open access

https://hdl.handle.net/2115/62699

On a Deterministic Property of the Category of k-almost Primes: A Deterministic Structure Based on a Linear Function for Redefining the k-almost Primes (∃n∈N, 1≤k≤n) in Certain Intervals

英語

Factorization

2014-08-28

1-10

Eleventh Algorithmic Number Theory Symposium（ANTS-XI）. August 7 – 11, 2014. Hotel Hyundai, GyeongJu, Korea

In this paper based on a sort of linear function, a deterministic and simple algorithm with an algebraic structure is presented for calculating all (and only) k-almost primes (where ∃n∊N, 1 ≤ k ≤ n) in certain intervals. A theorem has been proven showing a new deterministic property of the category of the k-almost primes. Through a linear function that we obtain, an equivalent redefinition of the k-almost primes with an algebraic characteristic is identified. Moreover, as an outcome of our function’s property some relations which contain new information about the k-almost primes (including primes) are presented.

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