From IWU Magazine, Spring 2013 edition
What's in a Number?
Professor TIan-Xiao He explains the significance of 17.
Alex Bellos, author of popular math books, set up a survey website (at www.favouritenumber.net) seeking responses to the question, “What’s your favorite number and why?” We put the same question to Professor Tian-Xiao He, who responded that he finds 17 “among the most interesting” numbers. Here are just a few reasons why:
- 17 is the smallest Trotter prime (as it is of the form 10 n 2 +7 for n =1).
- 17 is the only known prime that is equal to the sum of the digits of its cube (because 173=4913 and 4+9+1+3=17; see sequence A046459).
- 17 is the only prime that is the average of two consecutive Fibonacci numbers.
- 17 is the only positive Genocchi number that is prime.
- 17 is the first number that can be written as the sum of a positive cube and a positive square in two different ways (that is, the smallest n such that x 3 + y 2 = n has two different solutions for positive integers x and y . The next such number is 65). It is also the smallest prime of the form p 3 + q 2 , where p and q are prime, and the only prime of the form pq + qp , where p and q are primes.
- If the edges are colored with three different colors, the number 17 is the minimum number of vertices on a complete graph such that there is bound to be a monochromatic triangle.
- At age 17 , German mathematician Carl Friedrich Gauss had a thought to construct the famous 17 -gon and finished it in the following year.
- Hungary-born mathematician Paul Erdös “gave a beautiful elementary proof of Bertrand’s conjecture (i.e., there is always a prime between any positive integer n and its double 2 n ) at the age of 17 , which is considered the first significant theorem he ever proved,” says He.
- At 17 years, the periodical cicada has the longest cycle of development of any known insect. Its Latin name given by Swedish naturalist Carl Linnaeus, Cicada septendecim, has 17 letters.
- The Parthenon has 17 columns along its lengths.
Professor He’s home number is 1319 — the two closest prime numbers to
, i.e., 13 and 19.