Primes in tuples I
@article{Goldston2009PrimesIT, title={Primes in tuples I}, author={D. Goldston and J. Pintz and C. Yildirim}, journal={Annals of Mathematics}, year={2009}, volume={170}, pages={819-862} }
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… CONTINUE READING
Paper Mentions
Blog Post
News Article
Blog Post
190 Citations
References
SHOWING 1-10 OF 65 REFERENCES
Higher correlations of divisor sums related to primes III: small gaps between primes
- Mathematics
- 2007
- 32
- PDF
Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim
- Mathematics
- 2006
- 52
- Highly Influential
- PDF