857

857 is a prime number.

857 has a representation as a sum of two squares: 857 = 4² + 29².

857 and 859 form a twin prime pair.

857 is the hypotenuse of a primitive Pythagorean triple: 857² = 232² + 825².

142,857 x 5 = 714,285 = 857² - 142², where 857,142 = 142,857 x 6.

857 is 1011202 in base 3. It is 272 in base 19.

857 is the sum of three consecutive primes: 857 = 281 + 283 + 293.

Glasenappia 857 is an asteroid discovered in 1916.

Source: Wikipedia

311

311 is a prime number.

311 and 313 form a twin prime pair.

311 is the 11th three-digit prime for which the sum of the squares of its digits is also a prime: 3² + 1² + 1² = 11, a prime.

311 is the smallest number expressible as the sum of consecutive primes in four ways: 311 = 101 + 103 + 107 = 53 + 59 + 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47 + 53 + 59 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

311 is a rock/reggae band.

Source: Prime Curios!

521

521 is a prime number.

521 has a representation as a sum of two squares: 521 = 11² + 20².

521 is the 13th Lucas number.

521 and 523 for a twin prime pair.

521 is the hypotenuse of a primitive Pythagorean triple: 521² = 279² + 440².

521 has the representation 521 = 2⁹ + 9.

521 is the exponent of the Mersenne prime 2⁵²¹ - 1.

521 is the smallest prime whose reversal is a cube: 125 = 5³.

Galaxy cluster Abell 521 is located about 2.9 billion light-years from Earth.

Source: Prime Curios!

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!

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!

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

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!

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!

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

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!

829

829 is a prime number.

829 has a representation as a sum of two squares: 829 = 10² + 27².

827 and 829 form a twin prime pair.

829 is the hypotenuse of a primitive Pythagorean triple: 829² = 540² + 629².

829 is a divisor of 5⁹ - 1.

829 is a centered triangular number.

829 is the sum of three consecutive primes: 829 = 271 + 277 + 281.

829 is a telephone area code for the Dominican Republic.

Source: WolframAlpha

811

811 is a prime number.

809 and 811 form a twin prime pair.

811 is the smallest prime that is a sum of primes beginning and ending with the digit 7: 811 = 7 + 7 + 797.

811 is the sum of five consecutive primes: 811 = 151 + 157 + 163 + 167 + 173.

811 is a prime of the form 4n + 3 that is the sum of two consecutive composite numbers: 811 = 4(202) + 3 = 405 + 406.

In the United States, the telephone number 811 has traditionally been a direct line to the business off of the telephone company providing service on the line.

Source: Prime Curios!

809

809 is a prime number. It is a Sophie Germain prime because 2 x 809 + 1 = 1619 is also a prime.

809 has a representation as a sum of two squares: 809 = 5² + 28².

809 and 811 form a twin prime pair.

809 is the hypotenuse of a primitive Pythagorean triple: 809² = 280² + 759².

809 is a divisor of 44⁸ - 1.

809 is the only three-digit pime. Pimes are primes whose digits contain circles (that is, use only 0, 6, 8, and 9).

809 was the hotel room number in the 1952 film Don't Bother to Knock, starring Richard Widmark and Marilyn Monroe.

Source: Number Gossip

1301

1301 is a prime number.

1301 has a representation as a sum of two squares: 1301 = 25² + 26².

1301 and 1303 form a twin prime pair.

1301 is the hypotenuse of a primitive Pythagorean triple: 1301² = 51² + 1300².

1301 can be represented as 2⁴ 3⁴ + 5.

Bromotrifluoromethane, also known by the trade name Halon 1301, is a colorless, odorless gas that was used to extinguish fires.

Source: Prime Curios!

283

283 is a prime number.

281 and 283 form a twin prime pair.

283 = (6! - 5! - 4! - 3! - 2! - 1! - 0!)/2.

283 is the smallest prime number that is less than the sum of the cube roots of all primes less than itself.

283 is the (2*8*3 + 2+8+3)th (or 61st) prime.

NGC 283 is a galaxy in the constellation Cetus.

Source: Prime Curios!

271

271 is a prime number.

269 and 271 form a twin prime pair.

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

271 is the sum of eleven consecutive primes: 271 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.

271 is a Google number. The nth Google number is the first n-digit prime found in the decimal expansion of e. This sequence of numbers was originally featured in an unusual job ad placed by Google. The first few numbers in the sequence are

2,

71,

271,

4523,

74713,

904523, . . .

271 is a centered hexagonal number.

Source: Number Gossip

227

227 is a prime number.

227 and 229 form a twin prime pair.

227 is the number of composite days in a year.

227 is the smallest three-digit prime that is changed into a composite number if any digit is deleted.

227 is the number of connected planar graphs with eight edges.

227 was an NBC sitcom set in Washington, D.C., that ran from 1985 to 1990.

Source: Number Gossip

229

229 is a prime number.

227 and 229 form a twin prime pair.

229 has a representation as a sum of two squares: 229 = 2² + 15².

229 is the hypotenuse of a primitive Pythagorean triple: 229² = 60² + 221².

The sum of the first 229 primes divides the product of the first 229 primes.

229 is the smallest prime that remains prime when added to its reversal: 229 + 922 = 1151.

229 is the difference between 3³ and 4⁴.

229 is the highest you can score in a standard game of bowling if your score in each of the ten frames is required to be a prime number.

Source: Prime Curios!

281

281 is a prime number. It is also a Sophie Germain prime because 2 x 281 + 1 = 563 is prime.

281 has a representation as a sum of two squares: 281 = 5² + 16².

281 and 283 form a twin prime pair.

281 is the hypotenuse of a primitive Pythagorean triple: 281² = 160² + 231².

The final repeated digit-products of consecutive integers 281, 282, and 283 are all 6: 2 x 8 x 1 = 16, 1 x 6 = 6; 2 x 8 x 2 = 32, 3 x 2 = 6; 2 x 8 x 3 = 48, 4 x 8 = 32, 3 x 2 = 6. There are no four consecutive integers with the same final digit-product less than 6 x 24 x 10⁸.

281 is the sum of the first 14 primes (up to 43). If we add consecutive primes up to 281, the total is also a prime (7699). There are no other such primes with this behavior between 281 and 7699.

281 is a telephone area code for Houston, Texas.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.

150

150 = 2 x 3 x 5².

2¹⁵⁰ – 3 and 2¹⁵⁰ – 5 are twin primes.

150 is the largest gap between consecutive twin prime pairs less than a thousand. It occurs between {659, 661} and {809, 811}.

Each internal angle of a regular 12-sided polygon (dodecagon) is 150^o.


Sesquicentennial is a period of 150 years.

Source: Prime Curios!