Notes
The English word “prime” comes from the Latin “primus,” meaning “first.”
From a multiplicative perspective, prime numbers are these “first” numbers—numbers from which all other numbers arise via multiplication. All other positive integers can be measured (divided) by primes, but only primes themselves can only be measured by the unit. This makes them “first.”
Original Text
https://www.quora.com/Why-are-prime-numbers-called-prime
Question: Why are prime numbers called prime?
Well over two-thousand years ago Euclid defined prime numbers in his definitive Geometry textbook The Elements (Book 7, Definition 11), as follows:
Using our alphabet this is:
Prôtos arithmos estin ho monadi monêi metroumenos.
A prime number is one that can only be measured by the unit alone.
The Elements was the standard text for geometry in the West until the twentieth century; so it was the book that fixed our choice of terminology. Roughly transliterated, Euclid’s definition is:
Prime numbers are that which are measured by an unit alone.
Or translated:
A prime number is that which is measured by a unit alone.
Rather than say ‘measured,’ we now say ‘divisible,’ but the idea is simple. Prime numbers are not multiples of other numbers (the unit—one—was not viewed as a number). Aristotle used the same definition (Anal. post. II 13, 96 a 36) and along with Theon of Smyrna also viewed the unit not as a number (Metaph. 1088 a 6), but rather as the beginning of number.
So why the word ‘prôtos,’ and why should it be ‘prime’ in English?
The Greek philosophers used the word ‘prôtos’ in the sense of first in order of existence (see Henry George Liddell, Robert Scott, A Greek-English Lexicon, proteros and prôtos: B.I.3.c). This is one of the standard meanings of our ‘prime’ or ‘primary.’ In fact, the English word ‘prime’ is from the Latin word for first: ‘primus.’ In a multiplicative sense, prime numbers are thus the first numbers—the numbers from which all other numbers arise (through multiplication). All other numbers (positive integers) are measured by primes, but primes alone are measured only by units. This makes primes first.
This mathematical meaning of ‘prime’ (‘prôtos’) has essentially remained unchanged since ancient times and was apparently already in use at the time of Pythagoras.