• 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]