A new prime number of 9.3 million digits was found

A number of new elements have been found that are longer than 9 million digits. This new number is the seventh largest number ever found. It became the fifth potential answer for Sierpinski's problem set up dozens of years ago.

Concerned by the Polish mathematician Wacław Sierpiński in 1960, the Sierpinski problem asked which number was the smallest number that could meet the conditions he offered. Some Sierpinski must be a positive odd number, and the variable k in the formula k × 2n + 1 must be a number (ie not a prime number). In other words, if k is a Sierpinski number, then all the variables in the formula k × 2n + 1 are a combination.

So, to prove k is some Sierpinski, you have to prove that k × 2n + 1 is a number that satisfies all n. If n is a prime number, you have no correct answer.

"These conditions have made answers very few and they are far away from each other, making them very difficult to find," Timothy Revell told New Scientist magazine.

Currently, the smallest known Sierpinski number is 78,557, launched by American mathematician John Selfridge in 1962. But we are still not sure that there will be no other smaller ones.

New primes are found with a length of 9.3 million digits.(Artwork: Steve Johnson / Flickr).

For more than 50 years, mathematicians have found six potential numbers that may be the smallest Sierpinski number, including 10,223, 21,181, 22,699, 24,737, 55,459 and 67,607. But none of them has proven that their numbers are some Sierpinski.

"To make sure the number given is Sierpinski's number, you need to prove a lot of equations without pre-selecting numbers n, the formula k × 2n + 1 will never work with prime numbers. " Revell said.

To know the answer, you need to know which numbers are prime numbers. And that's where PrimeGrid 'Seventeen or Bust' project starts. The project was helped by volunteers to find larger prime numbers by giving the computer performance to demonstrate a specific number is a prime number.

"Users download software to their computers and join different groups depending on the type of prime number they are interested in searching," Iain Bethune from PrimeGrid told New Scientist magazine.

In an attempt to solve Sierpinski's problem, the project found the largest prime number and became the seventh largest prime number ever recorded: 10,223 × 231172165 + 1 . With 9,383,761 digits , a personal computer takes centuries to find this number. This number is found based on the power of thousands of computers at the same time over an 8-day period.

But this number of elements is special for another reason, it dropped one of the six potential results for the position of becoming Sierpinski. And besides it, there are only 5 other potential numbers."This is the largest prime number ever found in the attempt to solve Sierpinski's problem and its variable k = 10.223 is probably Sierpinski's number , " PrimeGrid said in a recent announcement.

However, this number is still not the longest digit number. The largest number of digits was found in January, with a length of 22 million digits.

That number is part of a rare number group of prime numbers, called Mersenne primes - that is, it has a power of 2 minus 1. The prime number is 9.3 million digits not a Mersenne number .

In fact, of the 10 largest prime numbers ever known, the newly discovered prime is the only non-Mersenne number, and also the non-Mersenne number of more than 4 million digits.

While the final result of the Sierpinski problem will be a work solved by mathematicians, finding the greatest prime number is very important for researchers to improve coding technology and power of the computer.