help - prime number confirming

2005-12-05, 00:16

Can anyone help confirm

prime number = (((2^2*2-1)^2*2-1)^2*2-1)...

amcfarlane · 2005-12-05, 00:43

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?

ewmayer · 2005-12-05, 20:57

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

2005-12-11, 23:12

Thank you for taking time, appreciate it!

Regards
George Karl

2005-12-05, 00:16	#1
georgekarl 1111111100₂ Posts	help - prime number confirming Can anyone help confirm prime number = (((2^22-1)^22-1)^2*2-1)...

2005-12-11, 23:12	#4
georgekarl 2⁴·3·41 Posts	Thank you Thank you for taking time, appreciate it! Regards George Karl

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2005-12-05, 00:43	#2
amcfarlane Nov 2004 UK 46₈ Posts	2^22-1 = 7 = prime (2^22-1)^22-1 = 97 = prime ((2^22-1)^22-1)^22-1 = 18817 = composite (31 * 607) (((2^22-1)^22-1)^22-1)^22-1 = 708158977 = prime ((((2^22-1)^22-1)^22-1)^22-1)^22-1 = 1002978273411373057 = composite (127 7897466719774591) (((((2^22-1)^22-1)^22-1)^22-1)^22-1)^22-1 = 2011930833870518011412817828051050497 = composite (22783 * 265471 * 592897 * C21) Hmm, how deep did you want to go?