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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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k002/k00215h.htm

Last modified: September 1, 2000