After 14 years of repeated attempts, an American engineer, Jonathan Pace, has managed to break a new record thanks to the discovery of the longest prime number in the world , M77232917 .
The numbers cataloged as “prime” are those, which, as is well known, are only divisible between themselves and the number 1: 2, 3, 5, 7, 11, 13, 17 …
Euclides, mathematician of Ancient Greece and nicknamed ‘Father of Geometry’, established a theorem more than 2,000 years ago by which he ensured that the number of prime numbers is infinite . On this basis, the challenge facing humans today is, ultimately, to reveal the ins and outs and each of the numbers that make up this endless list.
The new figure, 2 raised to 77,232,917 power -1, exceeds the previous record for this modality by one million, reaching a scandalous amount of more than 23 million digits (specifically 23,249,425). This extension is so large that it is estimated that it would occupy approximately 9,000 pages .
The find was made possible by six days of continuous computing with one of Pace’s personal computers, an Intel i5-6600 processor. In addition, the result has been verified by four volunteers with computers such as Intel Xeon, AMD RX Vega 64 GPU, NVidia Titan Black GPU, Amazon AWS and 32-core Intel Xeon.
More important than you think
M77232917 has been a real discovery because it belongs to a peculiar family of figures, that of the Mersenne prime numbers. These owe their name to the French philosopher and mathematician Marin Marsenne. These figures are obtained by subtracting 1 from a power of two (2 n – 1) . Thus, for example 2 2 – 1 = 3, 3 is Mersenne’s first prime. Very few digits with these characteristics are known, and the discovery ranks fiftieth among known Mersenne primes .
However, what is special about them? Prime numbers themselves are very useful for different areas of everyday life , such as cryptography and banking. The RSA cryptographic algorithm (Rivest, Shamir and Adleman), which is used to guarantee the security of information exchange on the web , is based on this decomposition of integers into prime numbers. The bigger these are, the harder it will be to break the code. For this reason, the privacy of communications or commercial transactions over the Internet depends, to a large extent, on prime numbers.
Pace, 51, is thus a member of what is known as the Great Internet Mersenne Prime Search , a collaborative project created in 1996 that seeks, through of free programs, prime numbers of this type.
