2465: Difference between revisions

Latest revision as of 21:17, 3 January 2012

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

The number 2465 is a square-free number with prime factors 5, 17, and 29.

$\!2465=5*17*29$

Property or family	Parameter values	First few numbers satisfying the property	Proof of satisfaction/containment/membership
Carmichael number (also called absolute pseudoprime)	fourth Carmichael number	561, 1105, 1729, 2465, 2821, 6601, [SHOW MORE] 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461 View list on OEIS	The universal exponent is $\operatorname {lcm} \{5-1,17-1,29-1\}=112$ which divides 2465 - 1 = 2464.
Poulet number (also called Sarrus number) (Fermat pseudoprime to base 2)	fourth Poulet number	341, 561, 645, 1105, 1387, 1729, 1905, 2047, [SHOW MORE] 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911, 10261, 10585, 11305, 12801, 13741, 13747, 13981, 14491, 15709, 15841, 16705, 18705, 18721, 19951, 23001, 23377, 25761, 29341 View list on OEIS	follows from its being a Carmichael number.

@@ Line 8: / Line 8: @@
 <math>\! 2465 = 5 * 17 * 29</math>
+===Properties and families===
+{| class="sortable" border="1"
+! Property or family !! Parameter values !! First few numbers satisfying the property !! Proof of satisfaction/containment/membership
+|-
+| [[satisfies property::Carmichael number]] (also called absolute pseudoprime) || fourth Carmichael number || {{#lst:Carmichael number|list}} || The [[universal exponent]] is <math>\operatorname{lcm} \{ 5-1,17-1,29-1 \} = 112</math> which divides 2465 - 1 = 2464.
+|-
+| [[satisfies property::Poulet number]] (also called Sarrus number) ([[Fermat pseudoprime]] to base 2) || fourth Poulet number || {{#lst:Poulet number|list}} || follows from its being a Carmichael number.
+|}