[quote=blob100;206813]The point is that I do learn, as I said: "by reading the book "solved and unsolved problems in number theory" I found this conjecture... and by playing with it..."
1) I think reading this book is learning.
2) I think playing with the materials help to understand it.
Please agree that I'm learning and I STOPPED conjecturing.
As I said, I didn't find any new conjecture.. I just played with an existed one.

[/quote]
Silverman,
As I said before...
I STOPPED conjecturing, and started learning.
By looking forward, I found this mistake. I wanted to change that horrible mistake, why do you say I still conjecture? By writing I mistaken, you understood I conjectured something? please agree that I do learn.
I hear my teachers, and do what they say.

BTW: what do you think about the book "Number Story" by Higgins?
Found it in the library and took it home to look inside, and when I will finish "solved and unsolved..." I'll read it, or what you will suggest me to read.

Is Legendre's conjecture unproven? By wikipedia it is.. but not by MathWorld.

[QUOTE=blob100;207680]Is Legendre's conjecture unproven? By wikipedia it is.. but not by MathWorld.[/QUOTE]

It's unproven. Further, both of those sources say as much.

I would be very surprised if it was proven in the next 20 years.

Wait, let me understand.
Unproven means, it wasn't proven, or it was proved as a false proposition?

[quote=blob100;207714]Wait, let me understand.
Unproven means, it wasn't proven, or it was proved as a false proposition?[/quote]
The first one. (unproven=not proven, disproved=proven as a false proposition)
A conjecture has not been proven (is unproven).
A theorem has been proven.
I'm not sure what something would be called that has been disproved (proven as false), but it wouldn't be conjecture or theorem.

Is there a theory or a conjecture that show the number of succesive prime pairs with the same gap between n to 0?
For example: G_2(15)=3.
Becuase there are 3 pairs of succesive prime numbers between 15 and 0.

[QUOTE=blob100;208556]Is there a theory or a conjecture that show the number of succesive prime pairs with the same gap between n to 0?
For example: G_2(15)=3.
Becuase there are 3 pairs of succesive prime numbers between 15 and 0.[/QUOTE]

If you don't require the numbers to be consecutive primes, and the gap is even and not too large (constant, or perhaps increasing as log x or so) then there should be about 2C_2 x / (log x)^2 such pairs up to x, where 2C_2 is about 1.3203.

This has not been proven; it's a generalization of the twin prime conjecture and a special case of the k-tuple conjecture.

What is a good book to learn calculus?

[QUOTE=blob100;208685]What is a good book to learn calculus?[/QUOTE]
AB or BC? Or both?

What do you mean by AB and BC? I ask for a nice calculus book to learn the basic of the calculus (to understand proofs, analyzing...).

[QUOTE=blob100;208685]What is a good book to learn calculus?[/QUOTE]


You are joking, right?

You have not mastered basic algebra yet.