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 2007-07-16, 22:35 #1 Unregistered   157178 Posts Primality If n(2^(n-1)) +1 is prime, prove n is prime if and only if n is not a composite prime square.
2007-07-17, 19:22   #2
ewmayer
2ω=0

Sep 2002
República de California

23·3·487 Posts

Quote:
 Originally Posted by Unregistered If n(2^(n-1)) +1 is prime, prove n is prime if and only if n is not a composite prime square.
n a composite prime square (or just composite, or just a prime square) would seem to rule out primality of n whether or not n(2^(n-1)) +1 is prime, would it not?

2007-07-17, 20:03   #3
VolMike

Jun 2007
Moscow,Russia

7·19 Posts

Quote:
 Originally Posted by Unregistered If n(2^(n-1)) +1 is prime, prove n is prime if and only if n is not a composite prime square.
All n in range [1,1500] for which n*(2^(n-1)) +1 is prime:
Code:
 {1, 2, 3, 6, 7, 14, 27, 66, 67, 87, 115, 134, 187, 295, 446, 867, 1326, 1479}
Check your guess-work on them to be sure your supposition doesn't have obvious contrary instance.

Last fiddled with by VolMike on 2007-07-17 at 20:07

2007-07-17, 22:12   #4
ewmayer
2ω=0

Sep 2002
República de California

23×3×487 Posts

Quote:
 Originally Posted by VolMike Check your guess-work on them to be sure your supposition doesn't have obvious contrary instance.
The very first composite among the numerous one you found that satisfy the condition already disproves the hypothesis. Sounds like it's back to the drawing board for Unregistered...

2007-07-18, 08:36   #5
VolMike

Jun 2007
Moscow,Russia

7×19 Posts

Quote:
 Originally Posted by ewmayer The very first composite among the numerous one you found that satisfy the condition already disproves the hypothesis. Sounds like it's back to the drawing board for Unregistered...
That's why I suggest him to recheck the formulating of his statement or admit the approval to be false.

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