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 2019-01-06, 19:41 #1 Blackadder     "Angelino Desmet" Mar 2018 Belgium 2B16 Posts Why 2^p-1 and not 2^p-2? Why is 2p-1 special, and not 2p-2?
2019-01-06, 19:43   #2
ET_
Banned

"Luigi"
Aug 2002
Team Italia

12B816 Posts

Quote:
 Originally Posted by Blackadder Why is 2p-1 special, and not 2p-2?
Because 2p-2 is even?

 2019-01-06, 19:45 #3 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 47·197 Posts In what sense special? 2p-2 is special in its own way, too
2019-01-06, 19:59   #4
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by Batalov 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.

2019-01-06, 20:02   #5

"Angelino Desmet"
Mar 2018
Belgium

538 Posts

Quote:
 Originally Posted by ET_ Because 2p-2 is even?
Is that rhetorical? I really should get back into my math books.

Quote:
 Originally Posted by Batalov 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?

Last fiddled with by Blackadder on 2019-01-06 at 20:02

2019-01-06, 20:17   #6
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

838410 Posts

Quote:
 Originally Posted by Blackadder 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

2019-01-06, 20:39   #7

"Angelino Desmet"
Mar 2018
Belgium

2B16 Posts

Quote:
 Originally Posted by science_man_88 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.

2019-01-06, 20:44   #8
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

220538 Posts

Quote:
 Originally Posted by ET_ 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.