What are unfactorable numbers called in simple terms?

Hopefully not being too obvious here, I have been frustrated (after searching each of seven home dictionaries, crossWordbooks, "Word finders", etc., etc,....) I'll just say the following. Anyone who wishes to correct me, does so at no peril of my wrath:

Unfactorable numbers are known as Prime Numbers. OK? Thanks for comments--- Mr. C.

well a unfactorable number is, to use the prefix meaning, a number that can't be factorised or doesn't have any factors and nosuch number exists as 0=any number times by 0, and 1=1 times itself.

both numbers above have been said to not fit into either the prime of composite number groups