| ||||
---|---|---|---|---|
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.
Seventeen is the sum of the first four prime numbers.
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 is the minimum number of vertices on a graph such that, if the edges are colored with three different colors, there is bound to be a monochromatic triangle; see Ramsey's theorem. [18]
There are also:
Seventeen is the highest dimension for paracompact Vineberg polytopes with rank mirror facets, with the lowest belonging to the third. [33]
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 .
In abstract algebra, 17 is the seventh supersingular prime that divides the order of six sporadic groups (J3, He, Fi23, Fi24, B, and F1) inside the Happy Family of such groups. [35] The 16th and 18th prime numbers (53 and 61) are the only two primes less than 71 that do not divide the order of any sporadic group including the pariahs, with this prime as the largest such supersingular prime that divides the largest of these groups (F1). On the other hand, if the Tits group is included as a non-strict group of Lie type, then there are seventeen total classes of Lie groups that are simultaneously finite and simple (see, classification of finite simple groups). In base ten, (17, 71) form the seventh permutation class of permutable primes. [36]
A positive definite quadratic integer 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 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.
Seventeen is:
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.
15 (fifteen) is the natural number following 14 and preceding 16.
21 (twenty-one) is the natural number following 20 and preceding 22.
45 (forty-five) is the natural number following 44 and preceding 46.
23 (twenty-three) is the natural number following 22 and preceding 24.
32 (thirty-two) is the natural number following 31 and preceding 33.
55 (fifty-five) is the natural number following 54 and preceding 56.
58 (fifty-eight) is the natural number following 57 and preceding 59.
63 (sixty-three) is the natural number following 62 and preceding 64.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
300 is the natural number following 299 and preceding 301.
600 is the natural number following 599 and preceding 601.
135 is the natural number following 134 and preceding 136.
1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001. With a number, "billion" can be abbreviated as b, bil or bn.
138 is the natural number following 137 and preceding 139.
257 is the natural number following 256 and preceding 258.
288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits.
60,000 is the natural number that comes after 59,999 and before 60,001. It is a round number. It is the value of (75025).