Tag

Prime Numbers

All articles tagged with #prime numbers

science2 months ago•7 min saved

Current Status of Prime Numbers in Pure Mathematics

The article discusses the significance of prime numbers in mathematics, highlighting the biggest unsolved problem, the Riemann Hypothesis, which concerns the distribution of primes and has profound implications for understanding their behavior. Despite centuries of study, many prime-related questions remain open, but recent progress and optimism suggest that solutions, especially for the Riemann Hypothesis, may be within reach, potentially revolutionizing mathematics.

via IFLScience|

#mathematics #number-theory #prime-numbers

science6 months ago•6 min saved

Mathematicians Uncover New Patterns and Methods in Prime Number Discovery

Mathematicians have discovered a remarkable new connection between prime numbers and partition functions, revealing infinitely many ways to detect primes without divisibility checks, which could influence future research in number theory and cryptography.

via IFLScience|

#diophantine-equations #mathematical-breakthrough #number-theory

science6 months ago•4 min saved

Mathematicians Unveil New Method for Counting Prime Numbers

Two mathematicians, Ben Green and Mehtaab Sawhney, have developed a new method using additive combinatorics and Gowers norms to study the distribution of prime numbers, successfully proving that infinitely many primes fit the form p² + 4q², which opens new avenues for understanding prime patterns and their applications in fields like cryptography.

via Earth.com|

#additive-combinatorics #gowers-norms #mathematical-discovery

mathematics1 year ago•2 min saved

"Predicting Prime Numbers: A Groundbreaking Breakthrough"

Researchers at City University of Hong Kong and North Carolina State University have made a groundbreaking discovery in prime number theory, challenging the long-held belief that prime numbers are unpredictable. Their research has led to the development of a Periodic Table of Primes (PTP) that can accurately predict the locations of prime numbers, with potential applications in fields such as cybersecurity. This breakthrough has the potential to significantly impact encryption and cryptography, making data more secure.

via Phys.org|

#city-university-of-hong-kong #mathematics #number-theory

mathematics2 years ago•3 min saved

"The Quest for the Ultimate Prime: Unveiling the Largest Known Prime Number"

The largest known prime number is 2^(82,589,933) - 1, also known as M82589933, which has a staggering 24,862,048 digits. It was discovered in 2018 by the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project that involves volunteers running software on their computers. Mersenne primes, named after the French monk Marin Mersenne, are a specific type of prime number. GIMPS has found a total of 17 Mersenne primes, with M82589933 being the latest discovery. Finding larger prime numbers continues to be a quest for mathematicians, and while there are strategies for determining if Mersenne numbers are prime, the search for the next one remains unpredictable.

via Livescience.com|

#gimps #largest-known-prime-number #mathematics

mathematics2 years ago•8 min saved

Fermat's Legacy: High School Student Unlocks Prime Math Proof

High school student Daniel Larsen has proven a new theorem about Carmichael numbers, a type of not-quite-prime number, that had eluded mathematicians for decades. This theorem is related to Pierre de Fermat's "little theorem," which states that for any prime number, the quantity a^p - a is divisible by p for any integer a. While the converse of Fermat's little theorem is not true, Larsen's work explores the distribution of Carmichael numbers and builds on the research of famous mathematicians such as James Maynard and Terence Tao.

via Quanta Magazine|

#carmichael-numbers #daniel-larsen #mathematics