300 BCE
Euclid Proves Infinitude of Primes
Euclid's Elements includes a proof that there are infinitely many prime numbers, a foundational result in number theory. #mathematics #history
Chronological Storyline (39 Milestones)
240 BCE
Eratosthenes Develops the Sieve
Eratosthenes of Cyrene invents the Sieve of Eratosthenes, an algorithm for finding all primes up to a given limit. #mathematics #algorithm
By SKopp at German Wikipedia - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1506732
100 CE
Nicomachus Writes Introduction to Arithmetic
Nicomachus of Gerasa compiles Introduction to Arithmetic, which includes discussions on prime, composite, and perfect numbers, influencing medieval mathematics. #mathematics #history
By AnonymousUnknown author - Cambridge University Library, MS Ii.3.12, f.61v, Public domain, https://commons.wikimedia.org/w/index.php?curid=16282794
300 CE
Chinese Remainder Theorem Formulated
Sunzi Suanjing formulates the Chinese remainder theorem, a key tool in number theory allowing solving systems of congruences. #mathematics #chinese
By Cmglee - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=50938525
628 CE
Brahmagupta's Work on Number Theory
Brahmagupta's Brāhmasphuṭasiddhānta includes early work on quadratic Diophantine equations and arithmetic, influencing later prime number theory. #mathematics #indian
800 CE
Al-Khwarizmi's Arithmetic
Al-Khwarizmi writes on Hindu-Arabic numerals and arithmetic, foundational for later number theory developments in the Islamic world. #mathematics #islamic
By Zarateman - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=162213187
1202 CE
Fibonacci Publishes Liber Abaci
Fibonacci introduces the Fibonacci sequence and discusses prime factorization, stimulating European interest in number theory. #mathematics #history
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=720501
1585 CE
Stevin Introduces Decimal Fractions
Simon Stevin publishes De Thiende, promoting decimal fractions which simplify calculations, including prime-related computations. #mathematics #history
By Unknown author - Digitool Leiden University Library, http://digitalcollections.universiteitleiden.nl, Public domain, https://commons.wikimedia.org/w/index.php?curid=72690
1640 CE
Fermat's Little Theorem Announced
Pierre de Fermat states his Little Theorem, a foundational result in modular arithmetic and primality testing. #mathematics #history
1737 CE
Euler Introduces Product Formula
Leonhard Euler presents the Euler product formula linking primes and the zeta function, laying groundwork for analytic number theory. #mathematics #history
1742 CE
Goldbach Proposes His Conjecture
Christian Goldbach conjectures that every even integer greater than 2 can be expressed as the sum of two primes, a still unsolved problem. #mathematics #conjecture
By Christian Goldbach - http://www.mscs.dal.ca/~joerg/pic/g-letter.jpg, Public domain, https://commons.wikimedia.org/w/index.php?curid=1721422
1770 CE
Lagrange Publishes on Sums of Squares
Joseph-Louis Lagrange proves Lagrange's four-square theorem, linking primes and quadratic forms, a milestone in additive number theory. #mathematics #history
By Cmglee - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=132463072
Mar 30, 1796 CE
Gauss Begins Disquisitiones Arithmeticae
Carl Friedrich Gauss makes a seminal contribution to number theory with his work on quadratic reciprocity and prime distribution. #mathematics #history
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=641724
1808 CE
Legendre Conjectures Prime Number Theorem
Adrien-Marie Legendre conjectures the prime number theorem, approximating π(x) roughly as x/(log x - 1.08366). #mathematics #conjecture
1859 CE
Riemann Formulates the Zeta Hypothesis
Bernhard Riemann publishes his memoir on the zeta function, hypothesizing that all nontrivial zeros lie on the critical line, deeply linked to prime distribution. #mathematics #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 Independently
Jacques Hadamard and Charles de la Vallée-Poussin independently prove the prime number theorem using complex analysis. #mathematics #history
1914 CE
Ramanujan and Hardy Collaborate on Primes
Srinivasa Ramanujan and G. H. Hardy publish joint work on the distribution of primes and highly composite numbers. #mathematics #history
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
Hardy-Littlewood Circle Method Developed
G. H. Hardy and John Littlewood create the circle method, a powerful technique for additive number theory problems like Waring's problem and prime sums. #mathematics #method
1920 CE
Vinogradov Proves Odd Goldbach Conjecture
Ivan Vinogradov proves that every sufficiently large odd integer can be expressed as the sum of three primes, a major advance. #mathematics #theorem
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
Selberg and Erdős Give Elementary Proof of PNT
Atle Selberg and Paul Erdős independently produce an elementary proof of the prime number theorem, avoiding complex analysis. #mathematics #proof
1950 CE
Selberg Develops Sieve Methods
Atle Selberg introduces the Selberg sieve, a versatile combinatorial tool for prime number problems. #mathematics #sieve
By Konrad Jacobs, Erlangen - Mathematisches Institut Oberwolfach (MFO), https://opc.mfo.de/detail?photoID=3792, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=3898325
1966 CE
Chen Jingrun Proves Chen's Theorem
Chen Jingrun shows that every sufficiently large even integer is the sum of a prime and a product of at most two primes, a near-twin prime result. #mathematics #theorem
By user:Iamdavidtheking - File:A statue of Chen Jingrun.JPG, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=8001620
1973 CE
Montgomery Conjectures Pair Correlation
Hugh Montgomery's pair correlation conjecture relates zeros of the zeta function to eigenvalue distributions, linking primes and physics. #mathematics #conjecture
By Renate Schmid - Mathematisches Institut Oberwolfach (MFO), https://opc.mfo.de/detail?photoID=10358, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=4331529
1975 CE
Miller-Rabin Primality Test Developed
Gary Miller and Michael Rabin devise a probabilistic primality test based on Fermat's little theorem, widely used in cryptography. #cryptography #algorithm
1985 CE
AKS Primality Test Conceived
Manindra Agrawal, Neeraj Kayal, and Nitin Saxena discover the first deterministic polynomial-time primality test (published 2004). #mathematics #algorithm
1994 CE
Wiles Proves Fermat's Last Theorem
Andrew Wiles proves Fermat's Last Theorem, a landmark in number theory linking elliptic curves and modular forms, indirectly impacting prime research. #mathematics #theorem
By "copyright C. J. Mozzochi, Princeton N.J" - http://www.mozzochi.org/deligne60/Deligne1/_DSC0024.jpg, Attribution, https://commons.wikimedia.org/w/index.php?curid=2635913
1997 CE
GIMPS Project Launched
The Great Internet Mersenne Prime Search (GIMPS) begins using distributed computing to find large Mersenne primes, discovering many record primes. #computing #primes
By Viliam Furík - https://mersenneforum.org/showpost.php?p=544483&postcount=21, Public domain, https://commons.wikimedia.org/w/index.php?curid=101163806
2004 CE
Green-Tao Theorem Published
Ben Green and Terence Tao prove that the primes contain arbitrarily long arithmetic progressions, a stunning result in additive combinatorics. #mathematics #theorem
2005 CE
Polymath Project Initiates
Timothy Gowers launches the Polymath Project, a collaborative online effort, addressing problems like the Hales-Jewett theorem and later prime gaps. #mathematics #collaboration
2008 CE
Polymath4 on Bounded Gaps
The Polymath4 project works on the Erdős discrepancy problem and later contributes to bounded gaps between primes. #mathematics #polymath
May 13, 2013 CE
Zhang Yitang Proves Bounded Gap Between Primes
Zhang Yitang proves that there are infinitely many pairs of primes with gap less than 70 million, a breakthrough on the twin prime conjecture. #mathematics #breakthrough
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 Prime Gap Bound
James Maynard reduces the bound on prime gaps to 600, and later to 246 through the Polymath8 project, advancing toward twin primes. #mathematics #theorem )
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
2014 CE
Polymath8 Achieves Gap 246
The collaborative Polymath8 project, led by Terence Tao, reduces the proven bound for prime gaps to 246. #mathematics #collaboration
2016 CE
Helfgott Proves Ternary Goldbach Conjecture
Harald Helfgott completes a proof of the ternary Goldbach conjecture: every odd integer greater than 5 is the sum of three primes. #mathematics #proof
By Exceptg - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=32941679
Dec 21, 2018 CE
Largest Known Prime Discovered by GIMPS
GIMPS discovers M82589933, a Mersenne prime with 24,862,048 digits, the largest known prime at the time. #computing #primes
2018 CE
Polymath16 on Hadwiger-Nelson Problem
Polymath16 focuses on the chromatic number of the plane, indirectly involving prime-related graph theory. #mathematics #collaboration
Jul 5, 2022 CE
Maynard Awarded Fields Medal
James Maynard receives the Fields Medal for contributions to analytic number theory, particularly on prime gaps and distribution. #mathematics #award
By Stefan Zachow for the International Mathematical Union; retouched by King of Hearts - File [1], Public domain, https://commons.wikimedia.org/w/index.php?curid=2277414
2023 CE
New Bounds on Prime Gaps by Polymath
The Polymath project extends techniques to improve unconditional bounds on gaps between primes, refining the work of Zhang and Maynard. #mathematics #collaboration
2024 CE
Ongoing Research on Riemann Hypothesis
The Riemann hypothesis remains unproven, but new computational and theoretical approaches continue to test its implications for prime distribution. #mathematics #openproblem