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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 |
1. $a^n \pm 1$ 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/] |
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/]