Prime number is one, which stands divided without any remainder, only by itself and the number one! Although computers have produced a list of prime numbers, no one has found any pattern in the way they occur nor can any one can predict the next higher prime number.
So the most sought-after-goal in Mathematics today, is to find a formula which can automatically produce an endless supply of prime numbers. Until this is found, the candidates competing to be prime numbers must be tested individually, one at a time!
In 1874, an English mathematician W.Stanley Jevons claimed that only he knew the divisors of the prime number 8,616,460,799. He had obtained this number by multiplying two of the largest prime numbers known then viz, 96079 and 89681!
The largest prime number discovered without the help of computers consisted of 39 digits. It reigned supreme from 1876 to the middle of the 20th century. With the help of the computers the quest for the largest prime number surged forward–faster than ever before.
In 1983, the largest known prime number was a monster with 39,000 digits in it. In 1986, the largest known prime number has an astounding 60,000 digits in it! It will occupy more than 500 lines and require 25 pages in order to be written down!
New and sophisticated methods have been evolved to determine whether or not a number is prime. No longer can we use the old method of successive divisions to check for remainders. In this method, even the super computer of today would not have time to explore a number with a mere 50 digits–even if it had worked non-stop for 15 billion years!