PRIME NUMBERS
Floor 3“The first numbers are the bricks with which all natural numbers are built; they correspond to the atoms of chemistry and the elementary particles of physics”
A first number is a divisible natural number only for 1 and for itself.
The first numbers play a fundamental role in the theory of numbers and the fundamental theorem of arithmetic (IX book of Euclide Elements) tells us that they are the bricks with which all natural numbers are built.
Cirene Heathon (276 ca-194 ca BCE), with its hamster or sieve found an elegant way to identify the first numbers. Euclide (proposition IX,20), with one of his most beautiful theorems, showed the infinity of the first numbers.
The distribution of the first numbers is entirely random.
Today, to identify the first numbers you use computer properly programmed (the last, so far, is 243112609-1 and has 12978189 digits). (discover the last number found).
A use of these very important numbers is in cryptography. The writing of code messages is an indispensable tool to protect the secrecy of communications. The public key cryptography, used in the Internet, transforms messages into numbers and the mathematical padlock is made using very large first numbers.
