What is the biggest prime number and who calculated it....?

Question

References please....

Answer 1

There is no largest prime, since there are an infinite number of prime numbers, but there is a largest *known* prime number. It's a Mersenne prime (of the form 2^p-1) where p is another prime. Specifically it is 2 ^ 30,402,457 - 1. The number is too big to represent here because it is 9,152,052 digits long.

This number and most of the recent Mersenne primes were calculated using a collective effort known as the 'Greater Internet Mersenne Prime Search' (or GIMPS) for short. Several tens of thousands of volunteers around the world are using background processing time on their PCs to check these high-digit Mersenne primes.

The number 30,402,457 was tested as the exponent in 2^p-1 and the result was found to be prime as part of this GIMPS project. The credit goes to both the project (all contributors to the GIMPS project) and to the people who were running that specific test. In this case it was Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University who discovered it December 15, 2005. The official credit for this new discovery is listed as "Cooper, Boone, Woltman, Kurowski, et. al.". By the way, I'm one of the et. al. having racked up several years of computational time running tests.

The search continues and there is a prize for the person that finds the next prime number of over 10 million digits... join now if you want to share part of the $100,000 pot.

If you want to know the English name of the current largest known prime, it starts, "three hundred fifteen tremillia millia quin quagin millia sescendo octo gintillion, four hundred sixteen tremillia millia quin quagin millia sescenun octo gintillion..." (See the last link for the full name.)

Answer 2

There are an infinite number of prime numbers
The oldest known proof for the statement that there are infinitely many prime numbers is given by the Greek mathematician Euclid in his Elements (Book IX, Proposition 20). Euclid states the result as "there are more than any given [finite] number of primes", and his proof is essentially the following:

Suppose you have a finite number of primes. Call this number m. Multiply all m primes together and add one. The resulting number is not divisible by any of the finite set of primes, because dividing by any of these would give a remainder of one. And one is not divisible by any primes. Therefore it must either be prime itself, or be divisible by some other prime that was not included in the finite set. Either way, there must be at least m + 1 primes. But this argument applies no matter what m is; it applies to m + 1, too. So there are more primes than any given finite number.

The largest prime found so far is the 43rd Mersenne Prime, The 42nd was found in February 2005, the 43rd in December 2005, so expect another larger one soon.

Mersenne Primes of the form 2^p -1 and when discovered
M1 p=2
M2 p=3
M3 p=5
M4 p=7
M5 p=13 1456 anonymous
M6 p=17 1588 Cataldi
M7 p=19 1588 Cataldi
M8 p=31 1772 Euler
M9 p=61 1883 Pervushin
M10 p=89 1911 Powers
M11 p=107 1914 Powers
M12 p=127 1876 Lucas
M13 p=521 1952 Robinson
M14 p=607 1952 Robinson
M15 p=1279 1952 Robinson
M16 p=2203 1952 Robinson
M17 p=2281 1952 Robinson
M18 p=3217 1957 Riesel
M19 p=4253 1961 Hurwitz
M20 p=4423 1961 Hurwitz
M21 p=9689 1963 Gillies
M22 p=9941 1963 Gillies
M23 p=11213 1963 Gillies
M24 p=19937 1971 Tuckerman
M25 p=21701 1978 Noll & Nickel
M26 p=23209 1979 Noll
M27 p=44497 1979 Nelson & Slowinski
M28 p=86243 1982 Slowinski
M29 p=110503 1988 Colquitt & Welsh
M30 p=132049 1983 Slowinski
M31 p=216091 1985 Slowinski
M32 p=756839 1992 Slowinski & Gage
M33 p=859433 1994 Slowinski & Gage
M34 p=1257787 1996 Slowinski & Gage
M35 p=1398269 1996 Armengaud, Woltman
M36 p=2976221 1997 Spence, Woltman,
M37 p=3021377 1998 Clarkson, Woltman, Kurowski
M38 p=6972593 1999 Hajratwala, Woltman, Kurowski
M39 p=13466917 2001 Cameron, Woltman, Kurowski
M40 p=20996011 2003 Shafer, Woltman, Kurowski
M41 p=24036583 2004 Findley, Woltman, Kurowski
M42 p=25964951 2005 Nowak, Woltman, Kurowski
M43 p=30402457 2005 Cooper, Boone, Woltman, Kurowski

Answer 3

There is a prize of $100,000 for the first person or team to hunt down a prime that is more than 10 million digits long.
.....As M42 was 7 and a bit million digits and M43 9 million and a bit digits, that prize is within reach, Presumably this is why there is so much interest in this subject and so many home PC users joining in the GIMPS project!
.....When attained, I believe there are two even larger prizes still to come, for the first 100-million-digit prime and the first billion-digit prime
.....A much healthier activity than fox hunting!

Answer 4

I think I'd start by creating an array of prime divisors from 3 to sqrt(10*18). Then, beginning from 10^18-1 — div.loop Get next divisor from array If next divisor > sqrt(test number), say test number is prime, EXIT If (test number)/divisor is an integer, test number is not prime, goto next.number goto div.loop next.number test number = current test number - 2 goto div.loop

Answer 5

There is no largest prime number dummies. Proof of this lies in the fact that if you take any number, call it x, and double it, 2x, then between x-2x there will be a prime number. Try it, it never fails.

Answer 6

there is no biggest prime number. as the set of N is infinite, whatever the current biggest prime is, there is always going to be a bigger one. We just have yet to find it.

Answer 7

, as of December 2005, is 2^30402457 − 1
by Curtis Cooper and Steven Boone

Answer 8

read: http://www.isthe.com/no.index/chongo/merdigit/long-m30402457/prime-c.html

WARNING: THIS SITE CONTAINS THE ENTIRE PRIME NUMBER, WHICH IS OVER 11 MEGABYTES!

Answer 9

2^30402457 in 2005 by Samuel Yates?

Answer 10

Graham's number - 2? They should make that the next RSA contest number...