Early Record of Divisibility and Primality

TL;DR

This paper uncovers ancient Indian textual evidence of divisibility and primality concepts, highlighting their historical significance and symbolic use of numbers without divisors to represent transcendence.

Contribution

It provides the earliest known textual references to divisibility and primality, linking mathematical ideas to cultural and astronomical concepts in Vedic texts.

Findings

Listing of all divisor pairs of 720 and 10,800

Number 720 associated with lunar cycle and divisibility

Numbers without divisors symbolized transcendence

Abstract

We provide textual evidence on divisibility and primality in the ancient Vedic texts of India. Concern with divisibility becomes clear from the listing of all the fifteen pairs of divisors of the number 720. The total number of pairs of divisors of 10,800 is also given. The motivation behind finding the divisors was the theory that the number of divisors of a certain periodic process is related to the count associated with some other periodic process. For example, 720 (days and nights of the year) has 15 pairs of divisors, and this was related to the 15 days of the waxing and waning of the moon. Numbers that have no divisors appeared to have been used to symbolize the "transcendent" that is beyond periodicity and change.