In today's article we are going to talk about 17 (number). 17 (number) is a topic that has captured the attention of people around the world, arousing great interest and generating numerous debates. Since its emergence, 17 (number) has been the subject of study and research, generating important advances in our understanding of this topic. In this article we will explore the different aspects of 17 (number), analyzing its impact on society, its evolution over time and possible future implications. We are excited to delve into this fascinating world and learn more about 17 (number).
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 the sixth Mersenne prime exponent for numbers of the form , yielding 131071.
It is also one of six lucky numbers of Euler which produce primes of the form for (I.e. for of 17 and of 16 there is 257.)
17 can be written in the form and ; and as such, it is a Leyland prime (of the first and second kind):
The number of integer partitions of 17 into prime parts is 17 (the only number such that its number of such partitions is ).
Fermat prime
Seventeen is the third Fermat prime, as it is of the form with . 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. It is one more than the smallest number with exactly seventeen divisors, 65,536 = 216.
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.
Also in two dimensions, 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.
On the other hand, 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".
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.
The number of elementary particles with unique names in the Standard Model of physics.
In languages
Grammar
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.
Age 17
In most countries across the world, it is the last age at which one is considered a minor under law.
In the UK, the minimum age for taking driving lessons, and to drive a car or a van
In the US and Canada, it is the age at which one may purchase, rent, or reserve M-rated video games without parental consent
In some US states, and some jurisdictions around the world, 17 is the age of sexual consent
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.
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.
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.
^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.
^McGuire, Gary (2012). "There is no 16-clue sudoku: solving the sudoku minimum number of clues problem". arXiv:1201.0749 .
^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.