19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
| ||||
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Cardinal | nineteen | |||
Ordinal | 19th (nineteenth) | |||
Numeral system | nonadecimal | |||
Factorization | prime | |||
Prime | 8th | |||
Divisors | 1, 19 | |||
Greek numeral | ΙΘ´ | |||
Roman numeral | XIX | |||
Binary | 100112 | |||
Ternary | 2013 | |||
Senary | 316 | |||
Octal | 238 | |||
Duodecimal | 1712 | |||
Hexadecimal | 1316 | |||
Hebrew numeral | י"ט | |||
Babylonian numeral | 𒌋𒐝 |
is the eighth prime number, and forms a sexy prime with 13,[1] a twin prime with 17,[2] and a cousin prime with 23.[3] It is the third full reptend prime in decimal,[4] the fifth central trinomial coefficient,[5] and the seventh Mersenne prime exponent.[6] 19 is the second Keith number, and more specifically the first Keith prime.[7] It is also the second octahedral number, after 6.[8]
19 is the maximum number of fourth powers needed to sum up to any natural number, and in the context of Waring's problem, 19 is the fourth value of g(k).[9]
The Collatz sequence for nine requires nineteen steps to return back to one, more than any other number below it.[10] On the other hand, nineteen requires twenty steps, like eighteen. Less than ten thousand, only thirty-one other numbers require nineteen steps to return back to one:
19 is the sixth Heegner number.[12] 67 and 163, respectively the 19th and 38th prime numbers, are the two largest Heegner numbers, of nine total.
The sum of the squares of the first 19 primes is divisible by 19.[13]
19 is the first prime number that is not a permutable prime in decimal, as its reverse (91) is composite; where 91 is also the fourth centered nonagonal number.[14]
19, alongside 109, 1009, and 10009, are all prime (with 109 also full reptend), and form part of a sequence of numbers where inserting a digit inside the previous term produces the next smallest prime possible, up to scale, with the composite number 9 as root.[18] 100019 is the next such smallest prime number, by the insertion of a 1.
R19 is the second base-10 repunit prime, short for the number 1111111111111111111.[20]
19 is the third centered triangular number as well as the third centered hexagonal number.[21][22]
The number of nodes in regular hexagon with all diagonals drawn is nineteen.[26]
can be used to generate the first full, non-normal prime reciprocal magic square in decimal whose rows, columns and diagonals — in a 18 x 18 array — all generate a magic constant of 81 = 92.[30]
The projective special linear group represents the abstract structure of the 57-cell: a universal 4-polytope with a total of one hundred and seventy-one (171 = 9 × 19) edges and vertices, and fifty-seven (57 = 3 × 19) hemi-icosahedral cells that are self-dual.[34]
In total, there are nineteen Coxeter groups of non-prismatic uniform honeycombs in the fourth dimension: five Coxeter honeycomb groups exist in Euclidean space, while the other fourteen Coxeter groups are compact and paracompact hyperbolic honeycomb groups.
There are infinitely many finite-volume Vinberg polytopes up through dimension nineteen, which generate hyperbolic tilings with degenerate simplex quadrilateral pyramidal domains, as well as prismatic domains and otherwise.[35]
On the other hand, a cubic surface is the zero set in of a homogeneous cubic polynomial in four variables a polynomial with a total of twenty coefficients, which specifies a space for cubic surfaces that is 19-dimensional.[37]
19 is the eighth consecutive supersingular prime. It is the middle indexed member in the sequence of fifteen such primes that divide the order of the Friendly Giant , the largest sporadic group: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}.[38]
In the Happy Family of sporadic groups, nineteen of twenty-six such groups are subquotients of the Friendly Giant, which is also its own subquotient.[46] If the Tits group is indeed included as a group of Lie type,[47] then there are nineteen classes of finite simple groups that are not sporadic groups.
Worth noting, 26 is the only number to lie between a perfect square (52) and a cube (33); if all primes in the prime factorizations of 25 and 27 are added together, a sum of 19 is obtained.
In the Bábí and Baháʼí Faiths, a group of 19 is called a Váhid, a Unity (Arabic: واحد, romanized: wāhid, lit. 'one'). The numerical value of this word in the Abjad numeral system is 19.
19 is a sacred number of the goddess Brigid because it is said to represent the 19-year cycle of the Great Celtic Year and the amount of time it takes the Moon to coincide with the winter solstice.[48]
Note that terms A186074(4) and A186074(10) have trailing 0's, i.e. 19900 = Sum_{k=0..199} k and 1999000 = Sum_{k=0..1999} k...". "This pattern continues indefinitely: 199990000, 19999900000, etc.
...so [sic] moonshine illuminates a physical origin for the monster, and for the 19 other sporadic groups that are involved in the monster.
...for all groups of Lie type, including the twisted groups of Steinberg, Suzuki and Ree (and the Tits group).
Assuming KIAs accurately represented age groups serving in Vietnam, the average age of an infantryman (MOS 11B) serving in Vietnam to be 19 years old is a myth, it is actually 22. None of the enlisted grades have an average age of less than 20.