January 7th, 2011, 06:52 AM  #1 
Newbie Joined: Jan 2011 Posts: 2 Thanks: 0  Nextnext primes
7 is a prime number, 3 is a prime number. When we write these numbers next to next we see 73 which is also a prime number. 13 is a prime number, 73 is a prime number. When we write these numbers next to next we see 1373 which is also a prime number. Lets name these numbers like 73, 1373 with nextnext primes ... Can we proof nextnext primes arent finite?

January 7th, 2011, 07:33 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Nextnext primes
This is Sloane's A105184. I think a proof that the sequence is infinite is beyond present technology, though Dirichlet's theorem gets us tantalizingly close.

January 7th, 2011, 08:41 AM  #3 
Senior Member Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0  Re: Nextnext primes
This is an interesting problem. So I assume the consensus is that there are infinitely many such primes? Is this problem thought to be easier than the twin prime conjecture?

January 7th, 2011, 10:39 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Nextnext primes Quote:
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