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What theorem is this called? For any gap size n, no more than n gaps 
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#1
Nov113, 08:01 PM

P: 85

of size n can consecutively occur in the sequence of primes.



#2
Nov113, 09:26 PM

Sci Advisor
Thanks
PF Gold
P: 1,908

The Prime Number Theorem? http://en.wikipedia.org/wiki/Prime_number_theorem



#3
Nov113, 09:28 PM

P: 533

Do you mean size exactly n? You can have gaps between primes that are as large as you want them to be.



#4
Nov213, 07:59 AM

P: 85

What theorem is this called? For any gap size n, no more than n gaps
Oops, I meant "occur in the sequence of prime gaps" not "occur in the sequence of primes", of course
e.g. for the gap size 12, no more than 12 gaps of size 12 can consecutively occur in the sequence of prime gaps 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, .... 


#5
Nov213, 08:09 AM

Sci Advisor
Thanks
PF Gold
P: 1,908

Are you looking for something like this: http://arxiv.org/pdf/math/0508185v1.pdf



#6
Nov213, 06:30 PM

P: 85

Much thanks for the link. I recently came across the GPY result while reading about Zhang's work on the Twin Primes Conjecture. 


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