A brief history of our passion with prime numbers – and where the hunting goes forward

Archaeologists dating a shad of smooth bone with irregular marks, who have not seen anything unique – Cuts, Cuts Representing prime numbersSimilarly, A Clay Tablet from 1800 BCE Describes a number system built on a prime numbers inscribed with Babylonian numbers.

As the Ishango bone, the performance of the entire history in the plimpton 322 tablets and other artifacts, prime numbers have fascinated and fascinated people throughout the history. Today, the prime number and their qualities are studied number theoryA branch of mathematics and the active field of research today.

History of prime numbers

Informally, a positive count number is larger than one Is prime If that number of dots can be arranged in a rectangular array with only a column or a row. For example, 11 are a major number because 11 dots make rectangular arrays of 1 size by only 11 and 11. Conversely, there is no 12 prime because you can use 12 dots to create an array of 3 by 4 dots with multiple rows and several columns. The textbooks of mathematics define a major number as more than one number, which only positively 1 and themselves are only 1 and themselves.

Mathematics historian Peter S. Rudman suggests that Greek mathematician Probably around 500 BCE, they were first to understand the concept of prime numbers

Around 300 BC, Greek mathematician and logicist Yular proved that there are there Unseen several major numbersYular started assuming that there is a limited number of prime. Then he came with a prime that was not on the original list to create a contradiction. Since a fundamental principle of mathematics is logically corresponding to any contradiction, the Euller concluded that his original perception should be false. So, there are many primes infinitely.

The logic infinitely established the existence of several prime, although it was not particularly creative. Yular had no efficient way to list all Primes in an ascending list.

In the Middle Ages, Arab mathematicians upgraded the principle of prime numbers referred to as Hasam numbers during this period. Persian mathematician Kamal al-Din al-Parsi The original theorem of arithmetic was designed, stating that any positive integer can be expressed uniquely as a product of one larger than one.

From this scene, there are basic building blocks for the creation of any positive entire number using the prime number multiplication – similar to the atoms that combine molecules in chemistry.

Prime numbers can be sorted in various types. In 1202, Leonardo Fibonacchi In his book introduced “Liber Abasi: Book of Count“Major Number of Forms (2)^P – 1) Where P is also prime.

Today, this form is called primes Mercene prime After French monk Marin marseneMany of the biggest known prime follow this format.

Many early mathematicians believed that many forms (2)^P – 1) Whenever there is P prime, it is prime. But in 1536, Mathematician Hardalikus Regius saw It is 11 main but not (2¹¹ – 1), which is equal to 2047. The number 2047 can be expressed as 11 times 89, which rejects the estimate.

While not always true, the number theorists realized that 2 (2^P – 1) Shortcut often produces prime and gives a systematic way to search for large prime.

Search for big prime

Number (2)^P – 1) P is very large relative to the value of P and provides opportunities to identify large prime.

When number (2)^P – 1) Gets enough to grow enough, it is very difficult to check what (2^P – 1) Prime is – that is, if (2^P – 1) Dots can be arranged in a rectangular array with only a column or a row.

fortunately, Édouard Lucas Developed a major number test in 1878, later proved Deeric henry lehmar In 1930. Their work resulted in an efficient algorithm to evaluate the potential Mersenne Primes. Using this algorithm with hand calculations on paper, Lucas showed in 1876 that 39-conductive number (2)¹²⁷ – 1) 170,141,183,460,469,231,687,687,303,303,715,715,884,105,727 equivalent to, and this value is prominent.

Also known as M127, this number is the largest prime verified by hand calculation. It kept the record for the biggest known Prime for 75 years.

Researchers began to use computers in the 1950s, and increased the speed of searching for new large prime. In 1952, Rafael M. Robinson identified five new Marson Primes Using a standard Western automatic computer to complete the Lucas-Lahamar Prime Number Test.

As computers improved, the list of Marson Primes increased, especially with Cre supercomputer arrival In 1964. Although there are many primes infinitely, researchers are uncertain how many types of fit (2)^P – 1) And Marson is primes.

In the early 1980s, the researchers confidently deposited enough data to assume that there are many Marson Prime. They could also guess How many times do these prime numbers appearon average. Mathematicians have not yet found evidence, but new data continues to support these estimates.

George voltmanA computer scientist, established the great internet Marson Prime Search, or Gimps in 1996. Through this collaborative program, no one can download the software available independently Gimps Website to search for marsenne prime numbers on your individual computers. There are specific instructions to participate in the website.

GIMPS has now identified 18 Mersenne Primes, mainly used on individual computers Intel chipsThe program makes a new discovery of every one to two years.

Biggest known Prime

Luke DuuntA retired programmer, discovered the current record for the biggest known Prime, (2^136,279,841 – 1), in October 2024. M136279841It was identified by 41,024,320-inguinal number 52nd Marsen Prime and was found to be publicly available on Gimps on available. Cloud-based computing network,

The network used NVIDIA chips and ran into 17 countries and 24 data centers. in Advanced chips Provide rapid computing by handling thousands of calculations simultaneously. The result is a low run time for prime number tests such as algorithms.

The Electronic Frontier Foundation is a Civil Liberty Group that offers cash prizes to identify large prime. It presented awards for the first in 2000 and 2009 Verified 1 million And Major numbers of 10 million points,

The next two challenges of the enthusiasts of the big Prime numbers are the first two challenges to identify 100 million points and 1 billion-chances. EFF Award The US $ 150,000 and $ 250,000 respectively, wait for the first successful personal or group.

Out of the 10 largest known prime numbers, eight are Marsene Prime, so Gimps and Cloud Computing Record-Breaking are set to play a major role in search of large prime numbers.

Large prime numbers have an important role in many encryption methods in cyber spaces, so each internet user benefits from the discovery of large prime numbers. These discoveries help keep helping Digital communication and sensitive information safe,

Jeremiah BartzMathematics Associate Professor, University of north dakotaThis article has been reinstated Conversation Under a Creative Commons License. read the Original article,