Mersenne Prime Numbers


On February 18, 2005, Dr. Martin Nowak from Germany, found the new largest known prime number, 225,964,951 - 1.   The prime number has 7,816,230 digits!   It took more than 50 days of calculations on Dr. Nowak's 2.4 GHz Pentium 4 computer.

On May 15, 2004, Josh Findley discovered the 41st Mersenne Prime, 224,036,583 - 1.   The number has 7,235,733 digits.   Josh's calculation took two weeks on his 2.4 GHz Pentium 4 PC.

In the December 22, 2003, issue of Newsweek magazine, Michael Shafer was quoted as saying, "I don't think I'm going to be recognized as I go down the street."   He had discovered the largest known prime number up to that time, which was 6,320,430 digits long.

On November 14, 2001, Michael Cameron, a 20-year-old Canadian had discovered the previously largest known prime number to date: 213,466,917 - 1

On June 1, 1999, in Orlando, Florida, Nayan Hajratwala discovered the first million-digit prime number.   The feat was accomplished using software written by George Woltman.
The prime number, 26,972,593 - 1, contains 2,098,960 digits.   Nayan used a 350 MHz Pentium II IBM Aptiva computer running part-time for 111 days to prove the number prime.   Running uninterupted, it would take about three weeks to test this number.

The new prime number is one of a special class of primes called Mersenne primes.   Mersenne primes are of the form 2p - 1.   They are named after Marin Mersenne, the French monk born in 1588 who investigated prime numbers of the form 2p - 1.
There are only 42 known Mersenne primes.
They are listed below:

Index Number Digits in Number Year Discoverer
1 2^2-1 1 - -
2 2^3-1 1 - -
3 2^5-1 2 - -
4 2^7-1 3 - -
5 2^13-1 4 1461 -
6 2^17-1 6 1588 Cataldi
7 2^19-1 6 1588 Cataldi
8 2^31-1 10 1750 Euler
9 2^61-1 19 1883 Pervushin
10 2^89-1 27 1911 Powers
11 2^107-1 33 1914 Powers
12 2^127-1 39 1876 Lucas
13 2^521-1 157 1952 Robinson
14 2^607-1 183 1952 Robinson
15 2^1279-1 386 1952 Robinson
16 2^2203-1 664 1952 Robinson
17 2^2281-1 687 1952 Robinson
18 2^3217-1 969 1957 Riesel
19 2^4253-1 1,281 1961 Hurwitz
20 2^4423-1 1,332 1961 Hurwitz
21 2^9689-1 2,917 1963 Gillies
22 2^9941-1 2,993 1963 Gillies
23 2^11213-1 3,376 1963 Gillies
24 2^19937-1 6,002 1971 Tuckerman
25 2^21701-1 6,533 1978 Noll
26 2^23209-1 6,987 1979 Noll
27 2^44497-1 13,395 1979 Slowinski
28 2^86243-1 25,962 1982 Slowinski
29 2^110503-1 33,265 1988 Colquitt
30 2^132049-1 39,751 1983 Slowinski
31 2^216091-1 65,050 1985 Slowinski
32 2^756839-1 227,832 1992 Slowinski
33 2^859433-1 258,716 1994 Slowinski
34 2^1257787-1 378,632 1996 Slowinski
35 2^1398269-1 420,921 1996 Armengaud
36 2^2976221-1 895,932 1997 Spence
37 2^3021377-1 909,526 1998 Clarkson
38 2^6972593-1 2,098,960 1999 Hajratwala
39 2^13466917-1 4,053,946 2001 Cameron
40 2^20996011-1 6,320,430 2003 Shafer
41 2^24036583-1 7,235,733 2004 Findley
42 2^25964951-1 7,816,230 2005 Nowak

source: Dr. Michael W. Ecker
Editor and Publisher
Recreational & Educational Computing
187 Ferguson Avenue, Suite D
Shavertown, PA 18708
e-mail: DrMWEcker@aol.com

Links:

Prime Pages

The Great Internet Mersenne Prime Search

Recreational & Educational Computing

Prime List of Primes

Math Facts Page

Handley Math Home Page