High density distribution of 3-primefactors numbers till 1 trillion

Prime numbers have been recently generalized to ‘k-PrimeFactors Numbers’, wherein instead of unique prime divisor, exactly k prime divisors are there to the concerned number. 3-PrimeFactors numbers are just a particular case with k = 3. Analogous to the analysis of 2-PrimeFactors numbers, in this work, 3-PrimeFactors numbers are considered for their maximum count in blocks of size of usual base powers, i.e., powers of 10, in range of 1 trillion. First and last blocks of different sizes along with number of such blocks containing maximum number of 3-PrimeFactors numbers are determined. Then block wise analysis is done by fixing block sizes and inspecting increasing ranges for each block size for occurrence of maximum number of 3-PrimeFactors numbers.