History of Prime number in Timeline
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. For instance, 5 is a prime number because it can only be produced by multiplying 1 and 5. On the other hand, 4 is a composite number because it can be formed by multiplying 2 and 2. Prime numbers are fundamental in number theory because every natural number greater than 1 is either a prime number or can be expressed as a product of prime numbers.
1912: Landau's Problems on Prime Numbers Proposed
In 1912, Edmund Landau posed four fundamental problems related to prime numbers, known as Landau's problems. These conjectures, despite their seemingly simple formulations, have remained unsolved to this day, posing significant challenges in number theory.
1935: Prime Numbers in Music Composition
In 1935, French composer Olivier Messiaen debuted "La Nativité du Seigneur," a piece using motifs based on prime numbers (like 41, 43, 47, and 53) to create unpredictable rhythms inspired by nature.
1949: Further Exploration of Prime Numbers in Music
Olivier Messiaen continued to explore prime numbers in his music with "Quatre études de rythme" in 1949, using their irregular patterns for a natural, ametrical effect.
1951: Computerized Prime Hunting Begins
The year 1951 marked a turning point in prime number discovery with the use of computers. From this year onwards, all record-breaking primes have been found using computers, accelerating the pace of discovery.
1956: The Debate over the Primality of 1 Continues
As recent as 1956, the debate over whether the number 1 should be considered prime was still ongoing, with some mathematical publications continuing to include it in lists of prime numbers.
1975: Prime Numbers as a Communication Tool
In 1975, Carl Sagan and Frank Drake discussed using prime factorization to create images for communication with extraterrestrials, an idea Sagan later used in his novel "Contact."
1992: Mersenne Primes Emerge as Record Holders
Since 1992, the title of the largest known prime number has been consistently held by a Mersenne prime. This is largely due to the Lucas-Lehmer test's efficiency in determining the primality of Mersenne numbers.
2004: Green-Tao Theorem Proves Existence of Arbitrarily Long Arithmetic Progressions of Primes
In 2004, the Green-Tao theorem was proven, a significant development in understanding the distribution of prime numbers. The theorem states that there exist arithmetic progressions of primes of any desired length.
2009: GIMPS Discovers 10-Million-Digit Prime
In 2009, the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project, achieved a significant milestone by discovering a prime number with at least 10 million digits, earning a $100,000 prize.
October 2012: Quantum Computing Factors 21
In October 2012, a quantum computer successfully factored the number 21 using Shor's algorithm. While a modest number, this event marked a significant step in the development of quantum computing and its potential to revolutionize factorization.
2013: Yitang Zhang's Proof on Bounded Prime Gaps
Yitang Zhang made a groundbreaking contribution to number theory in 2013 by proving the existence of infinitely many prime gaps with a bounded size, a significant step towards understanding the distribution of prime numbers.
2014: Goldbach's Conjecture Verified for Large Numbers
As of 2014, Goldbach's Conjecture, which states that every even number greater than 2 can be represented as the sum of two primes, had been verified for all numbers up to 4 × 10^18, a testament to the advancements in computational power and mathematical techniques.
2017: Verification of Fermat Numbers
As of 2017, all Fermat numbers beyond the first five (3, 5, 17, 257, and 65,537) have been verified to be composite, meaning they are not prime.
December 2018: Mersenne Primes Dominate Largest Known Primes
As of December 2018, the largest known prime numbers have consistently been Mersenne primes - numbers that are one less than a power of two. This is largely due to the efficient Lucas-Lehmer primality test, which is specifically designed for Mersenne numbers.
December 2018: Largest Known Prime Number Discovered
In December 2018, the largest known prime number to date was discovered, a Mersenne prime with 24,862,048 digits.
December 2019: RSA-240 Factored: A Milestone in Factorization
December 2019 marked a milestone in factorization with the successful factorization of RSA-240. This 240-digit (795-bit) number, a product of two large primes, was the largest number factored by a general-purpose algorithm at that time.
2048: 2048-bit Primes in Cryptography
The use of large prime numbers, particularly 2048-bit primes, has become common in public-key cryptography algorithms like RSA and the Diffie-Hellman key exchange. The security of these cryptographic systems relies on the difficulty of factoring large numbers into their prime factors.