958

958 = 2 x 479.

958 is the number of 3-colorable graphs with 5 vertices (A084279).

958 is a Smith number (A006753); the sum of its digits equals the sum of the digits of its prime factors: 9 + 5 + 8 = 2 + 4 + 7 + 9 = 22.

958² = 917764 and 959² = 919681 have the same digit sum (A202089): 34.

Source: What's Special About This Number?

749

749 = 7 x 107.

749 is the number of ways to divide a 7 x 7 grid of points into two sets using a straight line.

The odd powers of 749 all end in 749, and its even powers end with 001.

749 is the sum of three consecutive primes: 749 = 241 + 251 + 257.

749 is the numerical equivalent of the word SIX on a touch-tone telephone.

Source: Number Gossip

213

213 = 3 x 71.

The sum of the digits of 213 is the same as the product of its digits: 2 + 1 + 3 = 2 x 1 x 3 = 6.

213 is the number of perfect squared rectangles of order 13.

25,986 = 213 x 122 and (backwards) 312 x 221 = 68,952.

213 = 2³ + 2³ + 2³ + 4³ + 5³.

213 was the apartment number of the infamous serial killer Jeffery Dahmer, and the title of a song by the thrash metal band Slayer.

Source: What's Special About This Number?

2177

2177 = 7 x 311.

2177 is 100010000001 in base 2 (binary) and 2222122 in base 3.

2177 is the number of permutations of length 10 within a distance 2 of a fixed permutation (A002524).

2177 is a centered 16-gonal number (A069129).

2177 is the sum of three but no fewer nonzero fourth powers: 2177 = 6⁴ + 5⁴ + 4⁴ (A047714).

A transit of Mercury (as seen from Earth) is expected to take place in the year 2177 (A171466).

Source: On-Line Encyclopedia of Integer Sequences

1315

1315 = 5 x 263.

1315 is the middle semiprime of a semiprime triple n - 2, n, n + 2: 1313, 1315, 1317.

1315 is the concatenation of the sixth prime number (13) and the sixth lucky number (15).

The sum of the factorials of the digits of 1315 is a power of 2: 1! + 3! + 1! + 5! = 128 = 2⁷.

1315 is the sum of three consecutive primes: 1315 = 433 + 439 + 443.

Source: On-Line Encyclopedia of Integer Sequences

940

940 = 2 x 2 x 5 x 47.

940 has a unique representation as a sum of three squares: 940 = 2² + 6² + 30².

940 is the sum of the squares for four consecutive primes: 940 = 11² + 13² + 17² + 19².

The sum of the divisors of 940 is a triangular number: 1 + 2 + 4 + 5 + 10 + 20 + 47 + 94 + 188 + 235 + 470 + 940 = 2016, the 63rd triangular number.

940 is the maximum number of regions into which 15 spheres can divide space.

Source: What's Special About This Number?

847

847 = 7 x 11 x 11.

847 is a divisor of 27¹⁰ - 1.

847 is the sum of the digits of the 14th Mersenne prime.

847 is 1011101 in base 3.

847 is the sum of distinct factorials: 847 = 6! + 5! + 3! + 1!

Source: What's Special About This Number?

453

453 = 3 x 151.

453 is the only number n such that n, 2n, and 6n together contain every digit exactly once: 453, 906, and 2718.

453 is 381 in base 11 and 318 in base 12. It is 202 in base 15.

453 is the sum of distinct double factorials: 453 = 8!! + 6!! + 5!! + 3!! + 2!! + 1!!

Source: What's Special About This Number?

285

285 = 3 x 5 x 19.

285 is the smallest number whose sum of distinct prime factors is an odd prime to the power of an odd prime: 3 + 5 + 19 = 27 = 3³.

285 is 555 in base 7.

285 is a square pyramidal number (the sum of all squares of integers from 1 to 9): 285 = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9².

285² = 81225 uses the same digits as 135² (18225) and 159² (25281).

285 is the number of binary rooted trees with 13 vertices.

Source: Prime Curios!

733

733 is a prime number.

733 is the smallest multidigit number that can be represented in the following way: 733 = 7 + 3! + (3!)!

733 = 1⁷ + 2⁶ + 3⁵ + 4⁴ + 5³ + 6² + 7¹ + 8⁰.


733 has a representation as a sum of two squares: 733 = 2² + 27².

733 is the hypotenuse of a primitive Pythagorean triple: 733² = 108² + 725².

Hank Aaron hit a total of 733 home runs during the years that he played in the National League.

Source: Number Gossip

275

275 = 5 x 5 x 11.

275 is 101012 in base 3 and 10103 in base 4.

275 is the total number of parts in all partitions of 11. It is also the sum of the largest parts of all partitions of 11. And it is the number of partitions of 28 in which no part occurs only once.

275 is the sum of two distinct positive fifth powers: 275 = 3⁵ + 2⁵.

275 is the lesser of two consecutive numbers (275 and 276), each divisible by a square.

The Ferrari 275 was a 2-seat car produced between 1964 and 1968.

Source: What's Special About This Number?

554

554 = 2 x 277.

554 has a representation as a sum of two squares: 554 = 5² + 23².

554 is the maximum number of regions into which 24 circles can divide a plane.

554 is the number of self-dual planar graphs with 20 edges.

554 is 202112 in base 3 and 20222 in base 4. It is 464 in base 11.

Source: What's Special About This Number?

728

728 = 2 x 2 x 2 x 7 x 13. It is the smallest number n where n and n + 1 are both products of five or more primes.

728 is 222222 in base 3 and 888 in base 9.

Consecutive Smith numbers are called Smith brothers: 728 is the smaller brother of the smallest pair (728 and 729) of Smith brothers. The sum of its digits is equal to the sum of the digits of its prime factors: 7 + 2 + 8 = 2 + 2 + 2 + 7 + 1 + 3 = 17.

728 is the sum of two distinct positive cubes: 728 = 8³ + 6³.

728 is the number of nodes in a regular 13-gon with all diagonals drawn.

Source: Number Gossip

549

549 = 3 x 3 x 61.

549 has a representation as a sum of two squares: 549 = 15² + 18².

549 is 333 in base 13. It is 202100 in base 3 and 20211 in base 4.

The sum of the digits of 549 is six times the number of digits: 5 + 4 + 9 = 6 x 3 = 18.

549 is the number of primes less than 10⁴ having at least one digit 7.

549 is a number n such that n² contains no digit greater than 4: 549² = 301401.

Source: On-Line Encyclopedia of Integer Sequences

8331

8331 = 3 x 2777.

The base 2, 3, 4, 5, 6, 7, and 8 representations of 8331 use no digit greater than 3.

8331 is a centered 14-gonal number.

8331 is the sum of the primes in an ordered 3 x 3 prime square, which consists of nine consecutive primes arranged in a square.

UGC 8331 is an irregular galaxy in the constellation Canes Venatici.

Source: On-Line Encyclopedia of Integer Sequences

822

822 = 2 x 3 x 137.

822 is the smallest nonpalindromic composite number located between twin primes (821 and 823), whose reversal, which is less than it (288), is also located between twin primes (287 and 289).

822 is the number of planar graphs with 7 vertices.

822 is the sum of 12 consecutive primes: 822 = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

822 Lalage is an asteroid discovered in 1916.

Source: Prime Curios!

534

534 = 2 x 3 x 89. It is the product of three distinct Sophie Germain primes.

534 is 4114 in base 5. It is 321 in base 13.

534 is a divisor of 55⁴ - 1.

534 is the sum of four consecutive primes: 534 = 127 + 131 + 137 + 139.

534 is the sum of thirteen positive fifth powers.

534 was the fourth studio album produced by the rapper Memphis Bleek, released in 2005.

Source: On-Line Encyclopedia of Integer Sequences

135

135 = 3 x 3 x 3 x 5.

135 is the smallest number with exactly seven representations as a sum of four positive squares: 135 = 1² + 2² + 3² + 11² = 1² + 2² + 7² + 9² = 1² + 3² + 5² + 10² = 1² + 6² + 7² + 7² = 2² + 5² + 5² + 9² = 3² + 3² + 6² + 9² = 5² + 5² + 6² + 7².

135 is the number of integer partitions of 14.

135 is 99 in base 14.

135 = (1 + 3 + 5)(1 x 3 x 5).

135 is the smallest three digit number that is the sum of its first digit and the square of its second digit and the cube of its third digit: 135 = 1¹ + 3² + 5³.

The term 135 (ISO 2007) was introduced by Kodak in 1934 as a designation for cartridge film 35 millimeters wide, specifically for still photography.

Source: Number Gossip

312

312 = 2 x 2 x 2 x 3 x 13.

312 has a unique representation as a sum of three squares: 312 = 4² + 10² + 14².

312 is 2222 in base 5. Its is 624 in base 7 and 264 in base 11.

312² = 14³ + 15³ + 16³ + 17³ + 18³ + 19³ + 20³ + 21³ + 22³ + 23³ + 24³ + 25³ = 97344.

312 x 221 = 68952 and (backwards) 25986 = 213 x 122.

312 Urban Wheat Ale is produced by the Goose Island Beer Company in Chicago.

Source: Numeropedia

710

710 = 2 x 5 x 71.

710 is a divisor of 91⁷ - 1.

710 is 222022 in base 3. It is 868 in base 9.

The sum of the divisors of 710 is a square: 1 + 2 + 5 + 10 + 71 + 142 + 355 + 710 = 1296 = 36².

710 is the sum of nine positive fifth powers: 710 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵.

710 is the number of connected graphs with 9 edges.

Source: What's Special About This Number?

607

607 is a prime number.

607 is the smallest prime resulting from the concatenation of two consecutive numbers separated by 0.

607 is the exponent of the Mersenne prime 2⁶⁰⁷ - 1.

607 is the smallest prime that can be expressed as the sum of 11 consecutive Fibonacci numbers: 607 = 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233.

1650/607 is the closest fraction to e with a prime denominator less than 1000.

Halley's Comet was visible from Earth in the year 607.

Source: Prime Curios!

507

507 = 3 x 13 x 13.

507 is a divisor of 22³ - 1.

507 is 13323 in base 4 and 1323 in base 7.

507 is the lesser of two consecutive numbers (507 and 508) each divisible by a square.

The square of 507 contains exactly six different digits: 507² = 257049.

507 is the number of rooted ternary trees with 10 vertices.

Source: What's Special About This Number?

960

960 = 2⁶ x 3 x 5.

960 is equal to the sum of its digits plus the sum of the cubes of its digits: 960 = 9 + 6 + 0 + 9³ + 6³ + 0³.

960 is 1111000000 in base 2 (binary), 33000 in base 4, and 1700 in base 8. The representations of 960 in bases 2, 3, 4, 5, 6, 8, and 10 all end in 0.

960 is the sum of six consecutive primes: 960 = 149 + 151 + 157 + 163 + 167 + 173.

960 is a hendecagonal number.

Source: What's Special About This Number?

476

476 = 2 x 2 x 7 x 17.

476 is the number of different products of subsets of the set {1, 2, 3, . . . 11}.

476 is 122122 in base 3 and 2112 in base 6. It is 13130 in base 4.

476 is the sum of three distinct positive cubes: 476 = 7³ + 5³ + 2³.

476 is the lesser of two consecutive numbers (476 and 477) divisible by squares.

Source: What Special About This Number?

748

748 = 2² x 11 x 17.

748⁴ = 313,044,726,016 = (3 + 1 + 3 + 0 + 4 + 4 + 726 + 0 + 1 + 6)⁴.

The sum of the base 3 digits (1000201) of 748 equals the sum of the base 9 digits (1021) of 748.


748 is the sum of factorials of distinct integers: 748 = 6! + 4! + 2! + 1! + 0!.

748 is the number of 3 x 3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

Source: What's Special About This Number?

206

206 = 2 x 103.

206 is the smallest number m such that 111¹¹¹ + m is prime.

The squares of 206 and 208, two consecutive even numbers, use the same digits: 206² = 42436 and 208² = 43264.

206 = 1³ + 2³ + 2³ + 4³ + 5³.

206 is 248 in base 9.

206 is the smallest number whose English name (two hundred and six) contains all five vowels exactly once.

Source: Number Gossip

652

652 = 2² x 163. It is a power of 2 written backwards.

652 has a unique representation as a sum of three squares: 652 = 2² + 18² + 18².

652 is the maximum number of regions into which 26 circles can divide the plane.

652 is the only known non-perfect number whose number of divisors and sum of smaller divisors are perfect.

652 is 220011 in base 3. It is 543 in base 11, 464 in base 12, and 246 in base 18.

Source: What's Special About This Number?

9797

9797 = 97 x 101. It is the product of two consecutive primes.

The square root of 9797 includes the digits 9797 immediately to the right of the decimal point: 98.979795918 . . .

9797 has two representations as a sum of two squares: 9797 = 31² + 94² = 49² + 86².

9797 is the hypotenuse of two primitive Pythagorean triples: 9797² = 4995² + 8428² = 5828² + 7875².

9797 is a divisor of 91¹² - 1.

The sum of the digits of 9797 is eight times the number of digits: 9 + 7 + 9 + 7 = 8 x 4 = 32.

9797 is IBM in base 23.

Source: What's Special About This Number?

941

941 is a prime number.

941 has a representation as a sum of two squares: 941 = 10² + 29².

941 is the hypotenuse of a primitive Pythagorean triple: 941² = 580² + 741².

941 is the smallest prime formed by the reverse concatenation of three consecutive squares.

941 is the smallest number whose proper substrings sum to its reversal: 9 + 4 + 1 + 94 + 41 = 149.

941 is the smallest prime resulting from the nine-digit fraction equation (A + B)^C + (D + E)^F + (G + H)^I,  where the letters A through I represent any combination of the nine digits 1 through 9. Note that (4 + 5)³ + (6 + 8)² + (7 + 9)¹ is the only distinct solution for 941.

Source: Prime Curios!

737

737 = 11 x 67.

737 is the smallest multidigit number m such that m^m + 2 is prime.

737 is 515 in base 12 and 191 in base 21.

737 is the sum of two positive cubes: 737 = 9³ + 2³.

The Boeing 737 is a twin-engine, narrow-body jet airliner that first flew in 1967.

Source: Prime Curios!

358

358 = 2 x 179.

358 is the smallest number whose first two digits are distinct odd primes such that their sum equals the third digit.

The sum of the digit splits of 358 is equal to the product of the digits of 358: (3 + 58) + (35 + 8) + (3 + 5 + 8) = 120 = 3 x 5 x 8.

358 has a base 3 representation (111021) that ends with its base 7 representation (1021).

358 is the sum of six consecutive primes: 358 = 47 + 53 + 59 + 61 + 67 + 71.

The Jaguar XJ X358 is a luxury car that debuted in 2007.

Source: Prime Curios!

278

278 = 2 x 139.

278 is the sum of the first 18 nonprimes.

278 has the representation 2⁸ + 22.

278 is the closest integer to 6^π.

278 is 545 in base 7.

Telephone area code 278 serves Ann Arbor, Michigan, and the surrounding area.

Source: What's Special About This Number?

636

636 = 2² x 3 x 53.

The decimal part of the fifth root of 636 begins with the digits 636.

636 is 336 in base 14.

636 is the sum of 10 consecutive primes: 636 = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83.

Telephone area code 636 serves the east-central portion of the state of Missouri.

Source: What's Special About This Number?

4393

4393 = 23 x 191.

4393 is 1000100101001 in base 2 (binary).

4393 is a number such that each digit leaves the same nonzero remainder when each is divided into the number.

4393 is a multiple of 23 such that reversing the digits and subtracting 1 gives a result that is also a multiple of 23.

4393 is the sum of distinct 5th powers: 4393 = 5⁵ + 4⁵ + 3⁵ + 1⁵.

Parlophone recording R. 4393 featured the song "No Other Baby" by The Vipers, later recorded by Paul McCartney.

Source: On-Line Encyclopedia of Integer Sequences

438

438 = 2 x 3 x 73.

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

438 is 110110110 in base 2 (binary) and 666 in base 8. It is 3223 in base 5 and 141 in base 19.

438 divides 65⁶ - 1.

438 is the sum of 10 positive 5th powers: 438 = 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.

The term "438 match" or "438 game" has been used by cricket news media to describe the famous 2006 One Day International in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.

Source: What's Special About This Number?

724

724 = 2² x 181.

724 has a representation as a sum of two squares: 724 = 18² + 20².

724 divides 19⁴ - 1.

724 is the number of perfect connected undirected simple graphs on seven nodes.

724 is the number of different arrangements of 10 non-attacking queens on a 10 x 10 chessboard.

724 Hapag is an asteroid discovered in 1911, lost, then rediscovered in 1988.

Source: What's Special About This Number?

1293

1293 = 3 x 431.

The sum of the divisors of 1293 is a cube: 1 + 3 + 431 + 1293 = 1728 = 12³.

1293 is a divisor of 26¹⁰ - 1.

1293 is a structured truncated tetrahedral number.

1293³ = 2161700757 is the sum of three consecutive primes: 2161700757 = 720566909 + 720566921 + 720566927.

Southern Pacific 1293 is a retired switch engine built in 1924 and now on display in Tracy, California.

Source: What's Special About This Number?

1126

1126 = 2 x 563.

1126 is the number of 3 x 4 checkerboards in which the set of red squares is edge-connected.

1126 is the sum of the first 15 Sophie Germain primes.

1126³ (1427628376) includes the digits of 1126² (1267876).

In the year 1126, Adelard of Bath translated Muhammad ibn-Musa al-Kwarizmi's arithmetic and astronomical tables into Latin.

Source: On-Line Encyclopedia of Integer Sequences

826

826 = 2 x 7 x 59.

826 is the sum of seven positive 5th powers: 826 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

The sum of the digits of the 826th prime (6343) equals the sum of the digits of 826: 6 + 3 + 4 + 3 = 8 + 2 + 6 = 16.

The digits of 826² (68276) contain the digits of 826 as a subsequence.

826 National is a nonprofit organization that manages a network of writing and tutoring centers.

Source: On-Line Encyclopedia of Integer Sequences

423

423 = 3² x 47.

423 is a number that does not have any digits in common with its cube (75686967).

423 is the sum of 13 consecutive primes: 423 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59.

Inserting the digit 1 between adjacent digits of 423 produces a prime: 41213.

423 Diotima is one of the largest main-belt asteroids.

Source: What's Special About This Number?

537

537 = 3 x 179.

537 divides the sum of the cubes of the first 537 primes.

537 is 656 in base 9.

The sum of the digits of 537 is 5 times the number of digits: 5 + 3 + 7 = 5 x 3 = 15.

537 is the average of three successive primes: 537 = (523 + 541 + 547)/3.

In the final official count in the 2000 U.S. presidential election, George W. Bush defeated Al Gore by 537 votes in the state of Florida.

Source: What's Special About This Number?

816

816 = 2⁴ x 3 x 17.

816 is the 16th tetrahedral number.

816/(8 x 1 x 6) = 816/48 = 17, a prime. 816 is the largest three-digit integer that has this property.

816 is 30300 in base 4 and 330 in base 16. It is 2244 in base 7 and 424 in base 14.

816 is a telephone area code that covers the Kansas City area in Missouri.

Source: Prime Curios!

124

124 = 2² x 31.

124 is 444 in base 5.

124 is the smallest number whose sum of digits (1 + 2 + 4 = 7) as well as the number itself are one less than the cube of a prime.

124 is the smallest number with the property that its first three multiples contain the digit 2: 124, 248, and 372.

124 is the sum of eight consecutive primes: 124 = 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

124 = 2⁷ - 2².

124 = 5² + 5² + 5² + 7².

The Fiat 124 was a family car produced in Italy from 1966 to 1974.

Source: Prime Curios!

2012

2012 = 2² x 503.

2012, 2013, 2014, and 2015 are each the product of three prime numbers.

2012! has a square number of digits (5776 = 76²).

2012² = 4048144 and 4418404 = 2102².

2012 and its square (4048144) use only the digits 0, 1, 2, 4, and 8.

2012 is a year in which there are five Wednesdays in the month of February.

2012 is a blue moon year.

The end of the "longest period" (Long Count) Mayan calendar known to exist is said to be December 21, 2012.

2012 is the 100th anniversary of the sinking of the RMS Titanic. It is also the centennial of the birth of Alan Turing.

Source: On-Line Encyclopedia of Integer Sequences

524

524 = 2² x 131.

524 is a divisor of 53⁵ - 1.

6 x 7 x 9 x 524 x 831 = 164,597,832 uses each of the digits from 1 to 9 once on both sides of the equality.

524 is 201102 (palindromic) in base 3.

The USS Pickerel (USN-524) was a submarine commissioned in 1949.

Source: Positive Integers

1011

1011 = 3 x 337.

1011 is the smallest number without trailing zeroes such that the reversal of its cube is the cube of a different number (1101).

1011 has a square that is formed by inserting three 2s into it: 1011² = 1022121.

1011 is 323 (palindromic) in base 18. 1011 has a representation ending in 3 in base 4, 6, 7, 8, 9, 12, 14, and 18.

The Nokia 1011 was the first mass-produced GSM phone.

Source: Number Gossip

107

107 is a prime number.

107 is 1101011 in base 2 (binary).

107 and 109 form a twin prime pair.

2¹⁰⁷ - 1 is a Mersenne prime.

107 is the smallest three-digit prime that remains a prime when 2 is added to any one of its digits: 307, 127, and 109 are all primes.

107 is the maximum number of steps that a four-state Turing machine can make on an initially blank tape before it halts.

107 Camilla is one of the largest main-belt asteroids.

Source: Prime Curios!

383

383 is a prime number. It is a sexy prime because 383 + 6 = 389 is also prime.

383 is the only known multidigit palindromic Woodall prime.

383 is the sum of the first three three-digit palindromic primes: 383 = 101 + 131 + 151.

383 is the smallest prime that can be represented by the sum of a prime and its reversal: 383 = 241 + 142.

383 is a divisor of the Mersenne number 2¹⁹¹ - 1.

The Chevy 383 stroker engine uses an altered crankshaft to increase the stroke of the pistons.

Source: Prime Curios!

967

967 is a prime number. 967 in reverse is the prime 769.

967 is a divisor of 97⁷ - 1.

967 is the number of six-digit triangular numbers.

967 is 595 in base 13.

967 millimeters is the record for annual rainfall in Melbourne, Australia, set in 1916.

Source: Prime Curios!

743

743 is a prime number. It is a Sophie Germain prime because 2 x 743 + 1 = 1487 is a prime.

743 is the number of independent sets of the graph of the tesseract (four-dimensional cube).

648⁷ + 139968⁴ = 7558272³.

743 is 616 in base 11 and 212 in base 19.

The sun's mass is about 743 times the combined mass of all the planets in the solar system.

Source: Number Gossip