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Year Event
320 BC Eratosthenes of Cyrene invents the first prime sieve.
300 BC Euclid proves that there are infinitely many prime numbers by contradiction.

Euclid proves the fundamental theorem of arithmetic, which states that all natural numbers can be expressed as a product of one or more prime numbers.

1472 AD Goldbach conjectures that all every even integer greater than 2 can be expressed as the sum of two prime numbers.
1555 AD J. Scheybl discovers the prime 216217-1.
1644 AD Marin Mersenne discovers the Mersenne primes 8,191 and 131,071.
1732 AD Leonhard Euler shows that the fifth Fermat number is not prime, thus disproving Fermat's conjecture that all Fermat numbers are prime.
1750 AD Leonhard Euler discovers the 31st Mersenne prime.
1776 AD Antonio Felkel records the prime factorisation of all counting numbers up to 408 000.
1852 AD Pafnuty Chebyshev proves Bertrand's postulate, which states that, for n > 1, there is always a prime between n and 2n.
1856 AD A.L. Crelle determines the first 6 000 000 primes.
1861 AD Zacharias Dase compiles a list of the first 9 000 000 primes.
1896 AD Jacques Hadamard and Charles Jean de la Vallée-Poussin prove the Prime Number Theorem.
1996 AD George Woltman starts the Great Internet Mersenne Prime Search (GIMPS) by creating and distributing software that can be used to test Mersenne numbers for primality to find larger prime numbers.
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