What Is The Largest Prime Number Presently Known?
A prime number is a number other than 1, whose only divisors are 1 and itself—in other words, numbers (other than 1) with only two factors. Numbers with more than two factors are called composite numbers. (The number 1 is neither prime nor composite.) For example, the number 5 is prime because it is only divisible by 1 and itself. The number 6, which is divisible by 1, 2, 3, and 6, is composite. Other examples of prime numbers are: 2, 3, 7, 11,13, 17, and 19.
Ancient Greek mathematician Euclid (c. 330-c. 260 B.C.) proved that it is impossible to define a "largest prime number." This is because if you take the largest known prime number (P) and add 1 to the product of all primes up to and including P, you will get a number that is itself a prime number. For example, taking the prime number 7, you can multiply 2 x 3 x 5 x 7, and get 210. Adding 1 gives the number 211, which is prime.
In September 1997, Gordon Spence used a Pentium-based computer to determine the largest known prime number. The number, which is 895,932 digits long, is 22,976,221 -1.
Mathematicians since the days of Euclid have been trying, unsuccessfully, to find a pattern to the sequence of primes.
Sources: Motz, Lloyd, and Jefferson Hane Weaver. Conquering Mathematics, pp. 22-25; Science News, vol. 152, p. 164.