17 (number)

For other uses, see 17.

← 16 17 18 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventeen
Ordinal	17th (seventeenth)
Numeral system	septendecimal
Factorization	prime
Prime	7th
Divisors	1, 17
Greek numeral	ΙΖ´
Roman numeral	XVII
Binary	100012
Ternary	1223
Senary	256
Octal	218
Duodecimal	1512
Hexadecimal	1116
Hebrew numeral	י"ז
Babylonian numeral	𒌋𒐛

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.

Mathematics

• 17 forms a twin prime with 19, a cousin prime with 13, and a sexy prime with both 11 and 23.
• 17 is one of six lucky numbers of Euler, the positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k² − k + n produces a prime number.
• The number of integer partitions of 17 into prime parts is 17. It is the only natural number with this property.
• As seventeen is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. A proof by Carl Friedrich Gauss ultimately led him to choose mathematics over philology for his studies.
• There are seventeen crystallographic space groups in two dimensions. These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.
• Seventeen is the number of combinations of regular polygons that completely fill a plane vertex. Eleven of these belong to regular and semiregular tilings, while 6 of these (3.7.42, 3.8.24, 3.9.18, 3.10.15, 4.5.20, and 5.5.10) exclusively surround a point in the plane and fill it only when irregular polygons are included.
• 17 is the smallest $k$ for the Theodorus Spiral to complete one revolution.
• 17 is the longest sequence for which a solution exists in the irregularity of distributions problem.
• The minimum possible number of givens for a sudoku puzzle with a unique solution is 17.

The Spiral of Theodorus, with a maximum sixteen right triangles laid edge-to-edge before one revolution is completed. The largest triangle has a hypotenuse of ${\sqrt {17}}.$

In science

The elementary particles in the Standard Model of physics

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

• In the Yasna of Zoroastrianism, seventeen chapters were written by Zoroaster himself. These are the five Gathas.
• The number of surat al-Isra in the Qur'an is seventeen, at times included as one of seven Al-Musabbihat. 17 is the total number of Rak'as that Muslims perform during Salat on a daily basis.

Other fields

Seventeen is:

• The total number of syllables in a haiku (5 + 7 + 5).
• The maximum number of strokes of a Chinese radical.

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.

References

• Berlekamp, E. R.; Graham, R. L. (1970). "Irregularities in the distributions of finite sequences". Journal of Number Theory. 2 (2): 152–161. Bibcode:1970JNT.....2..152B. doi:10.1016/0022-314X(70)90015-6. MR 0269605.

External links

• Prime Curios!: 17
• Is 17 the "most random" number?