It is not usual to include 1 among the prime numbers. A natural number that is not a prime is a composite number. An Internet guide to the terminology of prime numbers, including some links to other pages with fuller definitions and information. The Prime Glossary is a part of the Prime Pages site, an index of information on prime numbers. Proof A method of constructing a valid argument, using deductive reasoning.
Proposition is used for something to be investigated.
A theorem is something for which there is a proof. A lemma is something to help in the proof of the theorem. The distinction is not a matter of mathematics, but of use and purpose. The four ways to generate sets of Pythagorean Triples. Of course, these formulas are all the same, more or less.