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Old 2019-01-06, 19:41   #1
Blackadder
 
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Default Why 2^p-1 and not 2^p-2?

Why is 2p-1 special, and not 2p-2?
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Old 2019-01-06, 19:43   #2
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Quote:
Originally Posted by Blackadder View Post
Why is 2p-1 special, and not 2p-2?
Because 2p-2 is even?
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Old 2019-01-06, 19:45   #3
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In what sense special?
2p-2 is special in its own way, too
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Old 2019-01-06, 19:59   #4
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Quote:
Originally Posted by Batalov View Post
In what sense special?
2p-2 is special in its own way, too
it's twice a repunit, it shows an iteration formula for Mersenne numbers, it's 6 mod 8 for p>2 . etc.
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Old 2019-01-06, 20:02   #5
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Quote:
Originally Posted by ET_ View Post
Because 2p-2 is even?
Is that rhetorical? I really should get back into my math books.

Quote:
Originally Posted by Batalov View Post
In what sense special?
2p-2 is special in its own way, too
Special as in: why are we calculating for 2p-1 and not 2p-2 as well. I guess the latter can't be prime?

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Old 2019-01-06, 20:17   #6
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Quote:
Originally Posted by Blackadder View Post
Is that rhetorical? I really should get back into my math books.

Special as in: why are we calculating for 2p-1 and not 2p-2 as well. I guess the latter can't be prime?
no number divisible by a number other than 1 or itself is prime 2p-2 = 2(2p-1-1) therefore is divisible by 2 except when p-1 = 1 and therefore p=2 -- 2p-1-1 = 1

Last fiddled with by science_man_88 on 2019-01-06 at 20:18
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Old 2019-01-06, 20:39   #7
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Quote:
Originally Posted by science_man_88 View Post
no number divisible by a number other than 1 or itself is prime. Now, 2p-2 = 2(2p-1-1) therefore is divisible by 2

there is only one exception: when p-1 = 1 (and p=2) -- 2p-1-1 = 1 doesn't hurt primality.
That makes sense. Thank you.
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Old 2019-01-06, 20:44   #8
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Quote:
Originally Posted by ET_ View Post
Because 2p-2 is even?
Just to state the obvious, what Luigi 'ET_' said:
the people-speak word 'even' means (in math-speak) 'divisible by 2'. No more, no less.


If something is even - it cannot be prime, except if something is '2' itself.
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