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

A flat bone consisting of a proper bone, 20,000-year-old archaeologists, lines like tally marks, when you see something unique The main numbers represented. Similarly, a Clay tablet from 1800 BCE Babylonians are written with numbers, describe a number of systems built in the main numbers.

As a historic display, like Ishangoo bone, Plimepton 322 tablets and other works, the head numbers fascinated and annoyed. Today is the head numbers and their features are studied Number theoryToday is a branch with a field of math and active research.

History of head numbers

Unofficially, the number of multiple positive counts is the basis The number of these points can be arranged in the form of a rectangular number with just one column or a number. For example, only 1 and 11 points and 11 and 11 and 11 measles in size from 11 to 11 points. Math tutories, only 1 and a number of positive divisions define a number of a number as a number of itself.

Date of Mathematics Peter S. Rudman offers it Greek mathematicians likely to understand the concept of happening around 500 BCE

Around 300 BCE, Greek Mathematician and Logist Eulerin proved Infinite numbers. Euler began assuming that the last number is a number of numbers. Then came with a president who was not on the original list to create a contradiction. Since the main principle of mathematics has a illegy contradiction, the original hypothesis of Euler came to the conclusion. So there are many prints in endless.

The controversy has determined the existence of an infinite prinion, but it was not particularly constructive. Euler did not have any effective way to list the entire Priya in an increasing list.

In the Middle Ages, the Arab mathematicians developed the theory of the main numbers of Greeks, called Hasam numbers during this period. Persian mathematician Kamal al-Din Al-Falisi It means that arithmetic shapes the main theorem of the arithmetic can be expressed unique as a prinning product of any positive integer.

From this point of view, using the head numbers, multiplication, the main building blocks to build any positive number – atoms in chemistry, combined for molecules, atoms according to atoms.

Prime numbers can be sorted into different types. In 1202 Leonardo Fibonacci presented in his book “Lamber ABACI: Book of computing“The main numbers of the form (2)^p – 1)

Today is called Primes in this form Mersenne Primes After the French monk Marin Mersenne. Many of the greatest well-known follow this format.

A few early mathematicians believed in a number of forms (2)^p – 1) P is the basis when the beginning is. But in 1536 Mathematician Hudalricus King This is 11 basic, but not (2)¹¹ – 1), equal to 2047. The number 2047 can be expressed 11 times to 89 times rejecting the livelihood.

Although not always correct, it realized that the numbered theorists (2)^p – 1) Shortcut often produces primes and gives you a systematic way to search for great premiums.

Search for great prizes

Number (2)^p – 1) Ps larger than the value P and offers opportunities for great principles.

If the number (2)^p – 1) It is very large, it is very difficult to check if^p – 1) is the basis – that is, (2)^p – 1) Dots can be arranged in a rectangular number with just one column or a row.

Fortunately, Dedouard Lucas Developed a number of tests in 1878 and proved later Derrick Henry Lehmer In 1930. The work resulted in an effective algorithm to assess potential Mersenne Primons. Using this algorithm with hand calculations on paper Lucas showed a 39-digit number (2) in 1876¹²⁷ – 1) 170,14,183,460,469,731,73,71,71,71,71,71,71,71,71,71,71,71,71,75,71,71,71,75,75,75,727 and this value is the basis.

It is also known as M127, this number remains the biggest basis for hand calculations. He had a record for the biggest well-known head for 75 years.

The researchers began to use computers in the 1950s and increased the pace between new major prinion. In 1952 Raphael M. Robinson set five new Mersenne Princu Lucas-Lehmer using a standard western automatic computer to implement the main numbers test.

As computers are improved, the list of MERSENne Primes, especially with Cray Supercomputer’s arrival In 1964. Although infertility is very printing, it is not sure how much the researchers fit into type (2)^p – 1) and Mersenne Primes.

In the early 1980s, researchers gathered sufficient information with confidence that there is an infinite Mersenne Primes. They could have been so guessed How often these basic numbers appearon average. Mathematicians have not been proven so far, but new information continues to support these estimates.

George WoltmanThe computer scientist in 1996 was a major Internet Mersenne General Search or Gimps. Through this cooperation program, everyone can download a free program Gimps Website to search for MERSENne Prime numbers on personal computers. There are special instructions on how to participate in the website.

Gimps, using now, primarily determined 18 Mersenne Prine on individual computers Intel chips. The program average a new discovery for each two years.

The largest well-known head

Luke DurantA retired programmer discovered the current record for the biggest well-known head (2)^136,279,841 – 1), in October 2024. As M136279841This 41,024,320 digit number was set to 52nd Mersenne Prime and found Gimps open to the public Cloud-based calculation network.

This network used the Nvidia chips and fled between 17 countries and 24 data centers. These Advanced chips At the same time, give thousands of calculations and make comparison faster. The result is a shorter time for algorithms such as the General Test.

Electronic Border Fund is a civil freedom group offering cash prizes to identify large prints. Gift was given to the first for the first 2000 and 2009 gifts Verified 1 million digits and 10 million-digit key numbers.

A large number of enthusiasts’ The next two challenges are the first 100 million digit and 1 billion digital prints. EFF Rewards The first successful individual or group of $ 150,000 and $ 250,000 respectively.

Eight of the 10 most well-known primes are Mersenne Primes, so Gimps and cloud computing are preparing to play a prominent role in search of large numbers.

Extensive basic numbers have a vital role in many encryption methods in ciberability, so each Internet user stands to take advantage of searching for large numbers. These searches help Digital communication and sensitive data are safe.

Jeremia BartzMathematical Associate Professor, University of North Dakota. This article is republished Conversation Under the Creative Commons license. Read original article.