Mersenne Prime Numbers


On April 12, 2009, the 47th known Mersenne prime, 2242,643,801 - 1, a 12,837,064 digit number was found by Odd Magnar Strindmo from Melhus, Norway! This prime is the second largest known prime number, a "mere" 141,125 digits smaller than the Mersenne prime found in August 2008.
 

On September 6, 2008, the 46th known Mersenne prime, 2237,156,667 - 1, a 11,185,272 digit number was found by Hans-Michael Elvenich in Langenfeld near Cologne, Germany!
 

On August 23, 2008, Edson Smith using a UCLA computer discovered the 45th known Mersenne prime, 2243,112,609 - 1, a mammoth 12,978,189 digit number!
 

On September 4, 2006, Dr. Curtis Cooper and Dr. Steven Boone's CMSU team, found the largest known prime number at that time, 232,582,657 - 1.   The prime number has 9,808,358 digits!   This is the 44th Mersenne Prime Number.
 

On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime, 230,402,457 - 1.   The prime number has 9,152,052 digits!
 

On February 18, 2005, Dr. Martin Nowak from Germany, found the 42nd Mersenne Prime, 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 47 known Mersenne primes (as of June 2009).
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 2^127-1 39 1876 Lucas
10 2^61-1 19 1883 Pervushin
11 2^89-1 27 1911 Powers
12 2^107-1 33 1914 Powers
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 2^132049-1 39,751 1983 Slowinski
30 2^216091-1 65,050 1985 Slowinski
31 2^110503-1 33,265 1988 Colquitt
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
43 2^30402457-1 9,152,052 2005 Cooper/Boone
44 2^32582657-1 9,808,358 2006 Cooper/Boone
45 2^243112609-1 12,978,189 2008 Edson Smith
46 2^237156667-1 11,185,272 2008 Hans-Michael Elvenich
47 2^242643801-1 12,837,064 2009 Odd Magnar Strindmo

sources:

Dr. Michael W. Ecker
Editor and Publisher
Recreational & Educational Computing
187 Ferguson Avenue, Suite D
Shavertown, PA 18708

Great Internet Mersenne Prime Search
http://www.mersenne.org/default.php

Links:

Prime Curios!

Prime Pages

The Great Internet Mersenne Prime Search

Prime List of Primes

Math Facts Page