History of Prime number in Timeline

Prime numbers are natural numbers greater than 1 that cannot be expressed as the product of two smaller natural numbers. Numbers greater than 1 that are not prime are called composite numbers. Prime numbers are fundamental in number theory due to the fundamental theorem of arithmetic, which states that every natural number greater than 1 is either prime or can be uniquely factorized into a product of primes, disregarding order.

1912: Landau's Problems

In 1912, Landau posed four problems about prime numbers, all of which remain unsolved, highlighting the enduring challenges in prime number theory.

1914: Lehmer's List of Primes

In 1914, Derrick Norman Lehmer published a list of primes less than ten million, which included 1, reflecting the varying historical views on the primality of 1.

1935: La Nativité du Seigneur

In 1935, Olivier Messiaen composed "La Nativité du Seigneur", using prime numbers to create ametrical music rhythms.

1949: Quatre études de rythme

From 1949 to 1950, Olivier Messiaen composed "Quatre études de rythme", employing prime numbers to generate unpredictable rhythms.

1950: Quatre études de rythme

From 1949 to 1950, Olivier Messiaen composed "Quatre études de rythme", employing prime numbers to generate unpredictable rhythms.

1951: Computer-aided Prime Search

Since 1951, the largest known primes have been found using primality tests on computers, marking a shift towards computational methods in prime number research.

1956: Continued Inclusion of 1 in Prime Lists

As recently as 1956, lists of primes continued to be published that included 1, showing the slow shift in mathematical consensus regarding the classification of 1.

1975: Sagan and Drake's Idea on Prime Factorization

In 1975, Carl Sagan and Frank Drake developed the idea of using prime factorization to establish two-dimensional image planes in communications with aliens.

1992: Mersenne Primes Dominate

Since 1992 as of October 2024, the largest known prime has always been a Mersenne prime due to the efficiency of Lucas-Lehmer primality test.

2004: Green–Tao theorem

In 2004, the Green–Tao theorem proved that there are arbitrarily long arithmetic progressions of prime numbers, advancing the mathematical theory of prime numbers.

2009: GIMPS Prize

In 2009, the Great Internet Mersenne Prime Search (GIMPS) project was awarded a US$100,000 prize for discovering a prime with at least 10 million digits, showcasing the impact of distributed computing in prime number research.

October 2012: Quantum Factorization of 21

As of October 2012, the largest number that has been factored by a quantum computer running Shor's algorithm is 21, illustrating the potential of quantum computing in number theory.

2013: Yitang Zhang's proof on prime gaps

In 2013, Yitang Zhang proved that there exist infinitely many prime gaps of bounded size, contributing to the progress in the mathematical theory of prime numbers.

2014: Verification of Goldbach's Conjecture

As of 2014, Goldbach's conjecture, which asserts that every even integer n greater than 2 can be written as a sum of two primes, has been verified for all numbers up to n = 4 * 10^18.

2017: Fermat Numbers Verified as Composite

As of 2017, all Fermat numbers that have been verified beyond the first five (3, 5, 17, 257, and 65,537) have been found to be composite, disproving Fermat's conjecture.

December 2019: Factorization of RSA-240

As of December 2019, the largest number known to have been factored by a general-purpose algorithm is RSA-240, which has 240 decimal digits (795 bits) and is the product of two large primes.

October 2024: Largest Known Prime is Mersenne Prime

As of October 2024, the largest known prime has always been a Mersenne prime since 1992, due to the efficiency of the Lucas–Lehmer primality test for Mersenne numbers.