19 (number)

19 (nineteen) is the natural number following 18 and preceding 20.

In mathematics

Nineteen is the 8th smallest prime number. The sequence continues 23, 29, 31, 37... 19 is the seventh Mersenne prime exponent.

Related Topics:
Prime number - 23 - Mersenne prime

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It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 1, 9, 10, 19...

Related Topics:
Keith number - Fibonacci

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With respect to divisibility, nineteen has a very simple test: 19 divides 100a + b if and only if it divides a + 4b.

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Nineteen is a centered triangular number, centered hexagonal number, and an octahedral number.

Related Topics:
Centered triangular number - Centered hexagonal number - Octahedral number

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Every positive integer is the sum of at most nineteen fourth powers (see Waring's problem).

Related Topics:
Positive - Integer - Four - Power - Waring's problem

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The decimal expansion of 1/19 has a period of maximum length: 18 digits.

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Nineteen is a Heegner number and a strictly non-palindromic number.

Related Topics:
Heegner number - Strictly non-palindromic number

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