13: Difference between revisions

Revision as of 22:02, 15 January 2012

This article is about a particular natural number.|View all articles on particular natural numbers

The number 13 is a prime number.

Below are some polynomials that give prime numbers for small input values, which give the value 13 for suitable input choice.

Polynomial	Degree	Some values for which it generates primes	Input value $n$ at which it generates 13
$n^{2}-n+11$	2	all numbers 1-10, because 11 is one of the lucky numbers of Euler.	2

Number	Prime factorization	What's interesting about it
1105	5 times 13 times 17	second Carmichael number, i.e., absolute pseudoprime
1729	7 times 13 times 19	third Carmichael number, i.e., absolute pseudoprime
2821	7 times 13 times 31	fifth Carmichael number, i.e., absolute pseudoprime

@@ Line 15: / Line 15: @@
 |-
 | <math>n^2 - n + 11</math> || 2 || all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. || 2
+|}
+==Multiples==
+===Interesting multiples===
+{| class="sortable" border="1"
+! Number !! Prime factorization !! What's interesting about it
+|-
+| [[1105]] || [[5]] times [[13]] times [[17]] || second [[Carmichael number]], i.e., absolute pseudoprime
+|-
+| [[1729]] || [[7]] times [[13]] times [[19]] || third [[Carmichael number]], i.e., absolute pseudoprime
+|-
+| [[2821]] || [[7]] times [[13]] times [[31]] || fifth [[Carmichael number]], i.e., absolute pseudoprime
 |}