English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper rather studies the behaviour of prime numbers bounded below and above by positive integers n! and (n+ k)!, and then after some numerical evidence, postulates that there is at least one pair primes of gap k ∈ 2Z in between n! and (n + k)! for every integer n ≥ 2 and every even integer k > 0. This assertion would eventually provide another structural form for Euclid theorem of infinitude of primes, a kind of projection of the form in the original Bertrand postulate (now Chebychev’s theorem). The truthfulness of the conjecture that emanated from this postulate implies the Polignac’s conjecture which aptly generalizes the twin prime conjecture. We thus present the new postulate and the conjectures for future research.

A New Postulate and Some Conjectures Concerning Pair Primes in the Interval [n!, (n + k)!]