← 16 17 18 →
Numeral systemseptendecimal
Divisors1, 17
Greek numeralΙΖ´
Roman numeralXVII

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

Seventeen is the sum of the first four prime numbers.

In mathematics

Seventeen is the seventh prime number. The next prime is nineteen, with which it forms a twin prime.

Seventeen is a permutable prime, a Leyland prime of the second kind and a supersingular prime.

Seventeen is the third Fermat prime, as it is of the form 22n + 1, specifically with n = 2.[1] Since 17 is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. This was proven by Carl Friedrich Gauss[2] and ultimately led him to choose mathematics over philology for his studies.[3]

There are 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.

There are 17 two-dimensional combinations of regular polygons that completely fill a plane vertex.[4] 11 of these belong to regular and semiregular tilings, while 6 of these (3.7.42,[5] 3.8.24,[6] 3.9.18,[7] 3.10.15,[8] 4.5.20,[9] and 5.5.10)[10] exclusively surround a point in the plane, and fill it only when irregular polygons are included.[11]

There are 17 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.[12]

Seventeen is the highest dimension for paracompact Vinberg polytopes of rank n+2, with the lowest belonging to the third.[13]

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

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".[14]

Seventeen is the minimum possible number of givens for a sudoku puzzle with a unique solution. This was long conjectured, and was proved in 2012–14.[15][16]

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

Seventeen is the sixth Mersenne prime exponent, yielding 131071.

Seventeen 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 ((1,4) or (2,3)). The next such number is 65.

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

Seventeen is the only prime number which is the sum of four consecutive primes (2,3,5,7). Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime.

The sequence of residues (mod n) of a googol and googolplex, for n = 1, 2, 3, ..., agree up until n = 17.

In science

In languages


In Catalan, 17 is the first compound number (disset). The numbers 11 (onze) through 16 (setze) have their own names.

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

In Italian, 17 is also the first compound number (diciassette), whereas sixteen is sedici.

Age 17

In culture


Main article: 17 (disambiguation) § Music






Anime and manga




In sports

In other fields

Seventeen is:

No row 17 in Alitalia planes
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. ^ 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 polygons) could be constructed with ruler and compasses."
  3. ^ Pappas, Theoni, Mathematical Snippets, 2008, p. 42.
  4. ^ Dallas, Elmslie William (1855), The Elements of Plane Practical Geometry, Etc, John W. Parker & Son, p. 134.
  5. ^ "Shield - a 3.7.42 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
  6. ^ "Dancer - a 3.8.24 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
  7. ^ "Art - a 3.9.18 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
  8. ^ "Fighters - a 3.10.15 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
  9. ^ "Compass - a 4.5.20 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
  10. ^ "Broken roses - three 5.5.10 tilings". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
  11. ^ "Pentagon-Decagon Packing". American Mathematical Society. AMS. Retrieved 2022-03-07.
  12. ^ Senechal, Marjorie; Galiulin, R. V. (1984). "An introduction to the theory of figures: the geometry of E. S. Fedorov". Structural Topology (in English and French) (10): 5–22. hdl:2099/1195. MR 0768703.
  13. ^ Tumarkin, P.V. (May 2004). "Hyperbolic Coxeter N-Polytopes with n+2 Facets". Mathematical Notes. Springer. 75 (5/6): 848–854. doi:10.1023/B:MATN.0000030993.74338.dd. Retrieved 18 March 2022.
  14. ^ Babbitt, Frank Cole (1936). Plutarch's Moralia. Vol. V. Loeb.
  15. ^ McGuire, Gary (2012). "There is no 16-clue sudoku: solving the sudoku minimum number of clues problem". arXiv:1201.0749 [cs.DS].
  16. ^ McGuire, Gary; Tugemann, Bastian; Civario, Gilles (2014). "There is no 16-clue sudoku: Solving the sudoku minimum number of clues problem via hitting set enumeration". Experimental Mathematics. 23 (2): 190–217. doi:10.1080/10586458.2013.870056. S2CID 8973439.
  17. ^ Glenn Elert (2021). "The Standard Model". The Physics Hypertextbook.
  18. ^ "Age Of Consent By State". Archived from the original on 2011-04-17.
  19. ^ "Age of consent for sexual intercourse". 2015-06-23.
  20. ^ Plutarch, Moralia (1936). Isis and Osiris (Part 3 of 5). Loeb Classical Library edition.
  21. ^ "random numbers". catb.org/.
  22. ^ "The Power of 17". Cosmic Variance.
  23. ^ Ratliff, Ben (7 August 2017). "Why Would You Go to a Phish Concert, Let Alone 13? I Found Out". The New York Times. Retrieved 30 April 2018.
  24. ^ "Phish Returns to Madison Square Garden for New Year's Eve; Here's What We Think Will Go Down (Hint: Cosmic Wristbands) - LIVE music blog". Live Music Blog. 27 December 2017. Retrieved 30 April 2018.