Seventeen is the sum of the first four prime numbers.
In mathematics
Seventeen is the seventh
prime number, which makes it the fourth
super-prime,[1] as
seven is itself prime. It forms a
twin prime with
19,[2] a
cousin prime with
13,[3] and a
sexy prime with both
11 and
23.[4] Seventeen is the only prime number which is the sum of four consecutive primes (
2,
3,
5, and
7), as any other four consecutive primes that are added always generate an even number divisible by two. It is one of six
lucky numbers of Euler which produce primes of the form ,[5] and the sixth
Mersenne prime exponent, which yields 131,071.[6] It is also the minimum possible number of givens for a
sudoku puzzle with a unique solution.[7][8] 17 can be written in the form and ; and as such, it is a
Leyland prime and
Leyland prime of the second kind:[9][10]
The number of
integer partitions of 17 into prime parts is 17 (the only number such that its number of such partitions is ).[11]
Seventeen is the third
Fermat prime, as it is of the form with .[12] On the other hand, the seventeenth
Jacobsthal–Lucas number — that is part of a
sequence which includes four Fermat primes (except for
3) — is the fifth and largest known Fermat prime:
65,537.[13] It is one more than the smallest number with exactly seventeen
divisors,
65,536 = 216.[14] 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.[15][16]
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".[17]
Seventeen distinct
fully supported stellations generated by an
icosahedron.[28] The seventeenth prime number is
59, which is equal to the total number of stellations of the icosahedron by
Miller's rules.[29][30] 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).[31]
Seventeen 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.[32]
Seventeen is the longest sequence for which a solution exists in the
irregularity of distributions problem,[34] while the sequence of residues (mod n) of a
googol and
googolplex, for , agree up until .
A positive
definite quadraticinteger matrix represents all
primes when it contains at least the set of seventeen numbers: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 67, 73}; only four prime numbers less than the largest member are not part of the set (53,
59, 61, and 71).[37]
In most US states, Canada and in the UK, the age at which one may
donate blood (without parental consent)
In many countries and jurisdictions, the age at which one may obtain a
driver's license
In the US, the age at which one may watch, rent, or purchase
R-rated movies without parental consent
The U.S.
TV Parental Guidelines system sets 17 as the minimum age one can watch programs with a TV-MA rating without parental guidance.
In the US, the age at which one can enlist in the armed forces with parental consent
In the US, the age at which one can apply for a
private pilot licence for powered flight (however, applicants can obtain a student pilot certificate at age 16)
The number 17 is a recurring theme in the works of
novelistSteven Brust. All of his chaptered novels have either 17 chapters or two books of 17 chapters each. Multiples of 17 frequently appear in his novels set in the fantasy world of
Dragaera, where the number is considered holy.
According to
Plutarch's
Moralia, the Egyptians have a legend that the end of Osiris' life came on the seventeenth of a month, on which day it is quite evident to the eye that the period of the full moon is over. Now, because of this, the Pythagoreans call this day "the Barrier", and utterly abominate this number. For the number seventeen, coming in between the square sixteen and the oblong rectangle eighteen, which, as it happens, are the only plane figures that have their perimeters equal their areas, bars them off from each other and disjoins them, and breaks up the
epogdoon by its division into unequal intervals.[41]
Described at
MIT as 'the least random number', according to the
Jargon File.[42] 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.[43]
The number of guns in a 17-gun
salute to U.S. Army, Air Force and Marine Corps Generals, and Navy and Coast Guard admirals.
Seventeen was the former name of a yacht prior to being commissioned in the
US Navy as the
USS Carnelian (PY-19).
In
Italian culture, the number 17 is considered unlucky. When viewed as the Roman numeral, XVII, it is then changed anagrammatically to VIXI, which in the
Latin language translates to "I lived", the
perfect implying "My life is over." (c.f. "Vixerunt",
Cicero's famous announcement of an execution.)
Renault sold its "
R17" model in Italy as "R177". See
Cesana Pariol in the sport section about the name of curve 17.
The fear of the number 17 is called '
heptadecaphobia' or 'heptakaidekaphobia'.
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).
The number to call police in France.
Force 17, a special operations unit of the Palestinian Fatah movement.
Malaysia Airlines Flight 17 was
shot down by Russian-controlled forces on 17 July 2014 after flying over eastern Ukraine. The first test flight of the plane, a
Boeing 777-200ER, was on 17 July 1997, exactly 17 years prior to the doomed flight.
^McGuire, Gary (2012). "There is no 16-clue sudoku: solving the sudoku minimum number of clues problem".
arXiv:1201.0749 [
cs.DS].
^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.
S2CID8973439.
^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."
^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.
MR0768703.