Maximum Spacing’s between 2-PrimeFactors Numbers till 1 Trillion

Neeraj Anant Pande

doi:https://doi.org/10.14445/22315373/IJMTT-V52P546

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 5 | Year 2017 | Article Id. IJMTT-V52P546 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P546

Maximum Spacing’s between 2-PrimeFactors Numbers till 1 Trillion

Neeraj Anant Pande

Citation :

Neeraj Anant Pande, "Maximum Spacing’s between 2-PrimeFactors Numbers till 1 Trillion," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 5, pp. 310-321, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P546

Abstract

k-Prime Factors number’ is defined to be a positive integer with precisely k number of prime factors. These divisors need not be always distinct. Particular type, viz., 2-PrimeFactors numbers are already analyzed for their low and high densities of occurrences and minimum spacing between successive 2-PrimeFactors numbers. The present work is about maximum spacings between them. This analysis is also from two perspectives : Within fixed range of 1 trillion, blocks of various sizes like 10, 100 and so on are analyzed and then for blocks of each fixed size like 10, 100 and so on, various ranges are probed. Both times, maximum in-block spacing between 2-PrimeFactors numbers, number of times pairs with maximum spacings occur, first and last starting 2-PrimeFactors numbers having maximum spacing with their successors, and number of blocks accommodating maximum spacing pairs in them are explored.

Keywords

Prime number, k-Prime Factors number, 2-PrimeFactors number, Maximum spacing.

References

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[8] Neeraj Anant Pande, Minimum Spacings between 2-PrimeFactors Numbers till 1 Trillion, Journal of Computer and Mathematical Sciences, Vol. 8 (12), 2017, 769-780.