New Formulas for Semi-Primes. Testing, Counting and Identification of the n^th and next Semi-Primes

2016/08/17 by Issam Kaddoura, Kaddoura, Issam, Samih Abdul-Nabi +3
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1608.05405

openalex publication_date 2016/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a new semiprimality test and we construct a new formula for π⁽²⁾(N), the function that counts the number of semiprimes not exceeding a given number N. We also present new formulas to identify the n^th semiprime and the next semiprime to a given number. The new formulas are based on the knowledge of the primes less than or equal to the cube roots of N : P₁, P₂....P_π( √[3]N) ≤ √[3]N.

Citations

• On formula to compute primes and the nth prime

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