D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yildirim
gaps between almost primes, the parity problem and some conjectures of Erdős on consecutive integers
D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yildirim
gaps between almost primes, the parity problem and some conjectures of Erdős on consecutive integers
Small gaps between products of two primes (2009)
Goldston, D. A., Graham, S. W., Pintz, J., Yildirim, C. Y.
Let qn denote the nth number that is a product of exactly two distinct primes. We prove that qn+1 − qn ≤ 6 infinitely often. This sharpens an earlier result of the authors, which had 26 in place...
Goldston, D. A., Graham, S. W., Pintz, J., Yildirim, C. Y.
In a previous paper, the authors proved that in any system of three linear forms satisfying obvious necessary local conditions, there are at least two forms that infinitely often assume $E_2$-values;...
ON THE NUMBER OF DIVISORS OF n! (2007)
Paul Erdős, S. W. Graham, Ar Ivić, Carl Pomerance
Abstract. Several results involving d(n!) are obtained, where d(m) denotes the number of positive divisors of m. These include estimates for d(n!)/d((n − 1)!), d(n!) − d((n − 1)!), as well as...
Small gaps between products of two primes (2006)
Goldston, D. A., Graham, S. W., Pintz, J., Yildirim, C. Y.
Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $$\liminf_{n\to \infty} (q_{n+1}-q_n) \le 6.$$ This sharpens an earlier result of the authors...
Small gaps between primes or almost primes (2005)
Goldston, D. A., Graham, S. W., Pintz, J., Yilidirm, C. Y.
Let $p_n$ denote the $n^{th}$ prime. Goldston, Pintz, and Yildirim recently proved that $ \liminf_{n\to \infty} \frac{(p_{n+1}-p_n)}{\log p_n} =0.$ We give an alternative proof of this result. We...
An estimate for the number of reducible Bessel Polynomials of bounded degree (1993)
n� j=0 (n + j)! 2 j (n − j)!j! xj.
An Estimate For The Number Of Reducible Bessel Polynomials Of Bounded Degree (1993)
this paper is to give a further sharpening. Theorem. The number of n t for which y n (x) is reducible is ø t