Euclid showed that there are infinite prime numbers. 2300 years later, distributed computing allows us to continue expanding the set of cousins with increasingly large numbers.
The largest known prime number is 2 82,589,933 -1. It has about 25 million digits and was discovered on December 7,
50 prime numbers of Mersenne were already known and, thanks to GIMPS, Laroche has found the fifty-first. However, it is not known if there are more Mersenne prime numbers between 45th and 51st, so these positions are provisional.
The number 2 82,589,933 -1 has a million and a half digits more than the previous largest cousin known, which had been discovered in December 2017. It was calculated for the first time with an Intel i5-4590T computer that Laroche used as a multimedia center. Several volunteers checked the finding later with more powerful processors and graphics. Thanks to this, Patrick will receive compensation of $ 3000.
Although they are supposed to be increasingly difficult to find, the GIMPS community has discovered 12 Mersenne cousins in the past 15 years, three times the expected total. If the trend continues, mathematicians may have to rethink some of the existing theories about the distribution of this type of cousins.
Prime numbers have a multitude of applications, especially in cryptography, but these cousins are so large that they have no practical use beyond testing the computing power of the current hardware. The next goal of GIMPS is to find a first cousin of 100 million digits, a feat that will be awarded $ 150,000 by the Electronic Frontier Foundation.
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