February 24th, 2019, 01:23 PM  #1 
Senior Member Joined: Dec 2015 From: iPhone Posts: 436 Thanks: 68  Prime number property
Let $\displaystyle p_n$ be the nth prime . Is the difference of $\displaystyle p_{n+1}$ and $\displaystyle p_{n}$ unlimited or not ? Example : 32=1 , 2319=4 ...etc Last edited by idontknow; February 24th, 2019 at 01:42 PM. 
February 24th, 2019, 01:56 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1276 
if you can label $p_n$ and $p_{n+1}$ how could the difference between them be unlimited?

February 24th, 2019, 02:33 PM  #3 
Senior Member Joined: Dec 2015 From: iPhone Posts: 436 Thanks: 68 
By the list of primes I am always finding a larger number . Just seen 8578185751=30. So how to know the answer ? 
February 24th, 2019, 02:49 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1276 
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. Last edited by romsek; February 24th, 2019 at 03:03 PM. 

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