17 (number)

"Seventeen" redirects here. For other uses, see 17 (disambiguation).
16 17 18
Cardinal seventeen
Ordinal 17th
Numeral system septendecimal
Factorization prime
Divisors 1, 17
Roman numeral XVII
Binary 100012
Ternary 1223
Quaternary 1014
Quinary 325
Senary 256
Octal 218
Duodecimal 1512
Hexadecimal 1116
Vigesimal H20
Base 36 H36

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 /sɛvənˈtn/ vs 70 /ˈsɛvənti/. However, in dates such as 1789 or when contrasting numbers in the teens, such as 16, 17, 18, the stress shifts to the first syllable: 17 /ˈsɛvəntn/.

The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. In a 24-hour clock, the seventeenth hour is in conventional language called five or five o'clock.

In mathematics

Seventeen is the 7th prime number. The next prime is nineteen, with which it forms a twin prime. 17 is the sum of the first four primes. 17 is the sixth Mersenne prime exponent, yielding 131071. 17 is an Eisenstein prime with no imaginary part and real part of the form 3n  1.

17 is the third Fermat prime, as it is of the form 22n + 1, specifically with n = 2,[1] and it is also a Proth prime.[2] Since 17 is a Fermat prime, regular heptadecagons can be constructed with compass and unmarked ruler. This was proven by Carl Friedrich Gauss.[3] Another consequence of 17 being a Fermat prime is that it is not a Higgs prime for squares or cubes; in fact, it is the smallest prime not to be a Higgs prime for squares, and the smallest not to be a Higgs prime for cubes.

17 is the only positive Genocchi number that is prime, the only negative one being −3. It is also the third Stern prime.[4]

17 is the average of the first two Perfect numbers.

17 is the thirteenth term of the Euclid–Mullin sequence.[5]

Seventeen is the aliquot sum of the semiprime 39, and is the aliquot sum of the semiprime 55, and is the base of the 17-aliquot tree.

There are exactly 17 two-dimensional space (plane symmetry) groups. These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.

Like 41, the number 17 is a prime that yields primes in the polynomial n2 + n + p, for all positive n < p  1.

In the Irregularity of distributions problem, consider a sequence of real numbers between 0 and 1 such that the first two lie in different halves of this interval, the first three in different thirds, and so forth. The maximum possible length of such a sequence is 17 (Berlekamp & Graham, 1970, example 63).

Either 16 or 18 unit squares can be formed into rectangles with perimeter equal to the area; and there are no other natural numbers with this property. The Platonists regarded this as a sign of their peculiar propriety; and Plutarch notes it when writing that the Pythagoreans "utterly abominate" 17, which "bars them off from each other and disjoins them".[6]

17 is the tenth Perrin number, preceded in the sequence by 7, 10, 12.[7]

In base 9, the smallest prime with a composite sum of digits is 17.

17 is the least random number,[8] according to the Hackers' Jargon File.

It is a repunit prime in hexadecimal (11).

17 is the minimum possible number of givens for a sudoku puzzle with a unique solution. This was long conjectured, and was proved in 2012.[9]

There are 17 orthogonal curvilinear coordinate systems (to within a conformal symmetry) in which the 3-variable Laplace equation can be solved using the separation of variables technique.

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 x3 + y2 = n has two different solutions for x and y positive integers. The next such number is 65.

17 is the minimum number of vertices on a graph such that, if the edges are coloured with 3 different colours, there is bound to be a monochromatic triangle. (See Ramsey's Theorem.)

17 is a full reptend prime in base 10, because its repeating decimal is 16 digits long.

In science

In languages


In French, 17 is the first compound number (dix-sept). The numbers 11 (onze) through 16 (seize) have their own names.

Age 17

In culture







Anime and manga




In sports

In other fields

Seventeen is:

No row 17 in Alitalia planes.


  1. "Sloane's A019434 : Fermat primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  2. "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  3. John H. Conway and Richard K. Guy, The Book of Numbers. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygon) could be constructed with ruler and compasses."
  4. "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  5. "Sloane's A000945 : Euclid-Mullin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  6. Babbitt, Frank Cole (1936). "Plutarch's Moralia". V. Loeb.
  7. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  8. "random numbers". catb.org/.
  9. McGuire, Gary. "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem" (PDF). arXiv:1201.0749Freely accessible. Retrieved 26 March 2012.
  10. Glenn Elert. "The Standard Model".
  11. "Age Of Consent By State".
  12. "Age of consent for sexual intercourse".
  13. For example, the patriarch Jacob lived 17 years after his son Joseph went missing and presumed dead, and lived 17 years after their reunion in Egypt, and the lifespans of Abraham aged 175, Isaac aged 180, and Jacob aged 147 are not a coincidence. "(The sum of the factors in all three cases is 17; of what possible significance this is, I have no idea.)" Leon Kass, The beginning of wisdom: reading Genesis,(Simon and Schuster, 2003), ISBN 978-0-7432-4299-8, p. 413 n. 10 (citing Genesis 47:28), quote from p. 629 n. 18, found at Google Books. Retrieved June 17, 2009.
  14. Plutarch, Moralia (1936). Isis and Osiris (Part 3 of 5). Loeb Classical Library edition.
  15. "The Power of 17". Cosmic Variance.

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