Back when I was taking a number theory first year seminar, I thought I had discovered a pattern in the primes, that they could be written as 2p+q where p and q are prime. After doing pretty extensive testing in Java to test this for a large data set, and then it turns out that both my professor and I had missed the fact that this was already covered by the Goldbach conjecture. I was pretty bummed. I thought I had finally discovered something in math.

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Joe Puccio 
Apr 23, 2013, 10:59 AM
to Daniel

Hey, 

Looks like Goldbach's conjecture already covers a more general form of my conjecture that stated that all primes >5 could be written as 2p+q? 

http://en.wikipedia.org/wiki/Goldbach's_conjecture


Daniel Orr 
Apr 23, 2013, 12:43 PM
to me

Hey Joe,

That appears to be correct. I didn't know about Goldbach's second
conjecture stating that every integer >5 can be written as a sum of
three primes. Sorry for missing/neglecting that point!

Best,
Dan



Joe Puccio 
Apr 23, 2013, 12:57 PM
to Daniel

Hey Daniel, 

I've begun to make comments about how Golbach's conjecture and similar conjectures (such as Levy's conjecture) affect my results. Would it be okay if I left my paper as is for our final project and then if publishing in some way is still an option, I'll make the changes to appropriately mention Golbach and Levy? The only remaining unique (as far as I can tell) conclusions I've made are about the cases where p and q are consecutive, which is fortunately the bulk of my paper. Perhaps if I still were to explore publishing something, I would look at the properties of the resulting primes when p and q are separated by 1 prime, or 2 primes, etc. 

Joe


Levy's conjecture: http://mathworld.wolfram.com/LevysConjecture.html



Daniel Orr 
Apr 23, 2013, 1:22 PM
to me

Hey Joe,

> I've begun to make comments about how Golbach's conjecture and similar
> conjectures (such as Levy's conjecture) affect my results. Would it be
> okay if I left my paper as is for our final project and then if
> publishing in some way is still an option, I'll make the changes to
> appropriately mention Golbach and Levy?
Sure, that won't be a problem. I'm going to look into publishing options
today or tomorrow.

Levy's conjecture is right up your alley! Sorry I wasn't aware of it
when you first asked me these questions! I'll take the blame for that one.

Best,
Dan


Joe Puccio 
Apr 23, 2013, 1:57 PM
to Daniel

Hey Daniel,

Thanks.

It's not a problem. My fault too as I couldn't find it until now. I'll just shift the main focus of my investigation to finding interesting cases of Levy and Goldbach that have p,q consecutive.

Joe