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October 18th, 2011, 08:44 AM   #1
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Help with an infinite primes of the form proof

My professor assigned this for class, and I am totally stuck.
Their were two questions,
A) prove their are infinitely many primes of the form ((X^2)-1)/2
B) prove their are infinitely many primes of the form Sqrt(2x-1)
I can barely start on both of these so any help would be much appreciated.
Thanks a billion,
-Wheepwhoop
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October 18th, 2011, 09:01 AM   #2
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Re: Help with an infinite primes of the form proof

Question B is easy -- equate the form with an arbitrary odd prime p and solve for x.

For question A, split it into two cases, where x is even and where x is odd.
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October 18th, 2011, 09:05 AM   #3
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Re: Help with an infinite primes of the form proof

A) is false if x is taken to be an integer. If x is taken to be merely real then just solve the equation and use the fact that there are an infinite number of primes.
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October 18th, 2011, 09:18 AM   #4
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Re: Help with an infinite primes of the form proof

Quote:
Originally Posted by mattpi
A) is false if x is taken to be an integer.
Indeed.
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October 19th, 2011, 10:13 PM   #5
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Re: Help with an infinite primes of the form proof

haha I managed to prove the second one was false about a minute after posting.
The second one though I want to make sure I have really right, so i say that the form sqrt(2x-1) is equal to some random odd prime. So I simply say 2y-1 where 2y-1 is an element of the primes. The plug that in as the f(x) side of my equation and solve for x?
How exactly does that help me? (Solving it out tells me that x is equal to 2(x^2)+2x+1. So do I know their are infinatly many primes of that form then?
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October 20th, 2011, 04:47 AM   #6
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Re: Help with an infinite primes of the form proof

Solve sqrt(2x+1) = p for p and tell me if you see some reason it might not be prime.
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October 20th, 2011, 01:06 PM   #7
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Re: Help with an infinite primes of the form proof

I realize I'm being slow here, so thank you for your patients, when I set it to p you were right, it was even. But when I set it to 2x-1 (i.e. some odd number) and said that number was a a prime, then I solved it and it came out odd. Is my second method not a legitimate one then? I ran it for the first few primes and it defiantly out put some of them (two so far and I've run it up to through 61. (output three and sixty one as whole numbers. The rest were all square roots)
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October 20th, 2011, 05:09 PM   #8
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Re: Help with an infinite primes of the form proof

Quote:
Originally Posted by WheepWhoop
I realize I'm being slow here, so thank you for your patients, when I set it to p you were right, it was even. But when I set it to 2x-1 (i.e. some odd number) and said that number was a a prime, then I solved it and it came out odd. Is my second method not a legitimate one then? I ran it for the first few primes and it defiantly out put some of them (two so far and I've run it up to through 61. (output three and sixty one as whole numbers. The rest were all square roots)
Think about what you're solving for in the second method and what it being odd represents.
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