FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 583-597

Analytical form of the Eratosthenes sieve

H. A. Smirnova (Bitner)

Abstract

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A solution of the problem for deducing the formula expressing $i+1$-st prime number $p$_i+1 through $p$_k, $1$£ k £ i, is offered. In so doing the integer table functions $$b_k(n) and $$b'_k(n) are introduced.

Two recurrence formulas of prime $p$_i+1 are derived. The second formula holds true under the assumption that between the squares of two neighbouring prime numbers there is at least one prime number.

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Last modified: September 1, 2000