fail...

by pythag011, Dec 2, 2008, 3:45 AM

Hmm...looking at some research ideas... I fail at research...

http://www.artofproblemsolving.com/Forum/viewtopic.php?t=199220

Also, do there exist infinitely many pairs of primes(p,q) such that q = 2p + 1? I realized that if there do, I can solve a lot of problems that I am trying to solve...

If it is true, we have that there are infinitely many primes such that 2 is a primitive root of that prime...however, this result is much weaker than the conjecture above...

I am unable to prove either conjecture.

Computer says there are 7748 such pairs with p < 1 million.

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4 Comments

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I am not quite sure, but it seems like an open problem (just from intuition)

like
the Twin Prime Conjecture $ q = p + 2$ and this wants conjecture wants $ q = 2p + 1$

flipped coefficients...

hmm
again don't take my word for it

by The QuattoMaster 6000, Dec 2, 2008, 5:30 AM

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Considering how this result would trivialize about 10% of the nt olympiad problems I have seen, you are probably right.

by pythag011, Dec 2, 2008, 5:58 AM

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hmm which Olympiad problems?

by The QuattoMaster 6000, Dec 2, 2008, 11:35 PM

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http://mathworld.wolfram.com/SophieGermainPrime.html
MathWorld wrote:
It is not known if there are an infinite number of Sophie Germain primes (Hoffman 1998, p. 190).

There you go.

by dysfunctionalequations, Dec 10, 2008, 11:54 PM

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