2005-12-05, 00:16 | #1 |
7×1,427 Posts |
help - prime number confirming
Can anyone help confirm
prime number = (((2^2*2-1)^2*2-1)^2*2-1)... |
2005-12-05, 00:43 | #2 |
Nov 2004
UK
2×19 Posts |
2^2*2-1 = 7 = prime
(2^2*2-1)^2*2-1 = 97 = prime ((2^2*2-1)^2*2-1)^2*2-1 = 18817 = composite (31 * 607) (((2^2*2-1)^2*2-1)^2*2-1)^2*2-1 = 708158977 = prime ((((2^2*2-1)^2*2-1)^2*2-1)^2*2-1)^2*2-1 = 1002978273411373057 = composite (127 * 7897466719774591) (((((2^2*2-1)^2*2-1)^2*2-1)^2*2-1)^2*2-1)^2*2-1 = 2011930833870518011412817828051050497 = composite (22783 * 265471 * 592897 * C21) Hmm, how deep did you want to go? |
2005-12-05, 20:57 | #3 |
∂^{2}ω=0
Sep 2002
República de California
2^{2}·3·5·193 Posts |
These are just the terms of the Lucas-Lehmer sequence S_0 = 4, S_n+1 = S_n^2 - 2, divided by 2. Here are the factorizations of the first few ('Cn' indicates an n-digit composite, 'PRPn' an n-digit probable prime):
Code:
S_1 = 2.7 S_2 = 2.97 S_3 = 2.31.607 S_4 = 2.708158977 S_5 = 2.127.7897466719774591 S_6 = 2.22783.265471.592897.2543310079.220600496383 S_7 = 2.113210499946729046527.71510428488234435849323250891975205208728978040847871 S_8 = 2.12289.665972737.3867637345756894712411491994657791.PRP100 S_9 = 2.1049179854847.27293256153178849431531258375109421840383.C241 S_10 = 2.C586 S_11 = 2.8191.4194619596652733275824127.PRP1143 Last fiddled with by ewmayer on 2005-12-05 at 20:58 |
2005-12-11, 23:12 | #4 |
2^{2}·769 Posts |
Thank you
Thank you for taking time, appreciate it!
Regards George Karl |
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