Minimum Spacings between 2-PrimeFactors Numbers till 1 Trillion

Neeraj Anant Pande

Associate Professor, Department of Mathematics and Statistics, Yeshwant Mahavidyalaya (College), Nanded – 431602, Maharashtra, INDIA.


Recently after defining ‘k-PrimeFactors number’ to be a positive integer with exactly k number of prime divisors, which need not be necessarily distinct, 2-PrimeFactors numbers have been analyzed in detail for their low and high densities of occurrences. This work deals with 2-PrimeFactors numbers with a view of minimum spacings between two successive 2-PrimeFactors numbers. This analysis is taken up from two perspectives, viz., for blocks of various sizes like 10, 100 and so on within fixed range of one trillion and then for various ranges like 10, 100 and so on for fixed block sizes of 10, 100, 1000 and so on. In both approaches, minimum in-block spacing, number of times it occurs, first and last numbers with minimum spacing with their successors, and number of blocks exhibiting minimum spacing between 2-PrimeFactors numbers in them are presented. Mathematics Subject Classification 2010 : 11A51, 11N05, 11N80.

Keywords :Prime number, k-PrimeFactors number, 2-PrimeFactors number, Minimum spacing.

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