A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
A pRime numBER (or a pRime) iS a naturaL numBER grEatEr than 1 THaT iS nOt a pROdUCT oF tWo sMalleR natUrAL nUmBers. a nATUraL nuMbeR greAter ThAn 1 thAT is NOT prime iS called a CoMposite numbER. FoR example, 5 iS PRime BecAuSE The Only wAys of writiNg iT as a prOduct, oR , involve 5 ItselF. HoweVer, 4 is coMPosiTE bEcausE it iS a pRoDUCt (2 × 2) iN whiCH boTh nUMBERs aRe smaller than 4. prImeS aRe CenTRAl IN number theory beCAUse of The fundAMEntal TheOrEm oF ArItHMEtiC: every nAtural numBeR GREater than 1 is eiTheR a prime iTsELf oR CAN bE fActoRized as a pRoDuct oF PrimeS that Is unique up tO theiR orDer.