701

701 is a prime number.

701, 7001, 70001, and 700001 are each prime.

2⁷⁰¹ + 701 is prime.

701 = 5⁴ + 4³ + 3² + 2¹ + 1⁰.

701 has a representation as a sum of two squares: 701 = 5² + 26².

701 is the hypotenuse of a primitive Pythagorean triple: 701² = 260² + 651².


The IBM 701 was the company's first production-line electronic digital computer, announced to the public in 1952.

Source: Prime Curios!

79

79 is a prime number.

79 is the smallest prime whose sum of digits is a fourth power: 7 + 9 = 16 = 2⁴.

79 = 2⁷ – 7².

79 is the maximum number of regions into which 12 lines divide a plane. It is possible to divide a flat pancake into 79 pieces by making 13 straight cuts.


The chemical element gold has atomic number 79.

Source: Prime Curios!

957

957 = 3 x 11 x 29, which makes 957 a sphenic number. A sphenic number is a positive integer that is the product of three distinct prime numbers.

957 is 12312 in base 5, 4233 in base 6, and 2535 in base 7.

957 is the product of three distinct primes such that the sum of the three primes is also a prime: 3 + 11 + 29 = 43, a prime.

957 is a number such that its base 2 (binary) representation is the juxtaposition of two identical strings: 1110111101.


The asteroid 957 Camelia was discovered in 1921.

Source: Positive Integers

164

164 = 2² x 41.

164 is the smallest concatenation of two squares in two ways: 1 and 64; 16 and 4.

164 is 20002 in base 3 and 202 in base 9.

164 has a representation as a sum of two squares: 164 = 8² + 10².

164 is a divisor of 81² - 1.

164 is the highest possible score of a word in the game Scrabble: playing “Quartzy” across triple-word square with “z” on a double-letter square and a premium of 50 for using all seven letters on the rack.

Source: Number Gossip

201

201 = 3 x 67.

201ⁿ + 2 is a prime number, for n = 14, 15, and 16.

The square of 201 is one of four square numbers using the same digits: 102² = 10404, 120² = 14400, 201² = 40401, and 210² = 44100.

201 is a Niven (or Harshad) number, which is divisible by the sum of its digits.

201 Penelope is a large asteroid discovered in 1879.

Source: Prime Curios!

302

302 = 2 x 151.

The square of 302 is one of three square numbers using the same digits: 148² = 21904, 203² = 41209, and 302² = 91204.

302 is the number of ways to play the first three moves in checkers.

302 is a number n such that n and n + 1 have the same number of divisors: 303 = 3 x 101.

302 is the telephone area code for the state of Delaware.

Source: What’s Special About This Number?

503

503 is a prime number.

503 is the smallest prime that is the sum of the cubes of the first n primes: 2³ + 3³ + 5³ +7³ = 503.

5! + 0! + 3! is a three-digit Mersenne prime.

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


503 is Clark Kent's Metropolis apartment number in the "Superman" series.

Source: Prime Curios!

905

905 = 5 x 181.

Most odd integers can be written as the sum of a prime and a power of two in at least one way. Ones that cannot are called obstinate numbers. They form an infinite set but are not all that common. The first composite obstinate number is 905. So 905 is the smallest composite number that is not the sum of a prime and a power of two.

905 is the sum of seven consecutive primes: 109 + 113 + 127 + 131 + 137 + 139 + 149 = 905.

905 has two representations as a sum of two squares: 905 = 8² + 29² = 11² + 28².

905 is the hypotenuse of two Pythagorean triples: 905² = 464² + 777² = 616² + 663².


A Neptune-Pluto conjunction occurred in Taurus in the year 905.

Source: Prime Curios!

889

889 = 7 x 127. It is a product of distinct Mersenne primes.

889 is an odious number because it has an odd number of ones in its binary expansion: 1101111001.

889 is a number such that the sum of its divisors is a square: 1 + 7 + 127 + 889 = 135 = 32 x 32.

889 is the sum of eight positive fifth powers: 889 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵.

In the Dewey Decimal System for classifying books, 889 is the code for literature in medieval and modern Greek

Source: Number Gossip

68

68 = 2² x 17.

68 is the smallest composite number that becomes prime when turned upside down: 89.

68 is the largest even number that is expressible as the sum of two primes in two different ways: 7 + 61 = 68 and 31 + 37 = 68.

68 has a representation as a sum of two squares: 68 = 2² + 8².

68 is 44 in base 16.


The chemical element erbium has atomic number 68.

Source: Prime Curios!

1117

1117 is a prime number.

1117 has a representation as a sum of two squares: 1117 = 21² + 26².

1117 is the hypotenuse of a primitive Pythagorean triple: 1117² = 235² + 1092².

1117 is the smallest four-digit unholey prime: Such primes do not have holes in their digits.

1117 is the smallest four-digit prime comprised of two two-digit primes.


"One Thousand One Hundred Seventeen" is the smallest number whose English name is spelled with exactly thirty letters.

Source: Number Gossip

681

681 = 3 x 227.

The sum of the digits of 681 is five times the number of digits: 6 + 8 + 1 = 15 = 3 x 5.

681 is the sum of 11 positive 5th powers: 681 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.


681 is a centered pentagonal number.


The galaxy NGC 681, more than 55 million light years away, resembles the striking Sombrero Galaxy (M104).

Source: Wolfram MathWorld

414

414 = 2 x 3² x 23

414 is a value of n for which n⁴, n⁵, n⁶, and n⁷ have the same digit sum.

414² = 171,396 = (17 + 1 + 396)².

414 is 636 in base 8.


414 is the telephone area code for Milwaukee, Wisconsin.

Source: What’s Special About This Number?

555

555 = 3 x 5 x 37.

555 is a spheric number. It is the product of three distinct prime numbers.

555 is 2323 in base 6 and 676 in base 9.

The sum of the digits of 555 is five times the number of digits: 5 + 5 + 5 = 3 x 5 = 15.


In North America, telephone numbers with the prefix 555 are widely used for fictitious telephone numbers in television shows, films, computer games, and other media.

Source: Wikipedia

825

825 = 3 x 5² x 11.

825 is the number of legal ways to add two sets of parentheses to a product of nine variables.

825 is a Smith number. The sum of its digits is equal to the sum of the digits in its prime factorization: 8 + 2 + 5 = 3 + 5 + 5 + 1 + 1.

825 is the sum of six positive fifth powers: 825 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵.


Asteroid 825 Tanina was discovered in 1916 and has a diameter of about 11 kilometers.

Source: What’s Special About This Number?

268

268 = 2² x 67.

268 has a unique representation as a sum of three squares: 268 = 6² + 6² + 14².

The product of 268 and the sum of its digits plus one is prime: 268 * (2 + 6 + 8) + 1 = 4289, a prime.

268 is the smallest number whose product of digits is six times the sum of its digits: 2 * 6 * 8 = 6(2 + 6 + 8).

268 is 414 in base 8.

268 inches of 1/8-inch copper wire weigh 1 pound.

Source: Prime Curios!

937

937 is a prime number.

937 in base 3 is palindromic: 1021201.

937 has a representation as a sum of two squares: 937 = 19² + 24².

937 is the hypotenuse of a primitive Pythagorean triple: 937 = 215² + 912².

937 is a star number. A star number is a centered figurate number that represents a centered hexagram, such as the one (below) that Chinese checkers is played on.

Telephone area code 937 covers much of the southwestern part of the state of Ohio.

Source: Wikipedia

999

999 = 3³ x 37.

999 is the smallest possible sum of three-digit primes that together include all nine digits: 149 + 263 + 587 = 999.

The odd powers of 999 end with 999, and its even powers end with 001: 999² = 998001; 999³ = 997002999.

999 is 4343 in base 6, 2625 in base 7, and 1747 in base 8.

999 is the Dewey Decimal Classification system call number for library books on the general history of extraterrestrial worlds.

Source: Numeropedia

789

789 = 3 x 263.

789 is the sum of three consecutive primes: 257 + 263 + 269 = 789.

789 are the first three digits of 9⁷⁸⁹.

789 occurs in the sequence generated by starting with 1, then repeatedly reversing the digits and adding 2: 1, 3, 5, 7, 9, 11, 13, 33, . . . , 787, 789, 989, . . .


In the Year 789, Charlemagne introduced the royal foot as the unit of length.

Source: What’s Special About This Number?

177

177 = 3 x 59.

177 is a digitally balanced number: In its binary representation (10110001), it has the same number of zeros as ones.

177 is the smallest possible magic constant for a 3 x 3 prime magic square.

177 is the number of graphs with seven edges.

Each internal angle of a regular 120-sided polygon is 177 degrees.

177 Irma is a fairly large, dark asteroid discovered in 1877.

Source: Number Gossip

321

321 = 3 x 107.

321 is a Delannoy number. The Delannoy numbers are the number of lattice paths from (0, 0) to (b, a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed.

The 321st prime is 2131, which can be written with all the digits of 321. It's the smallest composite number to have this property.

321 is generated by the following sieve: Keep the first number, drop every second number, keep first, drop every third, keep first, drop every fourth, and so on.

Telephone area code 321 serves Brevard County, Florida.

Source: Wolfram MathWorld

83

83 is a prime number. It is a Sophie Germain prime because 2 x 83 + 1 = 167, a prime.

83 is the smallest multidigit prime that consists of only curved digits.

83 is the only prime equal to the sum of the squares of the odd prime digits: 83 = 3² + 5² + 7².

83 is the smallest prime number that is the sum of a prime number of consecutive primes in a prime number of different ways: 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23.


Bismuth, with atomic number 83, is the heaviest stable element.

Source: Prime Curios!

1993

1993 is a prime number.

1993 has a representation as a sum of two squares: 1993 = 12² + 43².

1993 is the hypotenuse of a primitive Pythagorean triple: 1993² = 1032² + 1705².

1993 is a number n such that n and (n + 1)/2 are both prime: 1993 and 997 are both primes.

On June 24, 1993, Andrew Wiles presented his proof of Fermat's Last Theorem, a problem that had been unsolved for more than three centuries.

Source: Wikipedia

974

974 = 2 x 487.

974! – 1 is a factorial minus one prime.

974 is the number of multigraphs with 5 vertices and 10 edges.

974 is the sum of six positive fifth powers: 974 = 3⁵ + 3⁵ + 3⁵ + 3⁵ + 1⁵ + 1⁵.

974 was the year of a great earthquake in England.

Source: Prime Curios!

867

867 = 3 x 17²

867 is the number of graphs with 8 vertices that have chromatic number 5.

867 is a number n such that n times n + 7 gives the concatenation of two numbers m and m + 1: 867 x 874 = 757758.

867 is a number such that the sum of its digits is seven times the number of digits: 8 + 6 + 7 = 21 = 3 x 7.


"867-5309/Jenny" is a song written by Alex Call and Jim Keller and performed by Tommy Tutone. It peaked at number four on the Billboard Hot 100 chart and number one on the Billboard Top Tracks chart in 1982.

Source: What’s Special About This Number?

751

751 is a prime number.

751 is the largest prime that cannot be expressed as the sum of five or fewer squared composite numbers.

751 is the smallest integer with the following property: the sum of digits of 751 = the sum of digits of the 751st prime = the sum of digits of the 751st semiprime (product of two prime numbers).

The odd powers of 751 end with 751; and its even powers end with 001.

751 Magazine is an online magazine for poetry and short fiction.

Source: Prime Curios!

630

630 = 2 x 3² x 5 x 7.

630 is a triangular number. It is the sum of the first 35 integers: 1 + 2 + 3 + . . . + 34 + 35 = 630. 630 is also three times a triangular number (210) and six times a triangular number (105).

630 is 21312 in base 4.

630 is the sum of six consecutive primes: 97 + 101 + 103 + 107 + 109 + 113 = 630.


630 is the height and the span (in feet) of the stainless steel arch “Gateway to the West” in St. Louis, Missouri.

Source: What’s Special About This Number?

514

514 = 2 x 257.

514 is a centered triangular number.

514!/415! + 1 is a prime number.

514 is 20002 in base 4, 4024 in base 5, 1333 in base 7, and 1002 in base 8.


514 is a telephone area code that covers all of the island of Montreal, Quebec.

Source: Prime Curios!

411

411 = 3 x 137.

The polynomial 30x - 13 produces 411 primes for the first 1000 values of x.

411 is 12123 in base 4.

411 is a member of the Fibonacci-type sequence starting with 1 and 4.


411 is the telephone number within the U.S. for information or directory services.

Source: Prime Curios!

301

301 = 7 x 43.

301 is the product of the only two primes (7 and 43) that can be the last two digits of a fifth power.

301 is the maximum number of regions into which 24 lines divide a plane. It is a lazy caterer’s number. The lazy caterer's sequence describes the maximum number of pieces of a circle (pizza) that can be made with a given number of straight cuts.

301² = 90601 and 103² = 10609.

301 is the sum of three consecutive primes: 97 + 101 + 103 = 301.

301 is the telephone area code for parts of Maryland.

Source: Wikipedia

299

299 = 13 x 23.

299 is a number not divisible by any of its digits.

299 is the smallest number whose sum of digits is 20.

299 is a cake number. A cake number is the maximum number of pieces into which a 3-dimensional space can be cut with a given number of plane cuts: 12 cuts produce 299 pieces.

There are 299 composite numbers less than 1000 that are products of two primes.


299 Thora is a main belt asteroid discovered in 1890 by Johann Palisa in Vienna.

Source: Wikipedia

190

190 = 2 x 5 x 19.

190 has a unique representation as a sum of three squares: 190 = 3² + 9² + 10².

190 is the 19th triangular number; it is the sum of the first nineteen integers: 1 + 2 + 3 + . . . + 18 + 19 = 190.

190 is the largest number with only distinct prime Roman numeral palindrome factors that is itself a Roman numeral palindrome: 190 = CXC = II * V * XIX.

190 is 2332 in base 4 and 1230 in base 5.

190 is the sum of all the vertices, edges, and faces of the five Platonic solids.

Source: Prime Curios!

45

45 = 3² x 5.

45 is the ninth triangular number; it is the sum the first nine integers: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

45 is the only number that is the sum of its digits multiplied by 5.

If the first five powers of two are each subtracted from 45, all the results are prime: 45 – 2 = 43; 45 – 4 = 41; 45 – 8 = 37; 45 – 16 = 29; 45 – 32 = 11.


The chemical element rhodium has atomic number 45.

Source: Number Gossip

493

493 = 17 x 29.

The first few numbers not known to produce palindromes when applying the 196-algorithm (that is, a reverse-then-add sequence) are sometimes known as Lychrel numbers. The first few Lychrel numbers are 196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, . . . : 887 = 196 + 691 = 295 + 592 = 394 + 493 = 790 + 097.

493 is 13231 in base 4.

493 is the sum of seven consecutive primes: 59 + 61 + 67 + 71 + 73 + 79 + 83 = 493.


493 is the number of Pokémon species, from the first set through the fourth generation.

Source: Wolfram MathWorld

1517

1517 = 37 x 41 (the product of two consecutive prime numbers).

1517 has two representations as a sum of two squares: 1517 = 19² + 34² = 26² + 29².

1517 is the hypotenuse of two primitive Pythagorean triples: 1517² = 165² + 1508² = 795² + 1292².

The sum of the decimal digits of 2¹⁵¹⁷ is also a power of 2.

1517 divides the sum of the first 1517 Fibonacci numbers.

1517 was the record-breaking attendance at MAA’s MathFest 2009 in Portland, Ore.


Italian mathematician and Franciscan friar Luca Pacioli died in the year 1517.

Source: Wikipedia

290

290 = 2 x 5 x 29.

290 equals the tenth prime times ten: 29 x 10 = 290.

290 is the sum of four consecutive primes: 67 + 71 + 73 + 79 = 290.

290 has a base 3 representation (101202) that ends with its base 6 representation (1202).

290 has two representations as a sum of two squares: 290 = 1² + 17² = 11² + 13².

NGC 290 is an open cluster of stars in the Small Magellanic Cloud, which is located in the constellation Tucana.

Source: Wikipedia

172

172 = 2² x 43.

172 has a unique representation as a sum of three squares: 172 = 6² + 6² + 10².

172 is 444 in base 6.

Each internal angle of a regular 45-sided polygon is 172^o.

172 is the maximum number of regions into which 18 lines divide the plane. Hence, 172 is a member of the lazy caterer's sequence, which describes the maximum number of pieces of a circle (a pancake or pizza) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point, but up to seven if they do not.


Ethanol (ethyl alcohol) boils at 172 ^oF under standard conditions.

Source: Wikipedia

44

44 = 2² x 11.

44 is the smallest number that is the sum of a reversible pair of non-palindromic primes: 13 + 31 = 44.

44 is the first number such that it and the next number are the product of a prime and another distinct prime squared: 44 = 2² x 11 and 45 = 3² x 5.

44 is the maximum number of regions into which the plane can be divided by seven circles.


44 is the atomic number of the chemical element ruthenium.

Source: Number Gossip