Title. On the differences between consecutive primes

Abstract. In 1976, Gallagher proved that the Hardy-Littlewood prime k-tuple conjecture implies that, for the primes up to x, the number of primes in the interval (x, x + λ log x], for any fixed positive constant λ, has a Poisson distribution. Recently, Daniel A. Goldston and I showed that the number of consecutive primes with difference λ log x has the Poisson distribution superimposed on the conjectured formula for pairs of primes with this difference. In this talk, I will present more precise formulas if λ→ 0 as x → ∞. In order to obtain these formulas, it is necessary to prove some new singular series average results. If time permits, I will report new results on the limit points of the sequence (p

- Ph.D. student
**Alzaki Fadlallah**and Fast-track student**Alexandra Fry**won Best Lecture Award and Best Undergraduate Poster Award, respectively, at the 39th SIAM-SEAS conference held March 20-22 at UAB. Congratulations. - Ph.D. students
**Alzaki Fadlallah**and**Caleb Moxley**won first and second place, respectively, at the 2015 Graduate Student Research Days. Congratulations. **Terrence Muthoka**,**Jessica Barnett**, and**Rachel Ejem**were chosen as the department's Outstanding PhD Student, Outstanding Master's Student, and Outstanding Undergraduate Student, respectively. Congratulations to all.- Math and neuroscience major
**Hriday Bhambhvani**won first place for his poster at the Undergraduate Research Competition in Biological Sciences at the 91st Annual Meeting of the Alabama Academy of Sciences hosted recently by the University of West Alabama.