Numbers were invented to indicate quantity: how many of anything we had
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W.R.Hamilton
There is no one person who invented it there are several people who had contributed.
Well, no one knows who exactly 'invented' rational numbers. Most nations believed all numbers were rational until Pythagoreas proved this untrue by the square root of two.
prime numbers are invented by srinivasan ramanujan, an Indian mathematician.
Nobody invented them, they are just names for numbers. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.