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Old 2010-02-16, 15:13   #177
R.D. Silverman
 
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Quote:
Originally Posted by blob100 View Post
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, \sum_{n=1}^{\infty}n^{2}=1+3+5....2n-1
\sum_{n=1}^{\infty}n^{2}=1+3+5....2n-1+2n
STOP.

Stop conjecturing and start READING.
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Old 2010-02-16, 15:17   #178
blob100
 
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Silverman,
I can't read now so I conjecture..
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Old 2010-02-16, 15:27   #179
R.D. Silverman
 
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Quote:
Originally Posted by blob100 View Post
Silverman,
I can't read now so I conjecture..
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.
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Old 2010-02-16, 18:42   #180
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Quote:
Originally Posted by blob100 View Post
I conjecture that: between n^2 to n^2+2n there is always a prime number.
When n is an odd number.
You're 200 years too late!

This statement a special case of Legendre's conjecture. That conjecture is the same, but for any natural n rather than just an odd.
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Old 2010-02-16, 18:44   #181
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Great! is there a proof? (I mean, I really want to see know can it be proven!)
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Old 2010-02-16, 18:48   #182
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Quote:
Originally Posted by blob100 View Post
Great! is there a proof? (I mean, I really want to see know can it be proven!)
http://en.wikipedia.org/wiki/Conjecture
Quote:
A conjecture is a proposition that is unproven but appears correct and has not been disproven.
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 Poincare conjecture/theorem)

Last fiddled with by Mini-Geek on 2010-02-16 at 18:49
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Old 2010-02-16, 18:50   #183
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Yes, I know, but there are theorems that are called conjecture too.

Last fiddled with by blob100 on 2010-02-16 at 18:52
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Old 2010-02-16, 19:25   #184
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Quote:
Originally Posted by blob100 View Post
Yes, I know, but there are theorems that are called conjecture too.
Oh? Citation Please.
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Old 2010-02-16, 20:01   #185
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Quote:
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Oh? Citation Please.
May I suggest that you read R. Guy's "Unsolved Problems in Number Theory"???
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Old 2010-02-16, 20:43   #186
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Quote:
Originally Posted by R.D. Silverman View Post
Oh? Citation Please.
Poincare Conjecture. It's been proven by Perelman but is still commonly called the "Poincare Conjecture".
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Old 2010-02-16, 22:22   #187
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Quote:
Originally Posted by flouran View Post
Poincare Conjecture. It's been proven by Perelman but is still commonly called the "Poincare Conjecture".
See post #185

Luigi
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