300 BCE
Euclid Proves Infinite Primes
Euclid includes a proof that there are infinitely many prime numbers in his Elements, laying the foundation for number theory. #math #history
Chronological Storyline (32 Milestones)
240 BCE
Eratosthenes Invents the Sieve
Eratosthenes develops the Sieve of Eratosthenes, a simple algorithm for finding all prime numbers up to a given limit. #math #algorithm
By SKopp at German Wikipedia - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1506732
400 CE
Sunzi's Chinese Remainder Theorem
The Sunzi Suanjing presents the Chinese remainder theorem, which uses coprime moduli (related to primes) for solving simultaneous congruences. #math #china
By AnonymousUnknown author - Own work (my book), Public domain, https://commons.wikimedia.org/w/index.php?curid=12568381
500 CE
Aryabhata's Kuṭṭaka Algorithm
Aryabhata's Aryabhatiya describes the Kuṭṭaka algorithm for solving linear Diophantine equations, intimately linked to prime number theory. #math #india
By Cpjha13 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49883192
1000 CE
Alhazen Describes Wilson's Theorem
Ibn al-Haytham (Alhazen) formulates a precursor to Wilson's theorem, linking prime numbers to factorial congruences. #math #islamicgoldenage
By Adolph Boÿ, engraved by Jeremias Falck. Used as the frontispiece to Johannes Hevelius, Selenographia, 1647 - https://www.loc.gov/resource/rbctos.2017rosen1321/?sp=9&r=0.059,0.617,0.327,0.182,0, Public domain, https://commons.wikimedia.org/w/index.php?curid=165125519
1202 CE
Fibonacci Publishes Liber Abaci
Fibonacci's Liber Abaci introduces methods for testing primality, including the idea of dividing by smaller primes. #math #europe
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=720501
1588 CE
Cataldi Discovers Mersenne Primes
Pietro Cataldi finds the 19th and 23rd perfect numbers, corresponding to Mersenne primes, advancing the study of prime numbers. #math #history
By Cataldi, Pietro Antonio - Available in the BEIC digital library and uploaded in partnership with BEIC Foundation., Public domain, https://commons.wikimedia.org/w/index.php?curid=40911982
1640 CE
Fermat States His Little Theorem
Pierre de Fermat announces Fermat's Little Theorem, a fundamental result in prime number theory and cryptography. #math #cryptography
1737 CE
Euler Links Primes to Zeta Function
Leonhard Euler introduces the Euler product formula, connecting prime numbers with the Riemann zeta function. #math #analysis
1798 CE
Legendre's Prime Number Conjecture
Adrien-Marie Legendre conjectures a formula for the distribution of primes, later refined into the prime number theorem. #math #history
1801 CE
Gauss Publishes Disquisitiones Arithmeticae
Carl Friedrich Gauss's Disquisitiones Arithmeticae establishes the foundation of modern number theory, including work on prime numbers. #math #books
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=641724
1837 CE
Dirichlet's Theorem on Primes in Arithmetic Progressions
Peter Gustav Lejeune Dirichlet proves there are infinitely many primes in any arithmetic progression with coprime first term and difference. #math #history
By Unknown author - http://www.york.ac.uk/depts/maths/histstat/people/, Public domain, https://commons.wikimedia.org/w/index.php?curid=2914309
1850 CE
Chebyshev Proves Bertrand's Postulate
Pafnuty Chebyshev proves Bertrand's postulate: for any integer n>1, there is at least one prime number between n and 2n. #math #analysis
By Unknown author - http://scienceworld.wolfram.com/biography/Bertrand.html, Public domain, https://commons.wikimedia.org/w/index.php?curid=2818814
1852 CE
Chebyshev's Estimate on Prime Distribution
Chebyshev provides sharp inequalities on the distribution of primes, a crucial step toward the prime number theorem. #math #history
By Dantheox (talk) (Uploads) - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=113632968
1859 CE
Riemann Articulates the Riemann Hypothesis
Bernhard Riemann publishes a groundbreaking paper on the zeta function, conjecturing that all non-trivial zeros lie on the critical line, deeply linked to prime distribution. #math #hypothesis
By No machine-readable author provided. Conscious assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=939039
1896 CE
Prime Number Theorem Proved
Jacques Hadamard and Charles de la Vallée Poussin independently prove the prime number theorem, showing the asymptotic distribution of primes. #math #history
1913 CE
Ramanujan Publishes on Prime Numbers
Srinivasa Ramanujan publishes influential results on the distribution of primes and highly composite numbers. #math #india
By Unknown author - https://mss-cat.trin.cam.ac.uk/manuscripts/uv/view.php?n=Add.Ms.a.94.7#?c=0&m=0&s=0&cv=6&xywh=-2849%2C-273%2C9238%2C5258, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=153767257
1919 CE
Brun's Sieve on Twin Primes
Viggo Brun develops Brun's sieve to show the sum of reciprocals of twin primes converges, implying they are rare. #math #sieve
1930 CE
Schnirelmann's Density and Goldbach
Lev Schnirelmann introduces natural density and proves every integer >1 can be expressed as sum of at most C primes, a breakthrough on the Goldbach conjecture. #math #russia
1937 CE
Vinogradov's Three-Primes Theorem
Ivan Vinogradov proves that every sufficiently large odd integer is the sum of three primes, using the Hardy-Littlewood circle method. #math #russia
By Unknown author - Original publication: Газета «Алтайская правда» №120 (7277) от 19 июня 1945 годаImmediate source: warheroes.ru, Public domain, https://commons.wikimedia.org/w/index.php?curid=95028677
1949 CE
Elementary Proof of Prime Number Theorem
Atle Selberg and Paul Erdős give an elementary proof of the prime number theorem, avoiding complex analysis. #math #history
1950 CE
Turing Designs Prime Sieve Machine
Alan Turing outlines a mechanical procedure for eliminating non-prime numbers, contributing to computational number theory. #math #computing
By Elliott & Fry - https://commons.wikimedia.org/wiki/File:Alan_Turing_(1951).jpg, Public domain, https://commons.wikimedia.org/w/index.php?curid=158923803
1957 CE
Wang Yuan's Work on Goldbach Conjecture
Wang Yuan proves that every sufficiently even integer can be expressed as sum of a prime and a product of at most two primes (1+2). #math #china )
1966 CE
Chen Jingrun Proves Chen's Theorem
Chen Jingrun proves that every sufficiently large even integer is the sum of a prime and a product of at most two primes (1+2), a major milestone in Goldbach studies. #math #china
By user:Iamdavidtheking - File:A statue of Chen Jingrun.JPG, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=8001620
1976 CE
Miller-Rabin Primality Test Introduced
Gary Miller and Michael Rabin develop a probabilistic primality test based on Fermat's little theorem, widely used in cryptography. #math #cryptography
1985 CE
Goldwasser-Killian Primality Test
Shafi Goldwasser and Joe Killian introduce an elliptic curve primality test, providing a practical method for proving primality. #math #cryptography
1992 CE
Adleman-Huang Primality Test
Leonard Adleman and Ming-Deh Huang develop a deterministic primality test using elliptic curves. #math #cryptography
2002 CE
AKS Primality Test Discovered
Manindra Agrawal, Neeraj Kayal, and Nitin Saxena devise the AKS primality test, the first deterministic polynomial-time algorithm for primality. #math #algorithm
2004 CE
Green-Tao Theorem on Arithmetic Progressions
Ben Green and Terence Tao prove that there exist arbitrarily long arithmetic progressions of primes. #math #breakthrough
May 14, 2013 CE
Zhang Yitang Proves Bounded Gaps Between Primes
Yitang Zhang proves that there are infinitely many pairs of primes with gap less than 70 million, a landmark result on prime gaps. #math #china
By VOA - http://www.voachinese.com/media/video/i-america-math-zhang-yitang-20131204/1803128.html, Public domain, https://commons.wikimedia.org/w/index.php?curid=33336006
2014 CE
Maynard Improves Bounded Gap Result
James Maynard shows that for any integer m, there are infinitely many intervals of length C(m) containing at least m primes, refining Zhang's approach. #math #breakthrough )
By Petra Lein, Copyright is MFO - Mathematisches Forschungsinstitut Oberwolfach, https://owpdb.mfo.de/detail?photo_id=18228, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=43553945
Jan 19, 2016 CE
Largest Known Prime Discovered
The Great Internet Mersenne Prime Search (GIMPS) discovers the 49th Mersenne prime, 2^74207281-1, with over 22 million digits. #math #computing
By Nicoguaro - Own work, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=51383347