300 BCE
Euclid Proves Infinitude of Primes
In his Elements, Euclid provides the first known proof that there are infinitely many prime numbers, using a classic reductio ad absurdum argument. #mathematics #history
Chronological Storyline (34 Milestones)
240 BCE
Eratosthenes Develops Sieve Method
Eratosthenes of Cyrene devises an efficient algorithm to find all prime numbers up to a given limit, known as the Sieve of Eratosthenes. #mathematics #ancient
By SKopp at German Wikipedia - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1506732
100 CE
Sunzi's Mathematical Classic on Primes
The Chinese mathematical text Sunzi Suanjing includes early work on modular arithmetic and primality testing, influencing later developments. #mathematics #china
By AnonymousUnknown author - Own work (my book), Public domain, https://commons.wikimedia.org/w/index.php?curid=12568381
1202 CE
Fibonacci Investigates Prime Numbers
In his book Liber Abaci, Fibonacci introduces the concept of prime numbers to Europe and presents methods for testing primality. #mathematics #medieval
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=720501
1303 CE
Zhu Shijie's Jade Mirror of the Four Unknowns
Chinese mathematician Zhu Shijie discusses prime numbers and polynomial equations, advancing number theory in East Asia. #mathematics #china
By Zhu Shijie - mybook 唐戈藏书, Public domain, https://commons.wikimedia.org/w/index.php?curid=19268418
1585 CE
Stevin's Decimal Fractions and Primes
Simon Stevin publishes La Thiende, promoting decimal fractions, which indirectly aids prime number computation. #mathematics #renaissance
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 Stated
Pierre de Fermat announces his Little Theorem, stating that for prime p, a^p ≡ a (mod p), a foundational result in primality testing. #mathematics #numbertheory
1737 CE
Euler's Product Formula Links Primes and Zeta
Leonhard Euler introduces the product formula over primes for the zeta function, establishing the deep connection between prime distribution and analysis. #mathematics #euler
1742 CE
Goldbach's Conjecture Proposed
Christian Goldbach conjectures that every even integer greater than 2 is the sum of two primes, an unsolved problem inspiring millennia of research. #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
Waring's Problem on Prime Gaps
Edward Waring conjectures that every integer is a sum of at most 9 positive cubes, inspiring later work on prime gaps and additive number theory. #mathematics
1796 CE
Gauss's Disquisitiones Arithmeticae
Gauss publishes his seminal work, laying foundations for modern number theory and conjecturing the Prime Number Theorem regarding prime distribution. #mathematics #gauss
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1801 CE
Gauss's Prime Number Theorem Conjecture
At age 15, Gauss conjectures that the number of primes up to x is approximately x/ln(x), later known as the Prime Number Theorem. #mathematics #conjecture
1837 CE
Dirichlet's Theorem on Primes in Arithmetic Progressions
Dirichlet proves there are infinitely many primes in any arithmetic progression a, a+d, a+2d,... with coprime a and d, using L-functions. #mathematics #dirichlet
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's Work on Prime Distribution
Pafnuty Chebyshev proves Bertand's postulate and obtains the first explicit bounds for the prime-counting function, advancing toward the Prime Number Theorem. #mathematics #chebyshev
By Dantheox (talk) (Uploads) - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=113632968
1859 CE
Riemann's Hypothesis on Zeta Function Zeros
Bernhard Riemann publishes his memoir on the zeta function, hypothesizing that all non-trivial zeros lie on the line Re(s)=1/2, deeply linked to prime distribution. #mathematics #riemann
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1896 CE
Prime Number Theorem Proved Independently
Hadamard and de la Vallée-Poussin independently prove the Prime Number Theorem using complex analysis, confirming Gauss's conjecture. #mathematics #history
1914 CE
Hardy–Littlewood Circle Method and Prime Conjectures
Hardy and Littlewood develop the circle method and propose numerous conjectures on prime distribution, including the first Hardy-Littlewood conjecture. #mathematics #conjecture
By Eigenes Werk - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=5396458
1919 CE
Brun's Sieve and Twin Prime Constant
Viggo Brun introduces the Brun sieve, proving the sum of reciprocals of twin primes converges, and defines the Brun constant. #mathematics #sieve
By William Demchick (Kiwi128) - Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=12886421
1949 CE
Elementary Proof of Prime Number Theorem
Atle Selberg and Paul Erdős independently develop an elementary proof of the Prime Number Theorem, avoiding complex analysis. #mathematics #erdős
1950 CE
Chen's Theorem on Goldbach's Conjecture
Chen Jingrun proves that every sufficiently large even number is the sum of a prime and a semiprime, the strongest result towards Goldbach's conjecture. #mathematics #chen
By user:Iamdavidtheking - File:A statue of Chen Jingrun.JPG, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=8001620
1966 CE
Large Prime Records via Computers
The discovery of the prime 2^11213-1 (the 23rd Mersenne prime) using an IBM 7094 marks the beginning of computer-assisted prime hunting. #mathematics #computing
1975 CE
Fast Primality Test: Miller–Rabin
Gary Miller and Michael Rabin develop a probabilistic primality test based on Fermat's little theorem, widely used in cryptography. #mathematics #cryptography
1977 CE
RSA Cryptosystem Invented
Rivest, Shamir, and Adleman create the RSA public-key cryptosystem, whose security relies on the difficulty of factoring large primes. #mathematics #cryptography )
1983 CE
AKS Primality Test Discovery
Manindra Agrawal, Neeraj Kayal, and Nitin Saxena devise the first deterministic polynomial-time primality test (AKS), a landmark in computational number theory. #mathematics #algorithms
1985 CE
Elliptic Curve Primality Proving (ECPP)
Shafi Goldwasser and Joe Kilian develop a method using elliptic curves for primality proving, later refined by Atkin and Morain. #mathematics #ellipticcurves
1992 CE
First Mersenne Prime Found by GIMPS
The Great Internet Mersenne Prime Search (GIMPS) discovers M(756839), the first of many record primes found via distributed computing. #mathematics #computing
By Viliam Furík - https://mersenneforum.org/showpost.php?p=544483&postcount=21, Public domain, https://commons.wikimedia.org/w/index.php?curid=101163806
1995 CE
Green–Tao Theorem on Arbitrarily Long Arithmetic Progressions
Ben Green and Terence Tao prove that the primes contain arbitrarily long arithmetic progressions, a stunning result in additive number theory. #mathematics #primes
2004 CE
Zhang's Theorem on Bounded Prime Gaps
Yitang Zhang proves there are infinitely many prime pairs with gap less than 70 million, igniting rapid progress toward 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
2013 CE
Polymath8 Collaboration Cuts Prime Gap
A massive collaborative effort (Polymath8) reduces the bound on prime gaps to 246, demonstrating crowd-sourced mathematical research. #mathematics #collaboration
2016 CE
Maynard's Work on Small Prime Gaps
James Maynard independently improves bounds on prime gaps and proves that there are infinitely many primes with no digit 7 in base 10. #mathematics #maynard )
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
2018 CE
Largest Known Prime Discovered (M82589933)
GIMPS discovers M82589933, the 51st known Mersenne prime, with over 24 million digits, continuing the quest for ever-larger primes. #mathematics #record
2020 CE
Riemann Hypothesis Verified for First 12 Trillion Zeros
Extensive computational verification of the Riemann hypothesis up to the 12 trillionth zero reinforces the conjecture, though still unproven. #mathematics #computation
2022 CE
Proof of Landau–Siegel Zero Existence?
A claimed proof of the non-existence of Landau–Siegel zeros (a critical step toward prime distribution) circulates, but remains unverified. #mathematics #conjecture
2024 CE
New Mersenne Prime Candidate Announced
GIMPS reports a possible new largest prime, pending verification, showing the ongoing excitement in prime records. #mathematics #primes