2047: Difference between revisions

Latest revision as of 21:32, 2 January 2012

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The number 2047 has the following prime factorization:

$\!2047=23*89$

Property or family	Parameter values	First few members	Proof of satisfaction/membership/containment
Mersenne number $M_{n}=2^{n}-1$	11, i.e., it is $M_{11}=2^{11}-1$		plug and check
Poulet number (also called Sarrus number), i.e., Fermat pseudoprime to base 2	eighth 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	Mersenne number for prime or Poulet implies prime or Poulet, 11 is prime, but $M_{11}$ is not prime, hence it must be Poulet.

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 | [[satisfies property::Mersenne number]] <math>M_n = 2^n - 1</math> || 11, i.e., it is <math>M_{11} = 2^{11} - 1</math> || {{#lst:Mersenne number|list}} || plug and check
 |-
-| [[satisfies property::Poulet number]] (also called Sarrus number), i.e., [[Fermat pseudoprime]] to base 2 || eight Poulet number || {{#lst:Poulet number|list}} || [[Mersenne number for prime or Poulet implies prime or Poulet]], 11 is prime, but <math>M_{11}</math> is not prime, hence it must be Poulet.
+| [[satisfies property::Poulet number]] (also called Sarrus number), i.e., [[Fermat pseudoprime]] to base 2 || eighth Poulet number || {{#lst:Poulet number|list}} || [[Mersenne number for prime or Poulet implies prime or Poulet]], 11 is prime, but <math>M_{11}</math> is not prime, hence it must be Poulet.
 |}