[QUOTE=blob100;205790]I have a new conjecture (it isn't about mersenne numbers),
I conjecture that: between n^2 to n^2+2n there is always a prime number.
When n is an odd number.
We can show n^2+2n as n(n+2).
So, [tex]\sum_{n=1}^{\infty}n^{2}=1+3+5....2n-1[/tex]
[tex]\sum_{n=1}^{\infty}n^{2}=1+3+5....2n-1+2n[/tex][/QUOTE]

STOP.

Stop conjecturing and start READING.

Silverman,
I can't read now so I conjecture..

[QUOTE=blob100;205792]Silverman,
I can't read now so I conjecture..[/QUOTE]

Making conjectures out of ignorance makes one look like a fool.

One can not make intelligent conjectures without being aware of
already existing conjectures. One needs to know what is known
and what isn't known.

[QUOTE=blob100;205790]I conjecture that: between n^2 to n^2+2n there is always a prime number.
When n is an odd number.[/QUOTE]

You're 200 years too late! :smile:

This statement a special case of Legendre's conjecture. That conjecture is the same, but for any natural n rather than just an odd.

Great! is there a proof? (I mean, I really want to see know can it be proven!)

[quote=blob100;205813]Great! is there a proof? (I mean, I really want to see know can it be proven!)[/quote]
[URL]http://en.wikipedia.org/wiki/Conjecture[/URL]
[quote]A [B]conjecture[/B] is a [URL="http://en.wikipedia.org/wiki/Proposition_%28philosophy%29"]proposition[/URL] that is [URL="http://en.wikipedia.org/wiki/Formal_proof"]unproven[/URL] but appears correct and has not been disproven.[/quote]If it were proven, it wouldn't be called a conjecture, it'd be called a theorem.
(unless of course it is in fact a theorem but people still call it conjecture out of habit, as with the [URL="http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture"]Poincare conjecture/theorem[/URL])

Yes, I know, but there are theorems that are called conjecture too.

[QUOTE=blob100;205815]Yes, I know, but there are theorems that are called conjecture too.[/QUOTE]

Oh? Citation Please.

[QUOTE=R.D. Silverman;205823]Oh? Citation Please.[/QUOTE]

May I suggest that you read R. Guy's "Unsolved Problems in Number Theory"???

[QUOTE=R.D. Silverman;205823]Oh? Citation Please.[/QUOTE]

Poincare Conjecture. It's been proven by Perelman but is still commonly called the "Poincare Conjecture".

[QUOTE=flouran;205838]Poincare Conjecture. It's been proven by Perelman but is still commonly called the "Poincare Conjecture".[/QUOTE]

See post #185 :smile:

Luigi