Primes in Tuples I

Details Primes in Tuples I Primes in Tuples I

2005-08-10

arxiv.org/abs/math/0508185v1

Mathematics

Number Theory

36 pages

Scientific paper

We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker conjecture implies that there are infinitely often primes a bounded distance apart. Unconditionally, we prove that there exist consecutive primes which are closer than any arbitrarily small multiple of the average spacing, that is, \[ \liminf_{n\to \infty} \frac{p_{n+1}-p_n}{\log p_n} =0 .\] This last result will be considerably improved in a later paper.

Affiliated with

Also associated with

No associations

Rating

Primes in Tuples I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Primes in Tuples I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Primes in Tuples I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-322465