Differences between revisions 5 and 21 (spanning 16 versions)
Revision 5 as of 2007-01-23 02:41:17
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Revision 21 as of 2008-11-14 13:41:51
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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
 * $3^n + 1$ L, M for . . . . 66
 * $5^n − 1$ where n is odd L, M for n = 10k − 5 ≤ 745 . . . .
                   n < 375 86
                   n ≤ 375
 * $5^n + 1$ .................. 94
 * $6^n − 1$ where n is odd n < 330 . . . . . . . . . . . . . . . . . . 102
                   n ≤ 330 L, M for n = 12k − 6 ≤ 654 . . . . 106
 * $6^n + 1$
 * $7^n − 1$ where n is odd n < 300 . . . . . . . . . . . . . . . . . . 116
                   n ≤ 300 L, M for n = 14k − 7 ≤ 595 . . . . 120
 * $7^n + 1$
 * $10^n − 1$ where n is odd n < 330 ..... ......... . . . . 129
                   n ≤ 330 n = 20k − 10 ≤ 650
 * $10^n + 1$ L, M for . . . . 133
 * $11^n − 1$ where n is odd n < 240 ..... ......... . . . . 142
                   n ≤ 240 n = 22k − 11 ≤ 473
 * $11^n + 1$ L, M for . . . . 145
 * $12^n − 1$ where n is odd n < 240 ..... ......... . . . . 152
                   n ≤ 240 n = 6k − 3 ≤ 477 .
 * $12^n + 1$ L, M for . . . . 155

 * $a^n \pm 1$ for $a ≤ 13$ and $a$ not a perfect number [http://wwwmaths.anu.edu.au/~brent/factors.html]
 * $a^n \pm 1$ 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 $a ≤ 13$ 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 $n ≤ 100$ [[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]]

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