Prime number property

Dec 2015
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Earth
Let \(\displaystyle p_n\) be the n-th prime .
Is the difference of \(\displaystyle p_{n+1}\) and \(\displaystyle p_{n}\) unlimited or not ?
Example : 3-2=1 , 23-19=4 ...etc
 
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romsek

Math Team
Sep 2015
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if you can label $p_n$ and $p_{n+1}$ how could the difference between them be unlimited?
 
Dec 2015
1,068
164
Earth
By the list of primes I am always finding a larger number .
Just seen 85781-85751=30.
So how to know the answer ?
 

romsek

Math Team
Sep 2015
2,958
1,672
USA
the maximum distance between primes certainly grows the further out you go on the prime list, but the distance between adjacent primes always has to be finite.

If it weren't then there would be a last prime which we know there is not.

......

Oh.. maybe I'm misunderstanding you.

Yes, the maximum distance between adjacent primes is an unbounded sequence, but the distance between any two adjacent primes is always finite.
 
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