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Old 2007-07-16, 22:35   #1
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Exclamation Primality

If n(2^(n-1)) +1 is prime, prove n is prime if and only if n is not a composite prime square.
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Old 2007-07-17, 19:22   #2
ewmayer
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Quote:
Originally Posted by Unregistered View Post
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?
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Old 2007-07-17, 20:03   #3
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Quote:
Originally Posted by Unregistered View Post
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
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Old 2007-07-17, 22:12   #4
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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...
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Old 2007-07-18, 08:36   #5
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Originally Posted by ewmayer View Post
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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