3208

3208 = 2³ x 401.

3208 has a representation as a sum of two squares: 3208 = 38² + 42².

3208 is a divisor of 45⁸ - 1.

3208 is a number that contains exactly three 2s in is base 7 representation: 12232.

3208 is a powerful number because it is the sum of some fixed power of its digits.

Caterpillar produces the 3208 diesel engine.

Source: On-Line Encyclopedia of Integer Sequences

316

316 = 2² x 79.

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

316 is a centered triangular number. It is also a centered heptagonal number.

316 has a digit product that is the digit sum of (3¹)⁶ = 729: 3 x 1 x 6 = 18; and 7 + 2 + 9 = 18.

316 is the telephone area code for the city of Wichita, Kansas.

Source: What's Special About This Number?

207

207 = 3² x 23.

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

207 is the smallest possible sum of primes that are formed using each of the digits 1 through 9: 207 = 89 + 61 + 43 + 7 + 5 + 2.

207 has a fourth power where the digits of the first half are a permutation of the digits of the last half: 207⁴ = 1836036801.

The Peugeot 207 is a supermini automobile first produced in 2006.

Source: Number Gossip

805

805 = 5 x 7 x 23.

805 is divisible by the sum of its prime factors.

805² = 648,025 = (-6 + 4 + 802 + 5)². The digits of the square of 805 include the digits of 805 as a subsequence.

805 degrees Celsius is 1481 degrees Fahrenheit, a prime temperature.

805 is the number of possible positions in the game of checkers after four moves.

Source: What's Special About This Number?

429

429 = 3 x 11 x 13.

429 is the seventh Catalan number.

429 is a divisor of 100³ - 1.

The sum of the digits of 429 is five times the number of digits: 4 + 2 + 9 = 15 = 5 x 3.

The sum of the fourth powers of the factors of 429 is a prime: 3⁴ + 11⁴ + 13⁴ = 43283.

The 429 Records label in indie rock/pop and adult alternative music, with a roster that includes Dr. John, Joan Armatrading, and Mick Fleetwood.

Source: On-Line Encyclopedia of Integer Sequences

687

687 = 3 x 229.

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

687 is 2001 in base 7 and 575 in base 11. It is 22233 in base 4 and 223 in base 18.

687 primes less than 10⁴ do not contain the digit 9.

In the Harry Potter books and movies, the Potter family vault number at Gringotts Bank is 687.

Source: Positive Integers

589

589 = 19 x 31.

589 is a centered tetrahedral number.

589 is the sum of three consecutive primes: 589 = 193 + 197 + 199.

589² contains exactly six different digits: 589² = 346921.

589 is the sum of the first 20 semiprimes.

The USS Scorpion (SSN-589) was a nuclear submarine of the U.S. Navy.

Source: What's Special About This Number?

781

781 = 11 x 71.

781 is a divisor of 5⁵ - 1.

781 is 11111 in base 5.

781 is a centered decagonal number.

781 is the maximum number of regions into which 39 lines divide the plane.

The oldest recorded eruption of Mt. Fuji in Japan occurred in the year 781.

Source: Positive Integers

483

483 = 3 x 7 x 23.

12 x 483 = 5796 and 42 x 138 = 5796. Each equality uses each of the nine digits, 0 to 9, exactly once.

185,472 = 672 x 276 = 384 x 483.

483 is a Smith number because the sum of its digits is equal to the sum of the digits of its prime factors: 4 + 8 + 3 = 3 + 7 + 2 + 3 = 15.

WP 483 is a Western Pacific Railroad caboose located at the Western Pacific Railroad Museum (Feather River Railroad Society) in Portola, California.

Source: Numeropedia

832

832 = 2⁶ x 13.

832 has a representation as a sum of two squares: 832 = 16² + 24².

832 is the maximum number of pieces into which 16 straight slices can cut a torus.

832 is 2266 in base 7; 832 is 31000 in base 4 and 1500 in base 8.

832 Karin is the largest member of a cluster of asteroids that formed only 5.8 million years ago.

Source: What's Special About This Number?

211

211 is a prime number.

211 is the smallest prime such that the sum of its even digits equals the sum of its odd digits.

211 is 111 in base 14.

211 is a centered decagonal number.

211 is the maximum number of regions into which 20 lines divide the plane.

211 is the number of primes that can appear on a 24-hour digital clock starting from 00:00 up to 23:59.

Source: Number Gossip

162

162 = 2 x 3⁴.

162 is the only number with a prime factorization of the form n * (n + 1)⁽ⁿⁿ⁾.

162 has a representation as a sum of two squares: 162 = 9² + 9².

162 is the smallest number with nine representations as a sum of four positive squares: 162 = 1² + 1² + 4² + 12² = 1² + 2² + 6² + 11² = 1² + 4² + 8² + 9² = 1² + 5² + 6² + 10² = 2² + 3² + 7² + 10² = 3² + 4² + 4² + 11² = 3² + 5² + 8² + 8² = 3² + 6² + 6² + 9² = 4² + 4² + 7² + 9².

162 is a divisor of 55³ - 1.

162 is an abundant number.

The digit sum of 162 is 9; the digit sum of the square of 162 is 18, and the digit sum of the cube of 162 is 27.

162 is the total number of baseball games each team plays during a regular season of Major League Baseball.

Source: Prime Curios!

661

661 is a prime number.

661 has a representation as a sum of two squares: 661 = 6² + 25².

659 and 661 form a twin prime pair.

661 is the hypotenuse of a primitive Pythagorean triple: 661² = 300² + 589².

661 is a centered decagonal number.

Physicist William Thomson, Lord Kelvin (1824-1907) published 661 papers on a wide range of scientific topics.

Source: Prime Curios!

4665

4665 = 3 x 5 x 311.

4665 is 33333 in base 6.

4665 is a divisor of 52²⁰ - 1.

The sum of the squares of the digits of 4665 is equal to the largest prime factor reversed, where the largest prime factor is not a palindrome: 4² + 6² + 6² + 5² = 113.

IC 4665 is one of the brighter clusters in the Milky Way galaxy.

Source: What's Special About This Number?

460

460 = 2² x 5 x 23.

460 has a unique representation as a sum of three squares: 460 = 6² + 10² + 18².

460 is a centered triangular number.

460 is the sum of twelve consecutive primes: 460 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

460 Scania is an asteroid discovered in 1900.

Source: Wikipedia

3546

3546 = 2 x 3² x 197.

3546 has a representation as a sum of two squares: 3546 = 39² + 45².

3546 is a divisor of 19¹⁴ - 1.

3546 is 1414 in base 14.

3546 is a number such that it together with its double and triple contain all digits: 3546, 7092, and 10638.

3546 is the maximum length of a rook tour on a 17 x 18 board.

Source: On-Line Encyclopedia of Integer Sequences

354

354 = 2 x 3 x 59.

354 is the sum of the first four fourth powers: 354 = 1⁴ + 2⁴ + 3⁴ + 4⁴.

354 is the smallest number whose first two digits are distinct odd primes and whose third digit is the arithmetic mean of the first two.

354 is the sum of two triangular numbers in exactly two ways: 354 = 351 + 3 = 276 + 78.

354 is the average number of days in a lunar year (rounded off).

Source: Number Gossip

947

947 is a prime number. The difference between any two of its digits is also a prime.

947 is a Chen prime because 947 + 2 = 949 = 13 x 73, so 949 is a semiprime.

947 is the maximum number of regions into which 43 lines divide the plane.

947 is the sum of seven consecutive primes: 947 = 113 + 127 + 131 + 137 + 139 + 149 + 151.

947 is the telephone area code for Oakland, Michigan. Note that the words "telephone code Oakland" have, respectively, 9, 4, and 7 digits.

Source: Prime Curios!

553

553 = 7 x 79.

553 is a rhombic dodecahedral number.

553 is the sum of nine consecutive primes: 553 = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79.

Inserting a zero between adjacent digits of 553 produces a prime: 50503.

The CN Tower in Toronto is about 553 meters tall.

Source: What's Special About This Number?

6213

6213 = 3 x 19 x 109.

6213 is a divisor of 46⁶ - 1.

6213 is 44433 in base 6 and 1133 in base 18.

6213 divides the sum of the digits of 21⁶²¹³.

6213 is the first of a triple of integers, each the product of three distinct primes: 6213 = 3 x 19 x 109; 6214 = 2 x 13 x 239; and 6215 = 5 x 11 x 113.

The CNR 6213 is a historic Canadian National Railways steam locomotive on display in Toronto.

Source: On-Line Encyclopedia on Integer Sequences

626

626 = 2 x 313. It is the smallest multidigit, palindromic, two-sided semiprime.

626 has a representation as a sum of two squares: 626 = 1² + 25².

626 is a palindrome in base 5 (10001), base 10 (626), and base 16 (272).

626 is the sum of two nonzero fourth powers: 626 = 5⁴ + 1⁴.

The Mazda 626 automobile was produced in Japan for the export market.

Source: Prime Curios!

548

548 = 2² x 137.

548 has a representation as a sum of two squares: 548 = 8² + 22².

548 is the maximum number of 9th powers needed to sum to any number.

548 is the sum of a positive square and positive cube in more than one way.

548 is the smallest of three consecutive numbers, each divisible by a square.

548 Kressida is an asteroid discovered in 1904.

Source: What's Special About This Number?

725

725 = 5² x 29.

725 has three representations as a sum of two squares: 725 = 7² + 26² = 10² + 25² = 14² + 23².

725 is the hypotenuse of two primitive Pythagorean triples: 725² = 333² + 644² = 364² + 627².

725² = 525,625, which involves, 525, 625, and 725.

The Europcopter EC 725 Super Cougar is a long-range tactical transport helicopter developed for military use.

Source: WolframAlpha

917

917 = 7 x 131.

917 is the only positive number known whose ninth power can be written as a sum of 10 ninth powers.

917 is the sum of five consecutive primes: 917 = 173 + 179 + 181 + 191 + 193.

917 is a number divisible by the sum of the squares of its digits: 9² + 1² + 7² = 131.

The Porsche 917 is a racing car that gave its manufacturer its first overall wins in the 24 Hours of Le Mans race.

Source: What's Special About This Number?

96

96 = 2⁵ x 3. It is the second smallest number with six prime factors.

96 has a unique representation as a sum of three squares: 96 = 4² + 4² + 8².

96 is 88 in base 11.

96 is the seventh number that stays the same when written upside down.

Ninety Six is a town in South Carolina.

Source: Phillips, R. 2004. Numbers: Facts, Figures and Fiction. Badsey Publications.

109

109 is a prime number.

109 has a representation as a sum of two squares: 109 = 3² + 10².

107 and 109 form a twin prime pair.

109 is the hypotenuse of a primitive Pythagorean triple: 109² = 60² + 91².

109 is a centered triangular number.

109 is the smallest number that contains more digits than its square: 109² = 11881.

109 is the smallest number that is palindromic in bases 5 (414) and 9 (131).

109 is the atomic number of the element meitnerium.

Source: Number Gossip

8120

8120 = 2³ x 5 x 7 x 29.

8120 is a divisor of 41⁴ - 1.

8120 is 4848 in base 12.

8120 is one-third the product of the 10th prime, the previous number, and the following number: 8120 = (28 x 29 x 30)/3.

Research in Motion produces the BlackBerry Pearl 8120 smartphone.

Source: On-Line Encyclopedia of Integer Sequences

801

801 = 3² x 89.

801 has a representation as a sum of two squares: 801 = 15² + 24².

801 = (7! + 8! + 9! + 10!)/(7 x 8 x 9 x 10).

801 is 1441 in base 8 and 171 in base 25.

801 was an English experimental rock band formed in 1976 for three live concerts.

Source: What's Special About This Number?

245

245 = 5 x 7².

245 has a representation as a sum of two squares: 245 = 7² + 14².

245 is a stella octangula number.

245² is one of three square numbers using the same digits: 245² = 60025, 160² = 25600, and 250² = 62500.

245 is the number of Jewish singers who returned from captivity in Babylon following the rise of Cyrus the Great and the Persian Empire (Nehemiah, chapter 7, verse 67).

Source: What's Special About This Number?

4884

4884 = 2² x 3 x 11 x 37.

4884 is a divisor of 43⁴ - 1.

66 x 64 = 4224

66 x 67 = 4422

66 x 68 = 4488

66 x 69 = 4554

66 x 74 = 4884

4884 is a palindrome whose sum of prime factors is also a palindrome: 2 + 2 + 3 + 11 + 37 = 55.

NGC 4884 is an elliptical galaxy in Coma Berenices.

Source: Numeropedia

486

486 = 2 x 3⁵.

486 is a Perrin number.

486 is 200000 in base 3 and 600 in base 9. It is 123 in base 21.

486 is a number with 12 divisors.

486 is the sum of two positive fifth powers: 486 = 3⁵ + 3⁵.

Intel's 486 (short for 80486) microprocessor chip powered many microcomputers, starting in 1986.

Source: What's Special About This Number?

672

672 = 2⁵ x 3 x 7.

672 has a unique representation as a sum of three squares: 672 = 4² + 16² + 20².

672⁶⁷² plus the 672nd prime is a prime number.

672 is a multiperfect number.

672 x 276 = 185,472 = 384 x 483.

672 is the number of hours in February of a non-leap year.

Source: Prime Curios!

2011

2011 is a prime number.

2011 has the representation 2¹¹ - 37.

2011 is the sum of 11 consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211.

2011 is a number such that first reversing the digits and then squaring equals the result of first squaring and then reversing the digits: 1102² =1214404 and 2011² = 4044121.

2⁸ is 2011 in base 5.

The sum of the digits of 2011 is equal to the number of digits: 2 + 0 + 1 + 1 = 4. The digit sum is a square and a power of 2.

The next prime date from now (month, day, and year are primes) is 2/2/2011. Note that 222011 is a prime.

In the Aeon Flux television series and film (2005), 99 percent of the world's population is wiped out by a mysterious virus in the year 2011.

The Peace Corps marks its 50th anniversary in the year 2011. It is also the 5oth anniversary of the first manned mission to space.

2011 is the 100th anniversary of the launch of the Titanic on May 31, 1911.

2011 is designated the International Year of Chemistry.

Source: Prime Curios!

982

982 = 2 x 491.

982 is the number of integer partitions of 39 into distinct parts.

982 is the number of ways to place four non-attacking queens on a 7 x 7 board.

Written backwards, 982 is the square 289.

NGC 982 is a spiral galaxy in the constellation Andromeda.

Source: On-Line Encyclopedia of Integer Sequences

165

165 = 3 x 5 x 11.

165 is 10100101 in base 2 (binary).

165 is the number of integer partitions of 26 into distinct parts.

165 is the ninth tetrahedral number.

165 is the sum of the divisors of the first 14 integers.

The Tahoe Rim Trail is a 165-mile hiking trail around Lake Tahoe.

Source: WolframAlpha

899

899 = 29 x 31. It is the product of two successive primes and the product of twin primes.

Any number consisting of an 8 followed by an even number of nines has prime factors 3 x (10^n/2) + 1 and 3 x (10^n/2) - 1, where n is the number of nines: 899 = 3(10¹) + 1) x 3(10¹) - 1 = 31 x 29. Similarly, 8999999 = 2999 x 3001.

899 is the smallest number whose sum of digits is 26.

899 is a number that can't be expressed as the sum of a prime number and a Fibonacci number.

The Benneli TNT 899 Sport is an Italian motorcycle.

Source: Prime Curios!

377

377 = 13 x 29.

377 has two representations as a sum of two squares: 377 = 4² + 19² = 11² + 16².

377 is the fourteenth Fibonacci number. It is the largest known Fibonacci number whose digits are all prime.

377 is the hypotenuse of two primitive Pythagorean triples: 377² = 135² + 352² = 152² + 345².

377 is the sum of the squares of the first six primes: 377 = 2² + 3² + 5² + 7² + 11² + 13².

The Aero Spacelines B-377 SG Super Guppy is a four-engine oversize-cargo freighter aircraft.

Source: Prime Curios!

1196

1196 = 2² x 13 x 23.

1196 is the one thousandth non-prime number.

1196 is the number of lines through exactly two points of a 9 x 9 grid of points.

1196 is 14241 in base 5 and 616 in base 14.

1196 is the number of assymetric polyominoes made up of 9 cells.

NGC 1196 is a galaxy in the constellation Eridanus, discovered by John Herschel in 1835.

Source: Number Gossip

359

359 is a prime number. It is a Sophie Germain prime because 2 x 359 + 1 = 719, a prime.

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

359 = -1 + 2³ x 45.

The 359th, 360th, and 361st decimal digits of pi are 360.

359 has a base 3 representation (111022) that ends with its base 7 representation (1022), which is also true for 357 and 358.

In the Star Trek imaginary universe, the Battle of Wolf 359 was the Federation's first major battle against a group of cyborgs.

Source: Prime Curios!

173

173 is a prime number. It is a Sophie Germain prime because 2 x 173 + 1 = 347, which is also prime.

173 has a representation as a sum of two squares: 173 = 2² + 13². It is the sum of the squares of two Fibonacci numbers, 2 and 13.

173 is the hypotenuse of a primitive Pythagorean triple: 173² = 52² + 165².

173 is the only prime whose sum of cubed digits equals its reversal: 1³ + 7³ + 3³ = 371.

173 is the largest known prime whose square (29929) and cube (5177717) have no digits in common.

173 = 1 + 2² + 2³ + 2⁵ + 2⁷, where the exponents are consecutive primes.

In the 1993 movie The Sandlot, The Beast (a ferocious dog) is said to have eaten 173 guys.

Source: Prime Curios!

21

21 = 3 x 7.

21 is 10101 in base 2 (binary) and 111 in base 4.

21 has a unique representation as a sum of three squares: 21 = 1² + 2² + 4².

21 is the smallest number with five representations as a sum of three primes: 21 = 2 + 2 + 17 = 3 + 5 + 13 = 3 + 7 + 11 = 5 + 5 + 11 = 7 + 7 + 7.

21 is the eighth Fibonacci number.

21 is the fifth Motzkin number.

21 is the sixth triangular number.

21 is the total number of spots on a normal die.

Source: Phillips, R. 2004. Numbers: Facts, Figures and Fiction. Badsey Publications.

364

364 = 2² x 7 x 13.

364 has a unique representation as a sum of three squares: 364 = 2² + 6² + 18².

364 is the twelfth tetrahedral number.

364 is 111111 in base 3.

The first two digits of 364 are the product of the first two primes to the power of the first prime and the last two digits are the first prime to the product of the first two primes: 36 = (2 x 3)² and 64 = 2^{(2 x 3)}.

Asteroid 364 Isara was discovered in 1893.

Source: Prime Curios!

954

954 = 2 x 3² x 53.

954 has a representation as a sum of two squares: 954 = 15² + 27².

954 is the smallest number n such that if you subtract its reverse from it, you get a number with the same digits as n: 954 - 459 = 495.

954 is 676 in base 12 and 585 in base 13.

Steak 954 is a steakhouse in Fort Lauderdale, Florida.

Source: Number Gossip

461

461 is a prime number.

461 has a representation as a sum of two squares: 461 = 10² + 19².

461 and 463 form a twin prime pair.

461 is the hypotenuse of a primitive Pythagorean triple: 461² = 261² + 380².

461 is the largest number for which ((10²ⁿ) + 1)/101 is known to be a prime number.

Eric Clapton recorded a solo album titled 461 Ocean Boulevard.

Source: Prime Curios!

565

565 = 5 x 113.

565 has two representations as a sum of two squares: 565 = 6² + 23² = 9² + 22².

565 is the hypotenuse of two primitive Pythagorean triples: 565² = 276² + 493² = 396² + 403².

565 is 474 in base 11.

565 is the sum of three consecutive primes: 565 = 181 + 191 + 193.

in the year 565, St. Columba reported seeing a monster in Loch Ness, Scotland.

Source: WolframAlpha

942

942 = 2 x 3 x 157.

942 is 666 in base 12.

942 is the smallest number whose cube contains five 8s: 942³ = 835,896,888.

942 is the sum of four consecutive primes: 942 = 229 + 233 + 239 + 241.

NGC 942/943 (also known as Arp 309) is a pair of interacting galaxies in the constellation Taurus.

Source: What's Special About This Number?

877

877 is a prime number.

877 has a representation as a sum of two squares: 877 = 6² + 29².

877 is the seventh Bell number.

877 is the hypotenuse of a primitive Pythagorean triple: 877² = 348² + 805².

877 is 1555 in base 8 and 611 in base 12.

877 is a telephone area code for toll-free service.

Source: Prime Curios!

451

451 = 11 x41.

451 is a decagonal number. It is also a centered decagonal number.

10⁴⁵¹ + 451 is a prime number.

3 plus the integer formed by the first 451 digits after the decimal point in pi is a prime number.

The title of the novel and film Fahrenheit 451 refers to the temperature at which book paper supposedly burns.

Source: Prime Curios!

933

933 = 3 x 311.

933 is a number that can't be expressed as a sum of a prime number and a Fibonacci number.

933 is a house number.

933 is a member of the sequence generated when you start with 1 and repeatedly reverse the digits and add 10 to get the next term: 1, 11, 21, 32, 33, . . . , 329, 933, 349, . . .

Asteroid 933 Susi was discovered in 1927.

Source: On-Line Encyclopedia of Integer Sequences