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Discovering the Largest Prime Number

By Katie Lee on 2018-09-17

Researchers have found the new highest prime number which has a magnitude of nearly infinity according to non-super calculators.

It is known that prime numbers are numbers that cannot be divided by other numbers to create a whole quotient other than itself. Prime numbers seem to appear randomly in the natural number sequence with the first prime number being one, though it is disputed if the number one is prime or not since the early Greeks did not consider one to even be a number thus it could not be prime. In modern times, moreover, there are mathematicians who consider one to prime, and there are others who claim one is not prime. If one is considered to not be prime, then the first prime number would be three.

The dispute over the first prime number is part of the reason researchers have been interested in finding the largest prime number. They believed that it is possible that the largest prime number could lead to the identification of the number one as prime or divisible.

GIMPS (or the Great Internet Mersenne Prime Search) has actually discovered the largest known prime number. The number was found to be an amazingly large number at 277,232,917, which contains 23,249, 425 digits. The number is written exponentially since it would be a real pain to write it out digit by digit.

The find was made on December 26, 2017 by a computer that was volunteered by Jonathan Pace, one of many people using the free GIMPS software.

The new number has been nicknamed M77232917 after the exponent involved in the number. The name is certainly easier to say than the number that would come up on a super calculator. The number is so high on the natural number scale that if you type the exponent in a scientific calculator, the result would simply be “infinity.”

The prime number was calculated by multiplying 2 times 2, 77,232,917 times since that is how exponents are calculated. After that, researchers subtracted one since any number multiplied by 2 will not be prime. By subtracting one, researchers were able to create a prime number. Subtracting one also works for smaller numbers in some cases such as 7 times 2 which is the equivalent of 14 and then 14-1 equals 13 which is prime.

This number is extraordinary considering the fact that it is nearly one million digits longer than the previous prime number recorded. M77232917 is also part of a special class of rare prime numbers known as the “Mersenne Primes,” which at the moment only includes 50 numbers. These fifty numbers, however, increase in their difficulty to find naturally. By find naturally, researchers allude to the fact that some numbers are found in nature. Sometimes prime numbers manifest in the diameter of a flower or as the radius of a planet. These “Mersenne Primes” are very rarely found in nature or they have never been found in nature.

The researchers did not stop at simply calculating M77232917, they then had to perform a proof calculation to see if the number is actually prime. This proof took six days of non-stop calculation on a computer with an intel i5-6600 Central Processing Unit.

The next goal of the GIMPS researchers is to claim the $150,000 reward for finding and providing a proof for a 100 million digit prime number.

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