## Timeline of Prime Numbers

Prime numbers are numbers that can only be divided by the number 1 and themselves, with no other factors involved. This rules out any multiples of other numbers such as all even numbers greater than 2 since they are all multiples of 2. Likewise, all multiples of 3, 5, 7 and so on cannot be prime numbers. The starting sequence of prime numbers is:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

There does not seem to be any easy to discern logical pattern to these numbers and that makes them fascinating as an oddity. Large prime numbers are used today to generate keys for cryptography because they are difficult to factor. The largest known prime number at this writing has nearly 13 million digits.

While it is possible that earlier groups knew about prime numbers, we have records of Greek studies of them.

**-0575 – Pythagoras** – the followers of Pythagoras believed primes to have mystical qualities.

**-0276 – Eratosthenes** – described the “sieve” method of finding prime numbers by eliminating all of the multiples of each prime, showing only the prime numbers left

**-0325 – Euclid** – proved that there an infinite number of primes

**1588 – Mersenne** – studied a variation of Fermat’s theory of prime numbers, 2^n – 1 (2 raised to the power of n then having 1 subtracted from it) which became associated with his name – not all of these candidates produce prime numbers, but there are currently 47 known Mersenne primes

**1601 – Fermat** – postulated that 2^n + 1 (2 raised to the power of n then having 1 added to it) it produces another prime number if n = a power of 2

**1707 – Euler** – showed that 2^32 (2 raised to the 32 power) fails as a prime and this disproved Fermat’s theory

**1752 – Legendre** and **1777 – Gauss** both created estimates that for large numbers, the density of prime numbers nearby is 1/log(n) – this is now known as the Prime Number Theorem

**1826 – Riemann** the famous Riemann Hypothesis deals with the roots of the zeta function and the distribution of prime numbers

SEE ALSO:

**GIMPS – Great Internet Mersenne Prime Search**

**The Largest Known Primes – A Summary**