1237

1237 is a prime number.

1237 has a representation as a sum of two squares: 1237 = 9² + 37².

1237 is the hypotenuse of a primitive Pythagorean triple: 1237² = 612² + 1275².

1237² - (1237 - 5)² = 12345.

1237 is also a prime number when its digits are reversed (emirp): 7321. It is the smallest 4-digit emirp with distinct digits. The sum of its digits, 1 + 2 + 3 + 7 = 13, is equal to the smallest double-digit emirp. 1237 is an emirp formed from the number 12 and the 12th prime; its reversal (7321) is formed from the 21st prime and the number 21.

1237 Geneviève is an asteroid discovered in 1931.

Source: Prime Curios!

179

179 is a prime number. 179 is a Sophie Germain prime because 2 x 179 + 1 = 359, a prime.

179 and 181 form a twin prime pair.

179 = (17 x 9) + (17 + 9).

179 has a square comprised of the digits 0 to 4: 179² = 32041.

179 x 79 = 14141.

There are 179 even days in one year.

Source: Number Gossip

686

686 = 2 x 7³.

686 is a divisor of 19⁶ - 1.

686 is the number of partitions of 35 in which no part occurs only once.

686 is 2000 in base 7 and 222 in base 18.

686 Clothing produces fashionable sportswear.

Source: What's Special About This Number?

861

861 = 3 x 7 x 41.

861 is the 41st triangular number. It is also a hexagonal number.

861 = 7 + 77 + 777.

144,648 = 861 x 168 = 492 x 294.

The USS Harwood (DD 861) was a destroyer in the U.S. Navy just after World War II.

Source: What's Special About This Number?

477

477 = 3² x 53,

477 has a representation as a sum of two squares: 477 = 6² + 21².

477 is a pentagonal number.

477 is the smallest number that is the sum of different primes by using twice all the digits greater than 0: 477 = 89 + 83 + 67 + 61 + 53 + 47 + 41 + 29 + 5 + 2.

477 is the smallest number whose cube contains four 3s: 477³ = 108,531,333.

Masonic Funeral Music in C by Wolfgang Amadeus Mozart is cataloged as KV 477.

Source: Number Gossip

380

380 = 2² x 5 x 19.

380 is a pronic number because it is the product of two consecutive numbers: 380 = 19 x 20. Hence, it is also twice a triangular number.

380 is the smallest number divisible by 5 of the form p(p + 1) where p is a prime and doesn't equal 5.

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

380 is the number of necklaces possible with 13 beads, each being one of two possible colors.

The Airbus A380 aircraft, the largest commercial aircraft flying today, was introduced in the year 2007.

Source: Number Gossip

62

62 = 2 x 31.

62 is 222 in base 5.

62 = 14 + 15 + 16 + 17.

62 is the smallest number that can be written as the sum of three distinct squares in two ways: 62 = 7² + 3² + 2² = 6² + 5² + 1².

62 is the only number whose cube (238328) consists of three digits, each occurring two times.

A truncated icosidodecahedron has 62 faces (12 decagons, 20 hexagons, and 30 squares).

Source: Wikipedia

668

668 = 2² x 167.

668 is the number of integer partitions of 36 into distinct parts.

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

668 = 3⁶ - 61.

334,668 = 668² - 334² = (334 + 668) x 334, where 668 = 2 x 334.

668 is the number of legal pawn moves in chess.

Source: What's Special About This Number?

462

462 = 2 x 3 x 7 x 11.

Assuming the Generalized Riemann Hypothesis, 462 is the largest number that is not of the form ab + bc + ca, for positive integers a, b, and c.

462⁴⁶² + 462 + 1 is a prime number.

462² = 213,444 = (21 - 3 + 444)².

462 is 3322 in base 5; 462 is 2050 in base 6 and 250 in base 14; 462 is 110 in base 21.

Mathematician Zu Chongzhi introduced the Daming calendar in China in the year 462.

Source: Number Gossip

363

363 = 3 x 11².

363 is a divisor of 40¹⁰ - 1.

363 and the 363rd triangular number (66,066) are both palindromic.

363⁴ = 17,363,069,361 and 630⁴ = 173,630,693,610,000.

363 is 11223 in base 4, 2423 in base 5, and 123 in base 18; 363 is 300 in base 11; 363 is 553 in base 8 and 443 in base 9.

On April 20 in the year 363, the planet Venus occulted the planet Jupiter.

Source: Numeropedia

287

287 = 7 x 41.

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

287 is a pentagonal number.

287 is the sum of consecutive primes in three different ways: 287 = 89 + 97 + 101 = 47 + 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

287 is the sum of the first three NSW primes: 287 = 7 + 41 + 239.

287 Nephthys is a large asteroid discovered in 1889.

Source: Prime Curios!

934

934 = 2 x 467.

934 has a fifth root that starts 3.25252225 . . .

934 is a number of the form n² + n + 4, for n = 30.

934 is the number of positions that the 3 x 3 x 3 Rubik's cube can be in after exactly five moves (under the full group of order 48 of the cube). This is the number of positions that can be reached in five moves, but which cannot be reached in fewer than five moves.

934 is the sixteenth Fibonacci number minus the sixteenth prime number: 934 = 987 - 53.

The Porsche 934, introduced in 1976, was a racing version of the Porsche 911 Turbo.

Source: What's Special About This Number?

6119

6119 = 29 x 211.

6119 is a number that cannot be written as a sum of three squares.

6119 is a divisor of 63¹⁴ - 1.

6119 is a strobogrammatic number. It appears the same whether viewed normally or upside down.

6119 is 143434 in base 5.

Lionel model trains included the D.L. & W. Work Caboose No. 6119 from 1955 to 1966.

Source: What's Special About This Number?

628

628 = 2² x 157.

628 has a representation as sum of two squares: 628 = 12² + 22².

628 is 444 in base 12.

628 is the sum of the squares of four consecutive primes: 628 = 7² + 11² + 13² + 17².

The Indian astronomer and mathematician Brahmagupta wrote the mathematics book The Opening of the Universe in the year 628.

Source: What's Special About This Number?

532

532 = 2² x 7 x 19.

532 has a unique representation as a sum of three squares: 532 = 8² + 12² + 18².

532 is 444 in base 11.

532 is a divisor of 11⁶ - 1.

532 is a pentagonal number.

532 is the smallest even number differing by a composite number from both of its prime neighbors.

532 was the first year in which the Anno Domini calendar was used for numbering the years.

Source: Number Gossip

850

850 = 2 x 5² x 17.

850 has three representations as a sum of two squares: 850 = 3² + 29² = 11² + 27² = 15² + 25².

850 is the number of trees on 14 vertices with graph diameter 7.

850 is 2323 in base 7 and 1144 in base 9.

850 is the maximum Fair Isaac credit score.

Source: What's Special About This Number?

419

419 is a prime number.

419 is also a Sophie Germain prime because 2 x 419 + 1 = 839 is also prime. It is the 22nd Sophie Germain prime, and 22 = 2 x 11 is the product of two Sophie Germain primes.

419 and 421 form a twin prime pair.

419 is a divisor of 13¹¹ - 1.

419 is the smallest number that when divided by 2, 3, 4, 5, 6, and 7 leaves remainders of 1, 2, 3, 4, 5, and 6, respectively. Also, 419 is 1 less than the least common multiple of the first seven integers.

419, 41, and 19 are all primes. Their reversals, 914, 14, and 91, are all semiprimes.

Dutch naturalist and microscopy pioneer Anton van Leeuwenhoek (1632-1723) ground a total of 419 lenses during his life.

Source: Prime Curios!

601

601 is a prime number.

599 and 601 form a twin prime pair.

601 has a representation as a sum of two squares: 601 = 5² + 24².

601 is the hypotenuse of a primitive Pythagorean triple: 601² = 240² + 551².

601 is a centered pentagonal number.

601 is the lesser member p of the least sexy prime pairs (p, p + 6) such that all numbers in between have the same number of prime divisors (counted with multiplicity).

The Minivac 601 Digital Computer Kit was a product created by Claude Shannon and sold by Scientific Development Corporation as early as 1961.

Source: Number Gossip

500

500 = 2² x 5³.

500 has two representations as a sum of two squares: 500 = 4² + 22² = 10² + 20².

There are exactly 500 prime numbers between 20,000 and 25,000.

166,500,333 = 166³ + 500³ + 333³.

500 is 4000 in base 5. It is 13310 in base 3 and 1313 in base 7.

A ream contains 500 sheets of paper.

Source: Numeropedia

433

433 is a prime number.

433 has a representation as a sum of two squares: 433 = 12² + 17².

431 and 433 form a twin prime pair.

433 is the hypotenuse of a primitive Pythagorean triple: 433² = 145² + 408².

The last 433 digits of 433⁴³³ form a prime number.

433⁴ = 35152125121 and 035 + 152 + 125 + 121 = 433.

433 Eros was the first Near-Earth asteroid to be discovered.

Source: Prime Curios!

195

195 = 3 x 5 x 13.

195 is 11000011 in base 2 (binary), 3003 in base 4, and 303 in base 8.

195 is the third integer that is the sum of the squares of three consecutive primes: 195 = 11² + 7² + 5².

195 is in the middle of the prime quadruplet 191, 193, 197, and 199.

IC 195 is one member of a pair of galaxies in the constellation Aries.

Source: Prime Curios!

909

909 = 3² x 101.

909 has a representation as a sum of two squares: 909 = 3² + 30².

909 is a value of n that has no digits in common with 2n, 3n, 4n, 5n, 6n, 7n, 8n, or 9n.

909² = 826,281 = (826 + 2 + 81)².

The Roland TR-909 was a drum machine produced in 1983.

Source: What's Special About This Number?

60

60 = 2² x 3 x 5.

60 is the smallest number with six representations as a sum of two primes: 60 = 7 + 53 = 13 + 47 = 17 + 43 = 19 + 41 = 23 + 27 = 29 + 31.

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

60 is 66 ion base 9.

60 is the least common multiple of the first five positive integers.

There are 60 seconds in one minute and 60 minutes in one hour.

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

998

998 = 2 x 499.

998 is the smallest number with the property that its first 55 multiples contain the digit 9.

998³ = 994,011,992 = (994 + 0 + 1 + 1 + 9 - 9 + 2)³.

998 is 4342 in base 6 and 828 in base 11.

The Ducati 998 motorcycle was produced from 2002 to 2004.

Source: What's Special About This Number?

184

184 = 2³ x 23.

184 has a unique representation as a sum of three squares: 184 = 2² + 6² + 12².

184 is the maximum number of regions into which 14 circles divide the plane.

184 is the smallest number that can be written as q * p^q + r * p^r, where p, q, and r are distinct primes: 184 = 3 x 2³ + 5 x 2⁵.

184 is the difference of two square numbers: 184 = 25² - 21².

In nuclear physics, 184 is believed to be a magic number.

Source: Prime Curios!

80

80 = 2⁴ x 5.

80 has a representation as a sum of two squares: 80 = 4² + 8².

80 is the smallest number with exactly seven representations as a sum of three distinct primes: 80 = 2 + 5 + 73 = 2 + 7 + 71 = 2 + 11 + 67 = 2 + 17 + 61 = 2 + 19 + 59 = 2 + 31 + 47 = 2 + 37 + 41.

80 is 2222 in base 3.

80 is the smallest number that is diminished by taking its sum of letters (writing out its English name and adding the letters using a = 1, b = 2, c = 3, . . .): EIGHTY = 5 + 9 + 7 + 8 + 20 + 25 = 74.

Around the World in Eighty Days is a novel by Jules Verne.

Source: Number Gossip

218

218 = 2 x 109.

218 has a representation as a sum of two squares: 218 = 7² + 13².

218 is the number of simple directed graphs of four nodes.

218 is 1333 in base 5, 1002 in base 6, 262 in base 9, and 118 in base 14.

218 is the number of votes required in the United States House of Representatives to achieve a majority.

Source: Number Gossip

166

166 = 2 x 83.

166 is a centered triangular number.

166 is the smallest number such that the number and its reversal are both congruent to 1 mod p for the same set of distinct odd primes: 166 = 661 = 1 mod (3, 5, 11).

166 is the smallest Smith number that is prime when reversed (661), turned upside down (991), and reversed-then-turned-upside-down (199). You get the next case by inserting a zero between the digits: 10606.

U-166 was the only German submarine lost in the Gulf of Mexico.

Source: Prime Curios!

772

772 = 2² x 193.

772 has a representation as a sum of two squares: 772 = 14² + 24².

772 is the sum of six distinct positive pentatope numbers.

772 is the sum of six positive cubes in exactly three ways.

772 is a structured truncated icosahedral number.

Telephone area code 772 serves that state of Florida.

Source: On-Line Encyclopedia of Integer Sequences

576

576 = 2⁶ x 3².

576 has a unique representation as a sum of three squares: 576 = 8² + 16² + 16².

576 is the number of 4 x 4 Latin squares.

576 is the smallest square such that it remains a square when its leading digit is increased by 1: 676 = 26².

576 = (2 + 3 + 5 + 7 + 11)² - (2² + 3² + 5² + 7² + 11²).

New Balance produces a 576 line of fitness walking shoes.

Source: Number Gossip

654

654 = 2 x 3 x 109.

654 has a square that is the sum of a cube and fifth power.

The sum 327 + 654 = 981 is one of only four cases in which the equality n + 2n = 3n uses each of the nine digits 1 to 9 once (n = 192, 219, 273, and 327).

654 is 545 in base 11.

654 is a Smith number. The sum of its digits is equal to the sum of the digits of its prime factors: 6 + 5 + 4 = 2 + 3 + 1 + 0 + 9 = 15.

The Auburn Company produced the Auburn 654 automobile in 1936, the year the company went out of business.

Source: What's Special About This Number?

149

149 is a prime number.

149 and 151 form a pair of twin primes.

149 has a representation as a sum of two squares: 149 = 7² + 10².

149 is the hypotenuse of a primitive Pythagorean triple: 149² = 51² + 140².

149 is the concatenation of the first three positive squares.

149 is the smallest number whose square starts with three identical digits: 149² = 22201.

149 is the smallest prime that retains the end (unit) digit of its predecessor (139).

149 is the smallest number that is the sum of proper substrings of its reverse: 149 = 1 + 4 + 9 + 94 + 41.

149 Medusa is an asteroid discovered in 1875.

Source: Number Gossip

351

351 = 3³ x 13.

351 is the 26th triangular number. It is the sum of the first 26 numbers. Hence, it is also the numeric value of all the letters of the English alphabet, taken together.

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

351 is a divisor of 53² - 1.

351 is the smallest number so that it and its immediate neighbors are each the product of four or more primes: 350 = 2 x 5 x 5 x 7; 351 = 3 x 3 x 3 x 13; 352 = 2 x 2 x 2 x 2 x 2 x 11.

The 1971 Ford Mustang Boss 351 was equipped with a powerful 351-cubic-inch V-8 engine.

Source: Number Gossip

874

874 = 2 x 19 x 23.

874 is a heptagonal number.

874 is the number of positive integer solutions to (1 + 1/a)(1 + 1/b)(1 + 1/c)(1 + 1/d)(1 + 1/e) = 2.

874 = 0! + 1! + 2! + 3! + 4! + 5! + 6!

874² = 763876 = (7 - 6 - 3 + 876)²

USS Duncan (DDR 874) was a U.S. Navy destroyer, launched in 1945.

Source: What's Special About This Number?

742

742 = 2 x 7 x 53.

742 is a decagonal number.

742 is the maximum number of regions into which 38 lines divide a plane.

742 is the smallest number that is one more than triple its reverse: 742 = 3 x 247 + 1.

742 is the eighth Keith number.

GJ 742 (Gliese-Jahreiss 742) is a white dwarf star located about 43 light years from Earth in the constellation Draco.

Source: What's Special About This Number?

625

625 = 5⁴. It is a perfect fourth power.

Two fourth powers use the same digits: 5⁴ = 625 and 4⁴ = 256.

625 has two representations as a sum of two squares: 625 = 7² + 24² = 15² + 20².

625 is the hypotenuse of a primitive Pythagorean triple: 625² = 336² + 527².

625 is a centered octagonal number.

625 is an automorphic number.

According to a 2010 White House news release, 625 people lost their health insurance every hour in 2009.

Source: What's Special About This Number?

856

856 = 2³ x 107. It is the product of the cube of a prime and a different prime.

856 is a nonagonal number. It is also a centered pentagonal number.

856 is 11411 in base 6 and 2332 in base 7.

856 is a member of the Fibonacci-like sequence that begins with 1 and 9: 1, 9, 10, 19, 29, 48, 77, 125, 202, 327, 529, 856, 1385, . . .

NWA 856 is a Mars meteorite found in Morocco in 2001.

Source: Positive Integers

714

714 = 2 x 3 x 7 x 17.

The sum of the prime factors of 714 is 2 + 3 + 7 + 17 = 29, and the sum of the prime factors of 715 (5 x 11 x 13) is 5 + 11 + 13 = 29. These numbers are known as Ruth-Aaron pairs.

714 is the smallest number that has equal numbers of every digit in bases 2 and 5: 1011001010 and 10324.

510,510 = 2 x 3 x 5 x 7 x 11 x 13 x 17 (the first seven prime numbers) = 714 x 715 (two consecutive numbers) = 13 x 21 x 34 x 55 (four consecutive Fibonacci numbers).

714 is the sum of twelve consecutive prime numbers: 714 = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83.

Babe Ruth hit 714 home runs in his baseball career.

Source: Prime Curios!

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!