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This is a Quantitative Study study.

October 16, 2025Open Access

Coprimality of elements in regular sequences with polynomial growth

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This analysis reveals the existence of k-wise coprime primes in arithmetic sequences, suggesting deeper patterns in primes.

Long blocks of k-wise coprime elements exist in certain regular sequences, highlighting unique prime structures.
The study establishes conditions under which the greatest common divisor (gcd) of specific sequences equals one, ensuring coprimality.
A subset of natural numbers with upper Banach density one exhibits coprimality, indicating rich arithmetic properties.
Such results enhance the understanding of prime distributions in number theory, pointing to potential applications in related fields.

Deshouillers et al. (2025) studied this question.

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