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arXiv · 1608.05405

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

Issam Kaddoura·Samih Abdul-Nabi·Khadija Al-Akhrass
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Abstract

In this paper we give a new semiprimality test and we construct a new formula for $\pi ^{(2)}(N)$, 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 $N : P_{1}, \; P_{2}....P_{\pi \left( \sqrt[3]{N}\right) }\leq \sqrt[3]{N}$.

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Issam Kaddoura, Samih Abdul-Nabi, Khadija Al-Akhrass. 2016-08-17. New Formulas for Semi-Primes. Testing, Counting and Identification of the $n^{th}$ and next Semi-Primes. https://arxiv.org/abs/1608.05405

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