## Prime Number History

Recently, I used N-ways hash table algorithm to apply it in my designed router software. Because I need to make my hash table size to be prime number size in my designed software, this prime usage sparks my desire to write down prime number history in my Blog such that  I will never forget to appreciate  the person who discovered the prime number. The following is the introduction of Prime number introduction and its history.

An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.  For example, the prime divisors of 10 are 2 and 5; and the first six primes are 2, 3, 5, 7, 11 and 13.  (The first 10,000, and other lists are available).  The Fundamental Theorem of Arithmetic shows that the primes are the building blocks of the positive integers: every positive integer is a product of prime numbers in one and only one way, except for the order of the factors. (This is the key to their importance: the prime factors of an integer determines its properties.)

The ancient Greeks proved (ca 300 BC) that there were infinitely many primes and that they were irregularly spaced (there can be arbitrarily large gaps between successive primes).  On the other hand, in the nineteenth century it was shown that the number of primes less than or equal to n approaches n/(log n) (as n gets very large); so a rough estimate for the nth prime is n log n (see the document "How many primes are there?")

The Sieve of Eratosthenes is still the most efficient way of finding all very small primes (e.g., those less than 1,000,000).  However, most of the largest primes are found using special cases of Lagrange’s Theorem from group theory.  See the separate documents on proving primality for more information.

In 1984 Samuel Yates defined a titanic prime to be any prime with at least 1,000 digits [Yates84, Yates85].  When he introduced this term there were only 110 such primes known; now there are over 1000 times that many!  And as computers and cryptology continually give new emphasis to search for ever larger primes, this number will continue to grow.   Before long we expect to see the first ten million digit prime.

The Prime Number Trick

###### · Divide by 12

Without knowing which prime number your friends picked, you can still tell them:
There will be a remainder of 6.

###### A Murderous Maths fan called OBAID pointed out that if you square ANY prime number bigger then 3, then subtract 1, the answer always divides by 24!

E.g. 112 = 121 then 121 – 1 = 120 and yes 120 does divide by 24.

WHY ?

Find the answer by youself or call me if you can