Diff for "factorization_of_integers_of_special_forms"

Differences between revisions 3 and 21 (spanning 18 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 3 as of 2007-01-23 02:01:03 → 
  Size: 1523
  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
-Deletions are marked like this.
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- *  $2^{n} - 1$  where n is odd
 *  $2^{n} + 1$  where n is odd
 *  $2^{n} + 1$  where n = 4k − 2
 *  $2^{n} + 1$  where n = 4k
 *  $3^{n} - 1$  where n is odd      n < 540  .....      .........          . . . . 60
                   n ≤ 540             n = 6k − 3 ≤ 1077
 3n + 1                       L, M for                    . . . . 66
 5n − 1 n odd                 L, M for n = 10k − 5 ≤ 745 . . . .
                   n < 375                                         86
                   n ≤ 375
 5n + 1                     ..................                     94
 6n − 1 n odd      n < 330  . . . . . . . . . . . . . . . . . . 102
                   n ≤ 330    L, M for n = 12k − 6 ≤ 654 . . . . 106
 6n + 1
 7n − 1 n odd      n < 300  . . . . . . . . . . . . . . . . . . 116
                   n ≤ 300    L, M for n = 14k − 7 ≤ 595 . . . . 120
 7n + 1
10n − 1 n odd      n < 330  .....      .........          . . . . 129
                   n ≤ 330             n = 20k − 10 ≤ 650
10n + 1                       L, M for                    . . . . 133
11n − 1 n odd      n < 240  .....      .........          . . . . 142
                   n ≤ 240             n = 22k − 11 ≤ 473
11n + 1                       L, M for                    . . . . 145
12n − 1 n odd      n < 240  .....      .........          . . . . 152
                   n ≤ 240             n = 6k − 3 ≤ 477 .
12n + 1                       L, M for                    . . . . 155
+ *  $a^{n} \pm 1$  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]]