The Greek mathematician Euclid very well proved, about 300 BCE, that there are numerous prime numbers. But it was the British mathematician Christian Loson Sun-Perfect who recently launched the computer game “Is this Prime?”

Launched five years ago, the game has surpassed three million attempts since July 16 – plus, it has hit 2,999,999 runs, after being increased to nearly 100,000 attempts by the H2, Tax News Post.

The aim of the game is to sort as many numbers as possible in “prime” or “not prime” in 60 seconds (because Lonson-Perfect originally described it on The Er Periodical, the mathematics blog of which he is the founder and editor).

The prime number is a whole number that has exactly two divisors, 1 and the same.

“It’s very simple, but very difficult,” says Lonson-Perfect, who works in the e-learning unit at Newcastle University’s School of Mathematics and Statistics. He created the game in his spare time, but it proved useful at work: Lonson writes Sun-Perfect e-assessment software (systems that evaluate learning). “The system I created is designed to randomly generate a math question, and get an answer from the student, who automatically marks and responds,” he says. “You can see Prime’s game as a kind of evaluation” – it was used during outreach sessions in schools.

It made the game a little easier with keyboard shortcuts – Y and N keys, click the corresponding yes-no-buttons on the screen to mouse to save mouse-moving time.

Give it a whirl:

Ancient-verification algorithms

There are practical utilities in calculating prime numbers – such as with error-correction code and encryption. But when the main factor is strict (hence its value in encryption), if difficult, it is easy to check the primacy. The Fields Medal – The winning German mathematician Alexander Gruthendik made a clever mistake of 57 for the Prime (“Gruthendik Prime”). When Lonson analyzed Sun-Perfect game data, he discovered that different numbers showed a certain “grouthendicineness”. The most commonly mistaken numbers for Prime were 51, followed by 57, 87, 91, 119, and 133 nemesis of Son Perf Sun-Perfect (he also devised a simple primitive verification service: https://isthisprime.com/2).

The simplest algorithm to check the priority of a number is the trial division – divide the number by its square root (the product of two numbers over the square root will be greater than the number in question).

However, this naive method is not very efficient, nor have some other techniques been devised over the centuries – as the German mathematician Carl Friedrich Gauss observed in 1801 – Falls.

The game-coded algorithm Lawson-Perfect is called the Miller-Rabin primacy test (not a 17th-century method, a “small theorem of format”, based on a very efficient but low iron knuckle). The Miller-Robin test works surprisingly well. As far as Loson Sun-Perfect is concerned, it’s “basically magical” – “I don’t understand how it really works, but I’m sure I could if I had spent more time looking at it more deeply.” , ”He says.

The test uses randomness, so it produces a potential result. Which means sometimes the test goes wrong. Carl Pomerance, a mathematician and co-author of the book at Dartmouth College Ledge, says, “An imposter, a composite number that is trying to pass as prime, has a chance to come out. Prime Numbers: A Computational Perspective. The probability of the impositor slipping through the algorithm’s clever checking mechanism is probably one in a trillion, so the test is “very safe.”

But as far as clever primitive checking algorithms are concerned, the Miller-Robin test is the “top of the iceberg,” says Pomerance. Notably, 19 years ago, three computer scientists from Indian computer technology Kanpur – Maninder Agarwal, Neeraj Kayal and Nitin Saxena – announced the AKS primacy test, which eventually passed a test to disprove it. Was provided. That number is no minister, without any randomization and (theoretically, at least) with impressive speed. Alas, fast in theory does not always translate to fasting in real life, so the AKS test is not useful for practical purposes.

Unofficial world record

But practicality is not always the point. Occasionally receives emails from people eager to share high scores in Lawson-Perfect game. Recently one player reported 60 primes in 60 seconds, but this record is 127 potential. (Lonson-Perfect doesn’t track high scores; he knows there are some computer-assisted attempts that produce spikes in the data.)

Ravi Fernando, a mathematics graduate student at the University of California, Berkeley, scored 127, posting the results in July 2020. He is still his personal best and considers it an “unofficial world record”.

Since last summer, Fernando has not played the game much with the default settings, but he has tried with customized settings, opting for a larger number and allowing more time limits – he scored 240 with a five minute limit. “Which made a lot of guesses, because the numbers have come down to a four-digit range and I’ve only made 3,000.” “I think it’s too much even if some argue.”

Fernando’s research is in algebraic geometry, which to some extent includes prime. But, he says, “my research has more to do with why I stopped playing this game than why I started” (he began his PhD in 2014). Plus, it will be very difficult to beat the figure 127. And, he says, “it feels right to hang on to a prime-number record.”