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The largest known prime number is 2 82,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. [1] A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer.
The largest number reliably factored [clarification needed] by Shor's algorithm is 21 which was factored in 2012. [ 23 ] 15 had previously been factored by several labs. In April 2012, the factorization of 143 = 13 × 11 by a room-temperature (300 K) NMR adiabatic quantum computer was reported by a group led by Xinhua Peng. [ 24 ]
In number theory, the general number field sieve ( GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity for factoring an integer n (consisting of ⌊log2 n⌋ + 1 bits) is of the form. in O and L-notations. [1] It is a generalization of the special number field sieve ...
Graham's number was used by Graham in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on. In 1977, Gardner described the number in Scientific American, introducing it to the general public. At the time of its introduction, it was the largest specific positive ...
Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg , can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg ...
Greatest common divisor. In mathematics, the greatest common divisor ( GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. [ 1][ 2]
Rayo's number is a large number named after Mexican philosophy professor Agustín Rayo which has been claimed to be the largest named number. [ 1 ] [ 2 ] It was originally defined in a "big number duel" at MIT on 26 January 2007.
The Ancient Greeks used a system based on the myriad, that is, ten thousand, and their largest named number was a myriad myriad, or one hundred million. In The Sand Reckoner, Archimedes (c. 287–212 BC) devised a system of naming large numbers reaching up to. , essentially by naming powers of a myriad myriad. This largest number appears ...