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Very Large Gaps between Consecutive Primes

✍ Scribed by János Pintz

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
319 KB
Volume
63
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

Let G(X) denote the largest gap between consecutive primes below X. Improving earlier results of Erdo s, Rankin, Scho nhage, and Maier-Pomerance, we prove

where log & X denotes the &-fold iterated logarithm function and # is Euler's constant. The new tool used is a combinatorial result proved by probabilistic methods.

📜 SIMILAR VOLUMES

Linear Gaps between Degrees for the Poly
Linear Gaps between Degrees for the Polynomial Calculus Modulo Distinct Primes
✍ Sam Buss; Dima Grigoriev; Russell Impagliazzo; Toniann Pitassi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 214 KB

This paper gives nearly optimal lower bounds on the minimum degree of polynomial calculus refutations of Tseitin's graph tautologies and the mod p counting principles, p 2. The lower bounds apply to the polynomial calculus over fields or rings. These are the first linear lower bounds for the polynom