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 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
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Re: Nextnext primes

Quote:
 Originally Posted by DrSteve So I assume the consensus is that there are infinitely many such primes?
I would certainly think so.

Quote:
 Originally Posted by DrSteve Is this problem thought to be easier than the twin prime conjecture?
If I had to guess I would say yes -- there's usable structure as 10^d * p + q, and these numbers should be fairly common (at least compared to twin primes). In fact these numbers (counted with repetition) should be (heuristically) more common than the primes themselves! I haven't done a sufficiently careful analysis to say how common they should be once you remove this double-counting.

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