A Brief History of Our Obsession With Prime Numbers—and Where the Hunt Goes Next

Archaeologists of smooth bone with irregular marks 20,000 years ago are unless they notice anything unique – there may be lines like the Achings, Tallie Signs Represents the Prime NumberThe Likewise, a Clay tablet from 1800 BC Describes the system a number built in the original number engraved with Babylonian numbers.

As Ishango bone, Plimpton 322 tablets and other patterns throughout history display, the primary numbers have fascinated and fascinated people throughout history. Today, the initial numbers and their features are studied TheoryA branch of mathematics and the active field of research today.

A history of prime numbers

Informally, a positive count number greater than one Prime If the number of those points can only be arranged in a rectangular array with a column or a row. For example, a major number of 1, since 1 point only forms a rectangular array of 5 sizes by 1 and 5. Math textbooks define as the whole number as a major number whose only positive divisions are only 1 and itself.

Mathematical historian Peter S. Rudman suggested Greek mathematician The first number of the first number of BCE was to understand the idea of ​​the first number of AD

Before 7 BCE, Greek mathematician and Logisian proved that there is that there is Infinitely many initial numbersThe Ulers started with a restricted number of primes. Then he brought a prime that was not on the main list to create a conflict. Since a fundamental principle of mathematics is logically compatible with any conflict, Yuler then reached the conclusion that his original assumption must be false. So, there are many prime in infinity.

The argument established the existence of many Primes, but it was not particularly constructive. Uler had no skillful methods to listen to all Primes in the climb list.

In the Middle Ages, Arab mathematicians developed the theory of the Greek primary numbers, known as the number of laughter at this time. Persian mathematician Kamal al-Din al-Pharis Created the basic theorem of arithmetic, which says that one can be uniquely expressed as a product of any positive integer prime.

From this scene, the initial building blocks to create a positive whole number using the initial numbers – similar to the atom in combination for the creation of molecules in chemistry.

Prime numbers can be picked up in different types. 1202 at, Leonardo Fibonachi Introducing in his book “Liber Abaki: Book of Count“The initial number of form (2^P – 1) where PO is the main.

Today, this form is called primes Marsen primes After the French monk Marine MarsenThe Many of the largest familiar primes follow this format.

Several primary mathematicians believed that several forms (2)^P – 1) Whenever P is prime. However in 1536, The mathematician hoodalricous noticed the Royal 11 Main but nine (2)¹¹ – 1), which is equal to 2047. The number 2047 can be expressed as 89 times 89 by denying the estimate.

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

Search for Big Prims

Number (2^P – 1) provides the opportunity to detect much larger and larger than the quality of P.

When number (2)^P – 1) becomes bigger enough, it is more difficult to test (2^P – 1) prime – if this is (2)^P – 1) The points can only be arranged in a rectangular array with a column or a row.

Fortunately, Deadward Lucas A prime number was created in 1878, later proven Derrick Henry Lehmer In 1930. Their work created a skilled algorithm to evaluate the possible Mirsen prime. Lucas showed in 1876 using this algorithm with hand counting on paper that the number of 39-digits (2¹²⁷ – 1) 170,14183,460,469,231,731,687,303,715,884,105,727, and that value is the main.

Also known as M127, this number remains as the largest main main to verify by hand counting. It has retained the recorded prime record for 75 years.

Researchers started using computers in the 1950s and the new major primers were invented. In 1952, Rafale M. Robinson detected five new Mirsen Prime Lucas-Lehma uses a standard Western automatic computer to perform the prime number tests.

As the computers improved the list of Marsen primes increased, especially with it Cry Super Computer’s Arrival In 6645. Although infinite there are many prime, researchers are not uncertain how many types of adaptation (2)^P – 1) and Mirsen primes.

In the early sixties, researchers confidently collected adequate information to believe that many of the infinite Mirsen Prime existed. They could even guess How many times this initial number is displayedAverage. Mathematicians have not yet found evidence, but new data has been supporting these estimates.

George OltmanA Computer Scientist, ১ 1996 found the Great Internet Marsen Prime Search or Gimpus This Allied Program can download the software available freely from anyone Gym Website to search Marsen Prime numbers on their personal computers. There are specific instructions on how to participate in the website.

Gimps now detected 18 Mirsen primes, mainly using on private computers Intel chipsThe The program discovers almost a new one to two years.

The largest known principal

Luke DurantA retired programmer, the largest known prime current record (2^136,279,841 – 1), in October 2024. As mentioned M136279841The number of 41,024,320-digits was identified in the 52nd Mirsen Prime and it was found to be publicly available gimp Cloud-based computing networkThe

This network uses Nvidia Chips and ran over 17 countries and 24 data centers. This Advanced chips Provide quick computing by managing thousands of counts at once. The result is short run time for algorithms like the original number test.

The Electronic Frontier Foundation is a Civil Liberty Group that provides cash prizes to identify large primes. It provides rewards in 2000 and 2009 for the first one Have been verified 1 million-fig And Initial number of 10 million-digitsThe

The next two challenges of greater main number of enthusiasts are to identify the first 100 million-digit and 1 billion-digit primes. EFF Award Is waiting for the first successful person or group of $ 150,000 and $ 250,000 respectively.

Of the 10 largest known prime numbers, Eight is Mirsen Primes, so Gimps and Cloud Computing Record-Breaking Large are ready to play a prominent role in searching the number.

Many encryption methods have an important role in the majority in the cyberquacy, so each Internet users can benefit from the search for large numbers. Helps keep these searchs Secure digital contact and sensitive informationThe

Jeremia BertzAssociate Professor of Mathematics, North Dakota UniversityThe This article has been re -published from Conversation Under the Creative Commons License. Read KeyThe