19: Difference between revisions

Latest revision as of 22:06, 15 January 2012

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The number 19 is a prime number.

Below are some polynomials that give prime numbers for small input values, which give the value 19 for suitable input choice.

Polynomial	Degree	Some values for which it generates primes	Input value $n$ at which it generates 19
$n^{2} - n + 17$	2	all numbers 1-16, because 17 is one of the lucky numbers of Euler.	2

Number	Prime factorization	What's interesting about it
1729	7 times 13 times 19	third Carmichael number, i.e., absolute pseudoprime Smallest number expressible as a sum of two positive cubes in two different ways.

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 The number 19 is a [[prime number]].
+==Prime-generating polynomials==
+Below are some polynomials that give prime numbers for small input values, which give the value 19 for suitable input choice.
+{| class="sortable" border="1"
+! Polynomial !! Degree !! Some values for which it generates primes !! Input value <math>n</math> at which it generates 19
+|-
+| <math>n^2 - n + 17</math> || 2 || all numbers 1-16, because 17 is one of the [[lucky numbers of Euler]]. || 2
+|}
+==Multiples==
+===Interesting multiples===
+{| class="sortable" border="1"
+! Number !! Prime factorization !! What's interesting about it
+|-
+| [[1729]] || [[7]] times [[13]] times [[19]] || third [[Carmichael number]], i.e., absolute pseudoprime<br>Smallest number expressible as a sum of two positive cubes in two different ways.
+|}