A brief history of our obsession with the main numbers – and where the chase goes after that

A cat of the smooth bone engraved with irregular signs dating back to 20 thousand years of miraculous archaeologists until they noticed something unique – drilling, lines such as signs of the outcome, may have it Primary numbers actress. Likewise, a The clay tablet from 1800 BC The Babylonian numbers describe a system based on primary numbers.

As the ISHAngo bone, the PlimPton 322 Tablet and other artifacts throughout history, the priority numbers have fascinated and people throughout history. Today, the main numbers and their characteristics are studied in Issue theoryA branch of mathematics and the field of active research today.

History of the main numbers

Unofficially, a positive number is greater than one prominent If this number of points can only be arranged in a rectangular array with one column or one row. For example, 11 is a main number because 11 points constitute only rectangular sects of sizes 1, 11 and 11 in 1. On the contrary, 12 is not primary where you can use 12 points to make a set of 3 in 4 points, with multiple rows and multiple columns. Mathematics textbooks determine a primary number as a full number than one with its only positive division is only one.

Mathematics historian proposes Peter S. Rodman that Greek mathematics scholars It is likely to be the first to understand the concept of priority numbers, around 500 BC

About 300 BC, Greek mathematics and logic has proven that there is that there Without borders, many priority numbers. Urs began to assume that there are a limited number of priority numbers. Then he reached Prime was not in the original list to create a contradiction. Since the basic principle of mathematics is consistent logically without any contradictions, Urs concluded that his original assumption should be wrong. Therefore, there are many priority numbers.

The argument has proven the presence of many preliminary numbers without limits, however it was not particularly constructive. EULER had no effective way to list all the initial numbers in an upward menu.

In the Middle Ages, Arab mathematicians developed the Greek theory of priority numbers, referred to as HASAM numbers during this time. Persian mathematics world Kamal Al -Din Al -Farisi The basic theory of the account was developed, which states that any positive, positive number is greater than one that can be expressed uniquely as a product of the priority numbers.

From this opinion, the initial numbers are the basic building blocks to build any positive number of use using multiplication – closer to the atoms that combine molecules in chemistry.

The initial numbers can be sorted in different types. In 1202, Leonardo Fibonacci It was presented in his book “Lieber Abbasi: The Account Book“The primary numbers of the model (2^P – 1) where P is also prime.

Today, the initial numbers are called in this form Initial messenne After the French monk Marine Mersen. Many of the largest well -known primary numbers follow this format.

Many of the first mathematicians believed that a number of model (2^P – 1) It is a prime whenever p is main PRIME. But in 1536, Note the world of mathematics Hudalricus Regius That 11 is primary but not (2¹¹ – 1), which is equal to 2047. The number 2047 can be expressed as 11 times 89, refute the guess.

Although it is not always true, the theorists realize that (2^P 1) A shortcut often produces priority and gives a systematic method to search for large priority numbers.

Searching for large priority numbers

Number (2^P – 1) A much larger for the value of P and provides opportunities to determine the large primary numbers.

When the number (2^P – 1) It becomes large enough, it is difficult to verify if it is (2^P – 1) It is primary – that is, if (2^P – 1) The points can only be arranged in a rectangular array with one column or one row.

Fortunately, édouard Lucas The main number test was developed in 1878, proved later by Derek Henry Limmer In 1930, their work resulted in an effective algorithm to assess the possible numbers of Mersen. Using this algorithm with manual accounts on paper, Lucas showed in 1876 that the number of 39 figures (2¹²⁷ – 1) Equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and this value is primary.

Also known as the M127, this number remains the most verified by the manual accounts. I held the record for the largest prime known for 75 years.

The researchers began to use computers in the fifties, and the pace of discovery of new priority numbers increased. In 1952, Select Raphael M. Robinson five new MERSENNE Using a standard automatic computer to perform Lucas-Lehmer tests.

With computers improved, the metersenne primary list grew, especially with Access SuperCanter In 1964, although there are many priority numbers, researchers are not sure of the number of species (2^P – 1) And MERSENNE Premium Numbers.

By the early eighties of the last century, the researchers collected sufficient data to believe in the confidence of the presence of many Mersen numbers. They can even guess How many times do these initial numbers appear?On average. Mathematics have not found a guide yet, but new data continues to support these guesses.

George and LammanComputer world, the foundations of Great Internet Mersenne Prime Search, or GIMPS, in 1996. Through this cooperative program, anyone can download the programs available freely from Gimps Web site to search for MERSENNE Prime numbers on personal computers. The site contains specific instructions on how to participate.

GIMPS now set 18 MERSENNE, primarily on personal computers using Intel chips. The program mediates a new discovery for each year to two years.

The largest prime is known

Luke DurantDiscover a retired programmer, the current registry of the largest well -known Prim, (2^136,279,841 – 1), in October 2024. It is referred to as the name M136279841This number 41,024,320 was the number 52 Mersen Prime was determined by operating the style publicly available The computing network based on the group of theaps.

This network used NVIDIA chips and operated across 17 countries and 24 data centers. these Advanced chips Providing computing faster by dealing with thousands of accounts at the same time. The result is shorter operating times for algorithms such as primary numbers test.

Frontier Electronic Foundation is a civil freedom group that offers cash prizes to determine large priority numbers. Awards were awarded in 2000 and 2009 for the first time 1 million digital has been verified and 10 million numbers main numbers.

They are the two challenges for the number of the main number in the main number in determining the first amount of 100 million digital and primary numbers of two numbers. EFF Awards Of the $ 150,000 and $ 250,000, respectively, awaiting the first individual or successful group.

Eight of the 10 largest known main numbers are MERSENNE, so Gimps and cloud computing are about to play a prominent role in searching for big initial numbers.

Large preliminary numbers have a vital role in many methods of encryption in cybersecurity, so each user on the Internet benefits from searching for large numbers. These searches help Digital communications and sensitive information are safe.

Jeremia PartzAssociate Professor of Mathematics, North Dakota University. This article has been republished from Conversation Under the creative public license. Read The original article.