MATHINFINITY

PRIME NUMBER

A prime number, or a prime, is a natural number greater than 1 that has no divisors other than 1 and itself. Therefore, 2, 3, 5 and 7 are prime numbers, whereas 4, 6, 8 and 9 are not prime numbers. It is more difficult to find prime numbers as the number becomes larger. Around 300 BC, prime numbers are recorded in "Elements" by the Greek mathematician, Euclid. He proved that there is an infinite quantity of prime numbers.

Mersenne Prime

Mersenne Number is named after the 17th-century French scholar Marin Mersenne. If a Mersenne Number is a prime number, it is called Mersenne Prime. It can be expressed as 1 less than a power of 2, for example, 3=22-1 and 7=23-1. Until end of 2016, the largest prime number is 2 74207281 - 1, which has a total of 22,338,618 digits.

Prime Number and RSA Cryptosystem

The RSA cryptosystem got it name from the initial letters of the surnames of Ron Rivest, Adi Shamir and Leonard Adleman from Massachusetts Institute of Technology in the United States. In 1977, they proposed the public-key cryptography which was Asymmetric Cryptography that used prime numbers to protect confidential information. The computer can multiply two very large prime numbers, but it is difficult to factorize the product of these two prime numbers.

This kind of cryptosystem makes use of mathematics to generate a pair of keys, one being a private key and the other a public key. Simply speaking, if the encryption key is public, only the paired private key can be used for decryption. Besides encryption and decryption, public-key cryptography is also applied in Key Exchange and Electronic Signature.

Interactive Game

Come and learn prime numbers with gophers! There are three levels of each game. On the screen, you will see gophers with different numbers jumping out of their holes. When you see gophers with prime numbers, instantly catch them by pressing the buttons corresponding to the holes from which they jump out. 1 score will be added for each correct gopher, and 1 scored will be deducted for each wrong gopher. Let's play together!