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Old 2005-12-05, 00:16   #1
georgekarl
 

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Thumbs up help - prime number confirming

Can anyone help confirm

prime number = (((2^2*2-1)^2*2-1)^2*2-1)...
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Old 2005-12-05, 00:43   #2
amcfarlane
 
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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?
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Old 2005-12-05, 20:57   #3
ewmayer
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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
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Old 2005-12-11, 23:12   #4
georgekarl
 

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Smile Thank you

Thank you for taking time, appreciate it!


Regards
George Karl
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