341: Difference between revisions

Revision as of 21:20, 2 January 2012

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The factorization is as follows:

$341=11*31$

Property or family	Parameter values	First few members of the family	Proof of satisfaction/membership/containment
Poulet number (also called Sarrus number), i.e., Fermat pseudoprime to base 2	smallest 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	Note that $2^{10}=1024\equiv 1{\pmod {341}}$ , so $2^{340}\equiv 1{\pmod {341}}$ .

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 {| class="sortable" border="1"
-! Property or family !! Parameter values !! First few members of the family
+! Property or family !! Parameter values !! First few members of the family !! Proof of satisfaction/membership/containment
 |-
-| [[satisfies property::Poulet number]] (also called Sarrus number), i.e., [[Fermat pseudoprime]] to base 2 || smallest Poulet number || {{#lst:Poulet number|list}}
+| [[satisfies property::Poulet number]] (also called Sarrus number), i.e., [[Fermat pseudoprime]] to base 2 || smallest Poulet number || {{#lst:Poulet number|list}} || Note that <math>2^{10} = 1024 \equiv 1 \pmod {341}</math>, so <math>2^{340} \equiv 1 \pmod {341}</math>.
 |}