An Application of the Hardy-Ramanujan Theorem

dc.contributor.authorKamalu, Chukwunyere
dc.date.accessioned2024-03-16T13:27:57Z
dc.date.available2024-03-16T13:27:57Z
dc.date.issued2022-02-11
dc.descriptionSupplemental Materials: https://osf.io/g8946/
dc.description.abstractThis paper attempts to answer the riddle of why Ω(m), the sum of the exponents of the prime decomposition of m = (2x-2)(2x-3)(2x-5) …(2x-qb) [where qb is the bth prime and b = π(x), the number of primes not exceeding x], always appears to lie in the region of 2π(x), where π(x) is the number of primes not exceeding x. It turns out that an application of the Hardy Ramanujan Theorem shows Ω(m) is almost always exceeded by 2π(x), which has the logical implication the Goldbach’s Conjecture is “almost always true”.
dc.identifier.doihttps://doi.org/10.31730/osf.io/w3eqs
dc.identifier.urihttps://africarxiv.ubuntunet.net/handle/1/670
dc.identifier.urihttps://doi.org/10.60763/africarxiv/626
dc.identifier.urihttps://doi.org/10.60763/africarxiv/626
dc.identifier.urihttps://doi.org/10.60763/africarxiv/626
dc.subjectHardy Ramanujan Theorem
dc.subjectMathematical induction
dc.titleAn Application of the Hardy-Ramanujan Theorem

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