# Prime Numbers

--> Why are prime numbers so important to number theory? (Apart from speculations of being connected to energy levels of complex quantum systems.)

--> Let for time being, primes that we know of, be called primes of "type-2". Here '2' comes from the definition of primes. Since we consider primes as those numbers, which have no "pair" of factors, apart from 1 and itself.
If a number c is not prime, then c= a*b has atleast some a and b ≠1 or c.

--> Let us now call a number, a prime of "type-3",such that number has no 3-tuple of factors apart from 1 or number itself.
It's converse can be stated as:
d = a*b*c
where a,b,c ≠ 1or d.

--> it can be observed that primes of 'type 2' are actually subset of 'type 3'.
--> All 2-digit numbers are primes of type 3.
--> If we go on increasing our type numbers, all smaller types are actually subset of larger types.

--> Doesn't this makes idea of primes look abstract or random, and defining them on basis of 'pairs of factors' a kind-of bias?
--> My apolgies, if i said something wrong.