One definition of a prime number is: any positive number that has only two positive integer factors, itself and 1. The prime factorization of a number is the product of prime factors that make up that number.
More than 2300 years ago Euclid proved that the number of primes is infinite.
Before the age of computers many mathematicians formed tables of primes. The most widely distributed was D. N. Lehmer's table of primes to 10,006,721. By far the most amazing was a table by Kulik completed in 1867. This table listed the smallest factors of integers (hence all the primes) up to 100,330,200!