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- W2951032012 abstract "Let $p_n$ denote the $n^{th}$ prime. Goldston, Pintz, and Yildirim recently proved that $ liminf_{nto infty} frac{(p_{n+1}-p_n)}{log p_n} =0.$ We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $liminf_{nto infty} (q_{n+1}-q_n) le 26.$ If an appropriate generalization of the Elliott-Halberstam Conjecture is true, then the above bound can be improved to 6." @default.
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- W2951032012 date "2005-06-03" @default.
- W2951032012 modified "2023-10-17" @default.
- W2951032012 title "Small gaps between primes or almost primes" @default.
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