# Fun Facts About the Number 17

TR Smith is a product designer and former teacher who uses math in her work every day.

Seventeen is a special number that appears numerous times in the Old Testament of the Bible, in many legends in Islamic traditions, and is often cited as being the "least random number" -- owing to the fact that when people are asked to pick a random number between 1 and 20, they tend to pick 17 more frequently than any other number. Here are 34 curious facts and mathematical properties of the number 17.

## 17 Random Facts About 17

• There are 17 species of penguin: Adelie, African, Chinstrap, Emperor, Erect-Crested, Fiordland, Galapagos, Gentoo, Humboldt, King, Little, Macaroni, Magellanic, Rockhopper, Royal, Snares, and Yellow-Eyed.
• 17 is the number of syllables in a traditional haiku, a Japanese three-line poem: 5 + 7 + 5 = 17.
• Along with the numbers 666 and 13, 17 is considered unlucky in some cultures, especially in Italy. In roman numerals, 17 is XVII, which can be rearranged to form the Latin word "vixi" which means "I have lived," which means the speaker is dead. This is why some airlines have no row 17, nor row 13. Fear of the number 17 is called heptakaidekaphobia.
• 17-year cicadas live underground for 17 years before emerging to mate.
• Seventeen magazine is a print magazine for teenage girls. Its first issue was printed in 1944.
• Seventeen is a novel by Booth Tarkington that became a bestseller in 1916. Coincidentally, the digits of 1916 add up to 17.
• Iran is the 17th most populous country.
• Libya is the 17th largest country in area.
• The atomic number of chlorine is 17.
• Q is the 17th letter of the English alphabet and occurs with a frequency of about 0.17% as the starting letter of a words. Its total frequency in English is 0.095%.
• As of 2015, Spain is divided into 17 autonomous communities (similar to states in the US). This may change if Catalonia secedes.
• The Parthenon is 8 columns wide and 17 columns long.
• Benjamin Franklin was born on January 17 and died on April 17 in the 1700s. He was one of 17 children and ran away from home at age 17 to make a living in Philadelphia.
• The 17-tone equal temperament scale divides an octave into 17 equal frequency ratios. Some musicologists consider this alternative tuning system superior to the standard 12-tone equal temperament scale.
• The 17th episode of The Simpsons is "Two Cars in Every Garage and Three Eyes on Every Fish."
• The state of Nevada has 17 counties, including Carson City, which is its own county.

Shakespeare's 17th Sonnet

## 17 Math Facts About 17

• There are exactly 17 ways to write 17 as a the sum of primes (with repetition allowed). Equivalently, there are only 17 integers whose prime factors add up to 17 (counting repeated prime factors).
• 17 is a twin prime, meaning it is either two more than or two less than another prime. In this case, 17 is twin prime with 19. Although it is known there are infinitely many primes, it is unknown if there are infinitely many pairs of twin primes.
• 17 is the smallest integer that can be expressed in the form x^4 + y^4, where x and y are distinct integers.
• 17 is a Fermat prime since it is of the form 2^(2^n) + 1. This means that a regular 17-sided polygon (called a heptadecagon) can be constructed with only a ruler and compass.
• In order for a Sudoku puzzle to have a unique solution, the number of given entries must be at least 17.
• There are 17 non-abelian groups of order less than 17. (There is no non-abelian group of order 17.)
• 17 is a Leyland number, one that can be written in the form x^y + y^x for some integers x and y greater than 1. In this case, 17 = 3^2 + 2^3. 100 is also a Leyland number.
• 17 is also of the form x^y - y^x, since 3^4 - 4^3 = 17.
• 17 is an emirp, a prime number whose digit reversal is also a prime number (in base-10).
• No odd Fibonacci number can be divisible by 17. This is because 17 divides every 9th Fibonacci number, and the Fibonacci numbers follow the pattern odd, odd, even, odd, odd, even, odd, odd, even, ... The first Fibonacci number divisible by 17 is 34.
• The sum of squared primes up to seventeen squared is 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 = 666.
• Suppose human relationships are simplified to three categories: friends, enemies, and strangers. In any gathering of 17 people there will always be a subset of 3 people who are either all friends, all enemies with one another, or all strangers. 17 is the smallest number for which this is true. In terms of graph theory, this is a Ramsey Number for three colors.
• 17 is an element of the Perrin sequence 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39,... The sequence is generated by the recursive formula P(n+3) = P(n+1) + P(n). Notice that this is different from the recursive formula that defines Fibonacci numbers.
• The 17th triangular number is 153, a number with many curious mathematical properties as well.
• 17 is the maximum length of a sequence in the Irregularity of Distributions Problem. The problem states that {x1, x2, x3, ... xN} is a sequence of N numbers between 0 and 1 such that the first two numbers lie in different halves of the interval (0, 1), the first three numbers lie in different thirds of the interval (0, 1), the first four numbers lie in different fourths of the interval (0, 1), etc. up to N. It turns out there is a solution for every value of N up to N = 17. If N = 18 or greater there is no solution. One solution for N = 17 is the sequence {0.029, 0.971, 0.423, 0.710, 0.270, 0.542, 0.852, 0.172, 0.620, 0.355, 0.774, 0.114, 0.485, 0.926, 0.207, 0.677, 0.297}.
• The Pythagoreans (ancient followers of the Greek philosopher and mathematician Pythagoras) considered 17 an unlucky number. They were fond of the numbers 16 and 18 because a 4x4 square has an area and perimeter of 16, and a 3x6 rectangle has an area and perimeter of 18, and there are no other integers besides 16 and 18 that solve the area = perimeter problem for rectangles. Because 17 separates 16 and 18, the Pythagoreans did not like 17.
• There are 17 plane symmetry groups, also known as wallpaper groups. In a practical context, they describe all the possible rotational, reflectional, and translational symmetries of wallpaper. These are shown below.

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