[Guest]

Is there always a prime number between another number (x) and its double (y), except 1? If so, name some.

Example: 2(3)4

[EventHorizon]

Is there always a prime number between another number (x) and its double (y), except 1? If so, name some.

Example: 2(3)4

I am quite sure that this it is true. There is a function for the approximate number of primes...and it turns out to fit quite nicely.

The function increases a fairly large amount over any range equal to the range up to the beginning of it.

This is not a proof by any means...and I'm too lazy to try at the moment

Edited March 25, 2008 by EventHorizon

[Guest]

I can't think of any x's and y's that don't have a prime number between them.

3(5)6

5(7)10

7(11)14

11(13)22

13(17)26

17(19)34

19(23)36

23(29)46

and so on.

[Guest]

Is there always a prime number between another number (x) and its double (y), except 1? If so, name some.

Example: 2(3)4

Since there is no known function to actually find prime numbers, it would be difficult to prove this when numbers get large.

If the question is whether there is A prime number (only one) then the answer is obviously no, since 7 and 11 are between 6 and 12.

If the question is whether there are any prime numbers between x and y then the answer for at least the prime numbers less than 113 (list given in Wikipedia) would be yes. It would seem reasonable that this would continue, as the doubling window would grow larger, but iI don't have the time for a formal proof, if one is even possible

[EventHorizon]

Is there always a prime number between another number (x) and its double (y), except 1? If so, name some.

Example: 2(3)4

You didn't think I'd actually have a proof in that little amount of time....

But here is a link to a proof...

proof of Bertrand's Conjecture

[Guest]

Is there always a prime number between another number (x) and its double (y), except 1? If so, name some.

Example: 2(3)4

Taking P as a prime and P > 1, P + 1 is even, so P + 1 is some numbers double, for any prime P, you'll get:

(P + 1)/2 (P) P + 1

The only problem is that there could be more primes than just P in the range [ (P + 1) / 2; P + 1]

Upsss. Now I realize It's the other way around the proof needed. Is there a way to remove my post??

Edited February 16, 2009 by Apolo Program