Diff for "factorization_of_integers_of_special_forms"

Differences between revisions 14 and 21 (spanning 7 versions)

an±1 for a=2,3,5,6,7,10,11,12 and large exponents n http://homes.cerias.purdue.edu/~ssw/cun/index.html
an±1 for a≤13 and a not a perfect number http://wwwmaths.anu.edu.au/~brent/factors.html
2n±1 for 1200<n<10000 http://www.euronet.nl/users/bota/medium-p.htm
10n±1 for n≤100 http://www.swox.com/gmp/repunit.html
pp±1 where p is a prime number and p<180. http://homes.cerias.purdue.edu/~ssw/bell
22n+1 (Fermat numbers) http://www.prothsearch.net/fermat.html
23n±1 http://www.alpertron.com.ar/MODFERM.HTM
Fibonacci numbers (Fn) and Lucas numbers (Ln) for n<10000 http://home.att.net/~blair.kelly/mathematics/fibonacci/
n*2n±1 (Cullen and Woodall numbers) http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm
Euclid numbers http://en.wikipedia.org/wiki/Sylvester's_sequence#Divisibility_and_factorizations

factorization_of_integers_of_special_forms (last edited 2008-11-14 13:41:51 by anonymous)

-  ⇤ ← Revision 14 as of 2007-01-23 03:13:28 → 
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  Editor: TimothyClemans
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+   ← Revision 21 as of 2008-11-14 13:41:51 → ⇥
  Size: 1009
  Editor: anonymous
  Comment: converted to 1.6 markup
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-.  $a^{n} \pm 1$  for  $a = 2, 3, 5, 6, 7, 10, 11, 12$  and large exponents n [http://homes.cerias.purdue.edu/~ssw/cun/index.html]
 *  $a^{n} \pm 1$  for  $a \leq 13$  and  $a$  not a perfect number [http://wwwmaths.anu.edu.au/~brent/factors.html]
 *  $2^{n} \pm 1$  for  $1200 < n < 10000$  [http://www.euronet.nl/users/bota/medium-p.htm]
 *  $10^{n} \pm 1$  for  $n \leq 100$  [http://www.swox.com/gmp/repunit.html]
 *  $p^{p} \pm 1$  where  $p$  is a prime number and  $p < 180$ . [http://homes.cerias.purdue.edu/~ssw/bell/r1]
 *  $2^{2^{n}} + 1$  (Fermat numbers) [http://www.prothsearch.net/fermat.html]
 *  $2^{3^{n}} \pm 1$  [http://www.alpertron.com.ar/MODFERM.HTM]
+ *  $a^{n} \pm 1$  for  $a = 2, 3, 5, 6, 7, 10, 11, 12$  and large exponents n [[http://homes.cerias.purdue.edu/~ssw/cun/index.html]]
 *  $a^{n} \pm 1$  for  $a \leq 13$  and  $a$  not a perfect number [[http://wwwmaths.anu.edu.au/~brent/factors.html]]
 *  $2^{n} \pm 1$  for  $1200 < n < 10000$  [[http://www.euronet.nl/users/bota/medium-p.htm]]
 *  $10^{n} \pm 1$  for  $n \leq 100$  [[http://www.swox.com/gmp/repunit.html]]
 *  $p^{p} \pm 1$  where  $p$  is a prime number and  $p < 180$ . [[http://homes.cerias.purdue.edu/~ssw/bell]]
 *  $2^{2^{n}} + 1$  (Fermat numbers) [[http://www.prothsearch.net/fermat.html]]
 *  $2^{3^{n}} \pm 1$  [[http://www.alpertron.com.ar/MODFERM.HTM]] 
 * Fibonacci numbers ( $F_{n}$ ) and Lucas numbers ( $L_{n}$ ) for  $n < 10000$  [[http://home.att.net/~blair.kelly/mathematics/fibonacci/]]
 *  $n * 2^{n} \pm 1$  (Cullen and Woodall numbers) [[http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm]]
 * Euclid numbers [[http://en.wikipedia.org/wiki/Sylvester's_sequence#Divisibility_and_factorizations]]