Largest known prime number

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The largest known prime number (as of March 2018) is 2^77,232,917 - 1, a number with 23,249,425 digits. It was found by the Great Internet Mersenne Prime Search (GIMPS) in 2017.

Euclid proved that there is no largest prime number, and many mathematicians and hobbyists continue to search for large prime numbers.

Many of the largest known primes are Mersenne primes. As of January 2018, the seven largest known primes are Mersenne primes. The last 16 record primes were Mersenne primes.

The fast Fourier transform implementation of the Lucas-Lehmer primality test for Mersenne numbers is fast compared to other known primality tests for other kinds of numbers.

Video Largest known prime number

The current record

The record is currently held by 2^77,232,917 - 1 with 23,249,425 digits, found by GIMPS in December 2017. Its value is:

467333183359231099988335585561115521251321102817714495798582338593567923480521177207484311099740208849621368090038049317...

(23,249,185 digits omitted)

...285376004518786055402223376672925679282131965467343395945397370476369279894627999939614659217371136582730618069762179071

The first and last 120 digits are shown above.

Maps Largest known prime number

Prizes

The Great Internet Mersenne Prime Search (GIMPS) currently offers a US$3000 research discovery award for participants who download and run their free software and whose computer discovers a new Mersenne prime having fewer than 100 million digits.

There are several prizes offered by the Electronic Frontier Foundation for record primes. GIMPS is also coordinating its long-range search efforts for primes of 100 million digits and larger and will split the Electronic Frontier Foundation's US$150,000 prize with a winning participant.

The record passed one million digits in 1999, earning a US$50,000 prize. In 2008 the record passed ten million digits, earning a US$100,000 prize and a Cooperative Computing Award from the Electronic Frontier Foundation. Time called it the 29th top invention of 2008. Both the US$50,000 and the US$100,000 prizes were won by participation in GIMPS. Additional prizes are being offered for the first prime number found with at least one hundred million digits and the first with at least one billion digits.

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History

The following table lists the progression of the largest known prime number in ascending order. Here M_n = 2ⁿ - 1 is the Mersenne number with exponent n. The longest record-holder known was M₁₉ = 524,287, which was the largest known prime for 144 years. Almost no records are known before 1456.

GIMPS found the fourteen latest records (all of them Mersenne primes) on ordinary computers operated by participants around the world.

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The twenty largest known prime numbers

A list of the 5,000 largest known primes is maintained by Chris K. Caldwell, the twenty largest are listed below.

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See also

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References

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External links

• Press release about the largest known prime 2^77,232,917-1
• Press release about the former largest known prime 2^74,207,281-1
• Press release about the former largest known prime 2^57,885,161-1
• Press release about the former largest known prime 2^43,112,609-1
• Press release about the former largest known prime 2^32,582,657-1

Source of the article : Wikipedia