² + 420².

541 has the representation 541 = 2⁹ + 29.

Source: Number Gossip

1000

1000 = 2 x 2 x 2 x 5 x 5 x 5. 1000 is a perfect cube.

1000 can be expressed using the first three primes: 2³ x 5³.

The 147th prime (853) plus 147 equals 1000.

2⁹⁹⁹ + 1239 is the smallest 1000-bit prime.

1000 is 2626 in base 7. It is 1331 in base 9.

1000 has two representations as a sum of two squares: 1000 = 10² + 30² = 18² + 26².

T-1000 was the shape-changing robot from the 1991 film Terminator 2: Judgment Day.

Source: Prime Curios!

1672

1672 = 2 x 2 x 2 x 11 x 19.

1672 is 767 in base 15.

1672 is a number that can be expressed as the difference of the squares of primes in just one distinct way (A090781).

1672 is a multiple of 8 that has a digit sum that is a multiple of 8 (A216997).

On an 8 x 8 chessboard, there are 1672 3-step knight's tours summed over all choices for the starting position (A186441).

1672 is the number of obtuse isosceles triangles on a 10 x 10 grid (geoboard) (A190318).

Source: On-Line Encyclopedia of Integer Sequences

797

797 is a prime number.

797 is a left- and right-trunctable prime number that yields the primes 7, 79, and 97.

797 is the smallest number and the smallest prime n such that googol - n is prime.

797 is the number of functional graphs on 9 vertices.

797 has a representation as a sum of two squares: 797 = 11² + 26².

797 is the hypotenuse of a primitive Pythagorean triple: 797² = 555² + 572².

797 is 665 in base 11 and 565 in base 12. It is 494 in base 13.

Source: Number Gossip

395

395 = 5 x 79.

395 is the sum of three consecutive primes (A034961): 395 = 127 + 131 + 137. It is also the sum of five consecutive primes (A034964): 395 = 71 + 73 + 79 + 83 + 89.

395 is the smallest multiple of 5 with a digit sum of 17 (A069534).

395 is the smallest sum of 5 consecutive odd primes that is a multiple of 5 (A132810).

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

Source: On-Line Encyclopedia of Integer Sequences