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January 7th, 2011, 06:52 AM   #1
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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?
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January 7th, 2011, 07:33 AM   #2
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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.
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January 7th, 2011, 08:41 AM   #3
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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?
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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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