Register to reply

What theorem is this called? For any gap size n, no more than n gaps

by goldust
Tags: called, gaps, size, theorem
Share this thread:
goldust
#1
Nov1-13, 08:01 PM
P: 85
of size n can consecutively occur in the sequence of primes.
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
UltrafastPED
#2
Nov1-13, 09:26 PM
Sci Advisor
Thanks
PF Gold
UltrafastPED's Avatar
P: 1,908
The Prime Number Theorem? http://en.wikipedia.org/wiki/Prime_number_theorem
WWGD
#3
Nov1-13, 09:28 PM
P: 592
Do you mean size exactly n? You can have gaps between primes that are as large as you want them to be.

goldust
#4
Nov2-13, 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, ....
UltrafastPED
#5
Nov2-13, 08:09 AM
Sci Advisor
Thanks
PF Gold
UltrafastPED's Avatar
P: 1,908
Are you looking for something like this: http://arxiv.org/pdf/math/0508185v1.pdf
goldust
#6
Nov2-13, 06:30 PM
P: 85
Quote Quote by UltrafastPED View Post
Are you looking for something like this: http://arxiv.org/pdf/math/0508185v1.pdf
Upon reading over their intro, I would say it's similar, but not quite. I claim that, for any gap size n, at most n gaps of size n can consecutively occur in the sequence of prime gaps. The provided paper is an attempt at proving the Twin Primes Conjecture. I suppose my claim can be very easily proven and doesn't amount to much significance other than possibly getting school kids excited about learning remainders. For instance, it can be easily seen from remainders after dividing by 3 that the primes 3, 5, 7 produce the only instance of 2 gaps of size 2 appearing consecutively in the sequence of prime gaps.

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


Register to reply

Related Discussions
The so-called Myth of Multiple Size Infinities General Math 3
Why is Baye's theorem called inverse prob ? Set Theory, Logic, Probability, Statistics 7
What's it called when a 3D shape can be made of 2D surfaces of all the same size Differential Geometry 3
How to calculate how big of a sample size is needed for the Central Limit Theorem? Set Theory, Logic, Probability, Statistics 2
Any conclusions about the gaps between p and p^2? Linear & Abstract Algebra 5