A prime number is a natural number greater than 1 that cannot be formed by multiplying 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, 6 is composite, because it is the product of two numbers that are both smaller than 6. 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. The property of being prime is called primality. A simple, but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast, but has a small chance of error, and the AKS primality test, which always produces the correc...
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00:02:45 Definition and examples
00:05:10 History
00:09:11 Primality of one
00:11:05 Unique factorization
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