History of Prime number in Timeline

A prime number is a natural number greater than 1 that cannot be expressed as a product of two smaller natural numbers; otherwise, it's a composite number. For instance, 5 is prime, while 4 is composite. Prime numbers are crucial in number theory due to the fundamental theorem of arithmetic, which states that every natural number greater than 1 is either a prime number itself or can be uniquely factorized into a product of primes, disregarding their order. This property underscores the significance of prime numbers in understanding the structure of natural numbers.

1912: Landau's problems posed

In 1912, Landau's problems, a set of conjectures about prime numbers, were posed, and all four remain unsolved as of today.

1914: Lehmer includes 1 in list of primes

In 1914, Derrick Norman Lehmer included 1 in his list of primes less than ten million, reflecting the varied opinions on whether 1 should be considered prime.

1935: Messiaen's La Nativité du Seigneur

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

1949: Messiaen's Quatre études de rythme

From 1949 to 1950, Olivier Messiaen composed "Quatre études de rythme", using prime numbers like 41, 43, 47, and 53 to create unique rhythmic patterns.

1950: Messiaen's Quatre études de rythme

From 1949 to 1950, Olivier Messiaen composed "Quatre études de rythme", using prime numbers like 41, 43, 47, and 53 to create unique rhythmic patterns.

1951: Largest known primes found using computers

Since 1951, all the largest known primes have been found using tests on computers, marking a significant shift in prime number discovery.

1956: Publication of prime lists including 1 continues

Lists of primes that included 1 continued to be published as recently as 1956, indicating a lingering debate before the consensus against including 1 as prime.

1975: Sagan and Drake develop idea of using prime factorization for alien communication

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

1992: Largest known prime has always been a Mersenne prime

Since 1992, as of October 2024, the largest known prime has consistently been a Mersenne prime, due to efficient primality tests like the Lucas-Lehmer test.

2004: Green–Tao theorem

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

2009: GIMPS awarded prize for discovering large prime

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

October 2012: Largest number factored by quantum computer using Shor's algorithm

As of October 2012, the largest number factored by a quantum computer running Shor's algorithm is 21, demonstrating the potential but current limitations of quantum computing in factorization.

2013: Yitang Zhang's proof on prime gaps

In 2013, Yitang Zhang proved that there exist infinitely many prime gaps of bounded size, contributing significantly to the understanding of prime number distribution.

2014: Verification of Goldbach's conjecture

As of 2014, Goldbach's conjecture, which states that every even integer 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: All verified Fermat numbers beyond F5 are composite

As of 2017, all verified Fermat numbers beyond F5 are composite, disproving Fermat's initial conjecture that all Fermat numbers are prime.

December 2019: RSA-240 factored by general-purpose algorithm

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.