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Abstract
Prime numbers are building blocks of integers. Using prime numbers as base, this work defines a class of new types of numbers, namely, k-PrimeFactors numbers, for each non-negative integer k. Interestingly, k-PrimeFactors numbers are defined using prime numbers and they, in turn, generalize their own base, the prime numbers. First 100 k-PrimeFactors numbers for initial values of k up to 10 are presented for demonstration. The occurrence frequency of these numbers till 1 million is also presented.
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Euclid. Elements. Book IX, Prop. 14. ≈ 300BCE.