767

767 = 13 x 59.

767 is the smallest number n such that n⁴ contains a substring with all the digits exactly once: 767⁴ = 346083947521.

767 is a divisor of 60⁴ - 1.

767 is 1011111111 in base 2 and 23333 in base 4.

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

The Boeing 767 airliner entered service in 1982.

Source: Number Gossip

1133

1133 = 11 x 103.

1133 is 1112222 in base 3.

1133, 1135, 1137, 1139, and 1141 are all semiprimes.

1133 is a number n such that n² is the sum of two or more consecutive squares.

1133 is the sum of three nonzero squares in exactly seven ways.

NGC 1133 is a spiral galaxy in the direction of the constellation Eridanus.

Source: On-Line Encyclopedia of Integer Sequences

659

659 is a prime number. It is a Sophie Germain prime because 2 x 659 + 1 = 1319 is also a prime.

0659, 2659, 3659, 5659, and 6659 are all primes.

659 and 661 form a twin prime pair.

659 is a divisor of 12⁷ - 1.

659 is the sum of seven consecutive primes: 659 = 79 + 83 + 89 + 97 + 101 + 103 + 107.

659 Nestor is a Jupiter Trojan asteroid that orbits along Jupiter's path. It was discovered in 1908.

Source: Prime Curios!

374

374 = 2 x 11 x17.

374 is the smallest number with eight representations as a sum of three positive squares: 374 = 1² + 7² + 18² = 2² + 3² + 19² = 2² + 9² + 17² = 3² + 13² + 14² = 5² + 5² + 18² = 6² + 7² + 17² = 6² + 13² + 13² = 7² + 10² + 15².

374 is 2444 in base 5, 1422 in base 6, 566 in base 8, and 455 in base 9.

374, 375, and 376 have the same number of divisors: 1, 2, 11, 17, 22, 34, 187, 374; 1, 3, 5, 15, 25, 75, 125, 375; 1, 2, 4, 8, 47, 94, 188, 376.

374 is a powerful number; it is the sum of positive powers of its digits.

CPR Engine 374 is on display in Vancouver, Canada. It pulled the first transcontinental train into the city on May 23, 1887.

Source: What's Special About This Number?

951

951 = 3 x 317.

951 is 1110110111 in base 2 (binary) and 2526 in base 7.

951 is a centered pentagonal number.

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

Asteroid 951 Gaspra was photographed in 1991 by the Galileo spacecraft.

Source: WolframAlpha

3498

3498 = 2 x 3 x 11 x 53.

3498 is 110110101010 in base 2 (binary).

3498 is a divisor of 23⁴ - 1.

3498 is a number whose sum of divisors is a 5th power: 1 + 2 + 3 + 6 + 11 + 22 + 33 + 53 + 66 + 106 + 159 + 318 + 583 + 1166 + 1749 + 3498 = 6⁵.

Playmobil #3498 was a motorized boat produced in the 1980s.

Source: What's Special About This Number?

340

340 = 2² x 5 x 17.

340 has two representations as a sum of two squares: 340 = 4² + 18² = 12² + 14².

340 is the number of integer partitions of 31 into distinct parts.

340 is a divisor of 69² - 1.

340 is a value of n for which n! + 1 is a prime.

The Airbus A340 is a long-range, four-engine wide-body commercial passenger jet airliner.

Source: What's Special About This Number?

130

130 = 2 x 5 x 13.

130 has two representations as a sum of two squares: 130 = 3² + 11² = 7² + 9².

130 is the smallest number with eight representations as a sum of four positive squares: 130 = 1² + 1² + 8² + 8² = 1² + 2² + 2² + 11² = 1² + 2² + 5² + 10² = 1² + 4² + 7² + 8² = 2² + 3² + 6² + 9² = 3² + 6² + 6² + 7² = 4² + 4² + 7² + 7² = 4² + 5² + 5² + 8².

130 is a cake number.

130 is the sum of the factorials of the first five terms of the Fibonacci sequence: 130 = 1! + 1! + 2! + 3! + 5!.

130 is the only number that is equal to the sum of the squares of its first four divisors: 130 = 1² + 2² + 5² + 10².

The Lockheed C-130 Hercules is a four-engine turboprop military transport aircraft.

Source: Number Gossip

126

126 = 2 x 3² x 7.

126 is the sixth pentatope number.

126 is 99 in base 13.

126 is a decagonal number and a pentagonal pyramidal number.

126 is the number of prime days in a non-leap year.

The Ferrari 126C was Ferrari's first attempt at turbo-charged Formula 1 car.

Source: Number Gossip

263

263 is a prime number.

263 is the largest known prime whose square is strobogrammatic; that is, it is the same number when rotated 180 degrees: 263² = 69169.

263 is the smallest prime number that is the sum of primes beginning and ending with the digit 1: 263 = 11 + 101 + 151. Note that the digit sum of each prime is prime and that the digit sum of 263 is a prime and begins and ends with the digit 1.

263 is the only prime with three distinct digits, where one is the product of the other two.

263 is the smallest prime formed be inserting a semiprime, 6, between the semiprime's factors, 2 and 3.

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

Anne Frank (and her family) hid from the Nazis in an annex behind the house at 263 Prinsengracht 263 in Amsterdam.

Source: Prime Curios!

855

855 = 3² x 56 x 19.

855 is the sum of all the digits of all two-digit numbers.

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

855 is a decagonal number. It is also a centered cube number.

855 is the smallest number that is the sum of five consecutive squares and two consecutive cubes: 855 = 11² + 12² + 13² + 14² + 15² = 7³ + 8³.

855 Newcombia is a asteroid discovered in 1916.

Source: Number Gossip

430

430 = 2 x 5 x 43.

430 is the number of necklaces possible with six beads, each being one of four colors.

430 is 656 in base 8.

430 is the number of primes less than 3000.

430 is a number such that its square is the sum of two or more consecutive squares.

The Ferrari F430 is a sports car produced from 2004 to 2009.

Source: What's Special About This Number?

6011

6011 is a prime number. Rotating 6011 by 180 degrees (turning it upside down) produces 1109, another prime.

6011 is a member of the Fibonacci-like sequence starting with 3 and 8.

6011 is a prime p such that the product its digits (excluding 0) is a divisor of p + 1.

6011² uses only the digits 1, 2, 3, and 6: 36132121.

60/11 equals 5.4545. . . , the exact time difference between consecutive overlaps of the hour and minute hands, which occurs 11 times every 60 minutes.

6011 is the postal code for Peppermint Grove, Western Australia, a suburb of Perth.

Source: Prime Curios!

600

600 = 2³ x 3 x 5².

600 is the product of two consecutive integers, so it is a pronic number: 600 = 24 x 25.

600 and its reverse, 6, are both the averages of twin primes: 599 and 601; 5 and 7.

600 is 211020 in base 3 and 21120 in base 4; it is 4400 in base 5, 2440 in base 6, and 420 in base 12; it is 1515 in base 7.

600 is the value of the postal abbreviation for the District of Columbia, DC, in the United States, interpreted as Roman numerals.

Source: Number Gossip

298

298 = 2 x 149.

298 has a representation as a sum of two squares: 298 = 3² + 17².

298 = (2² + 9² + 8²) + (2² + 9² + 8²).

298 is the sum of four distinct squares a² + b² + c² + d², such that a² + b², c² + d², a² + d², and b² + c² are all prime.

298 Baptistina is an asteroid discovered in 1890.

Source: Numeropedia

335

335 = 5 x 67. It is divisible by the number of primes below it (67).

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

335 is a divisor of 66² - 1.

2³³⁵ is the smallest power of 2 that equals the sum of four consecutive primes.

335 is 656 in base 7.

The ES-335, a semi-acoustic electric guitar, was produced in 1958 by the Gibson Guitar Corp.

Source: Prime Curios!

457

457 is a prime number.

457 has a representation as a sum of two squares: 457 = 4² + 21².

457 is the hypotenuse of a primitive Pythagorean triple: 457² = 168² + 425².

457 is a divisor of 18¹² - 1.

457 is the index of a prime Euclid number.

457 is the sum of three consecutive primes: 457 = 149 + 151 + 157.

The German submarine known as U-457 was sunk in the Barents Sea by depth charges from the British destroyer HMS Impulsive during World War II.

Source: Prime Curios!

599

599 is a prime number.

599 and 601 form a twin prime pair.

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

599 is a divisor of 19¹³ - 1.

599 is the smallest number whose digits add to 23.

The Administrative building in the town of Saint-Prime, Quebec, is at the street address 599, rue Principale.

Source: Prime Curios!

445

445 = 5 x 89.

445 has two representations as a sum of two squares: 445 = 2² + 21² = 11² + 18².

445 is the hypotenuse of two primitive Pythagorean triples: 445² = 84² + 437² = 203² + 396².

445 is a divisor of 34⁴ - 1.

445 has a base 10 representation (445) that is the reverse of its base 9 representation (544).

The Skoda 445 automobile was produced in Czechoslovakia between 1955 and 1959.

Source: What's Special About This Number?

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?