17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. 17 was described at MIT as "the least random number", according to the Jargon File. This is supposedly because, in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice. This study has been repeated a number of times.

Mathematics

17 is a Leyland number and Leyland prime, using 2 & 3 (23 + 32) and using 4 and 5 , Since seventeen is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. This was proven by Carl Friedrich Gauss and ultimately led him to choose mathematics over philology for his studies. The minimum possible number of givens for a sudoku puzzle with a unique solution is 17.

Geometric properties

Two-dimensions

17 is the least k for the Theodorus Spiral to complete one revolution. This, in the sense of Plato, who questioned why Theodorus (his tutor) stopped at \sqrt{17} when illustrating adjacent right triangles whose bases are 1|units and heights are successive square roots, starting with 1. In part due to Theodorus’s work as outlined in Plato’s Theaetetus, it is believed that Theodorus had proved all the square roots of non-square integers from 3 to 17 are irrational by means of this spiral.

Enumeration of icosahedron stellations

In three-dimensional space, there are seventeen distinct fully supported stellations generated by an icosahedron. The seventeenth prime number is 59, which is equal to the total number of stellations of the icosahedron by Miller's rules. Without counting the icosahedron as a zeroth stellation, this total becomes 58, a count equal to the sum of the first seven prime numbers (2 + 3 + 5 + 7 ... + 17). Seventeen distinct fully supported stellations are also produced by truncated cube and truncated octahedron.

Four-dimensional zonotopes

Seventeen is also the number of four-dimensional parallelotopes that are zonotopes. Another 34, or twice 17, are Minkowski sums of zonotopes with the 24-cell, itself the simplest parallelotope that is not a zonotope.

Abstract algebra

Seventeen is the highest dimension for paracompact Vineberg polytopes with rank n+2 mirror facets, with the lowest belonging to the third. 17 is a supersingular prime, because it divides the order of the Monster group. If the Tits group is included as a non-strict group of Lie type, then there are seventeen total classes of Lie groups that are simultaneously finite and simple (see classification of finite simple groups). In base ten, (17, 71) form the seventh permutation class of permutable primes.

Other notable properties

In science

Physics

Seventeen is the number of elementary particles with unique names in the Standard Model of physics.

Chemistry

Group 17 of the periodic table is called the halogens. The atomic number of chlorine is 17.

Biology

Some species of cicadas have a life cycle of 17 years (i.e. they are buried in the ground for 17 years between every mating season).

In religion

Other fields

Seventeen is:

Music

Where Pythagoreans saw 17 in between 16 from its Epogdoon of 18 in distaste, the ratio 18:17 was a popular approximation for the equal tempered semitone (12-tone) during the Renaissance.