Mersenne primes are the Mersenne numbers are prime.

Mersenne numbers are like:

mersenne primes

In the sixteenth century at same time as Fermat the French philosopher Marin Mersenne conjectured that these are numbers we are primes for:

n=2,3,5,7,13,17,19,31,67,127 y 257

Later it was demonstrated that there were some errors:

    • M67 y M257 are not prime.

    • M61, M89 y M107 are prime.

Still it’ss unknown how Mersenne could do these conjectures because a number like M127 is very large to know is prime or not.

Today this type of primes ??have a some peculiarities that make thoose algorithmically “simple” to know the primality using tests such as the Lucas-Lehmer

At present, only 48 Mersenne primes are known, being the lastest M57.885.161 is the largest prime number discovered so far. It is unknown this numebers are finite or infinite but it has been conjectured that there are infinitely.

48 Mersenne prime number list:

M2 (Unknow data) – Unknow author
M3 (Unknow data) – Unknow author
M5  (Unknow data) – Unknow author
M7 (Unknow data) – Unknow author
M13 (1456) – Anonimous
M17 (1588) – Cataldi
M19 (1588) – Cataldi
M31 (1772) – Euler
M61 (1883) – Pervushin
M89 (1911) – Powers
M107 (1914) – Powers
M127 (1876) – Lucas
M521 (30-01-1952) – Robinson (SWAC)
M607 (30-01-1952) – Robinson (SWAC)
M1279 (25-06-1952) – Robinson (SWAC)
M2203 (07-10-1952) – Robinson (SWAC)
M2281 (09-10-1952) – Robinson (SWAC)
M3217 (08-09-1957) – Riesel
M4253 (03-11-1961) – Hurwitz
M4423 (03-11-1961) – Hurwitz
M9689 (11-05-1963) – Gillies
M9941 (16-05-1963) – Gillies
M11213 (02-06-1963) – Gillies
M19937 (04-03-1971) – Tuckerman
M21701 (30-10-1978) – Noll y Nickel
M23209 (09-02-1979) – Noll
M44497 (08-04-1979) – Nelson y Slowinski
M86243 (25-09-1982) – Slowinski
M110503 (28-01-1988) – Colquitt y Welsh
M132049 (20-09-1983) – Slowinski
M216091 (06-09-1985) – Slowinski
M756839 (19-02-1992) – Slowinski, Gage
M859433 (10-01-1994) – Slowinski, Gage
M1257787 (03-09-1996) – Slowinski, Gage
M1398269 (13-11-1996) – Joel Armengaud (GIMPS)
M2976221 (24-08-1997) – Gordon Spence (GIMPS)
M3021377 (27-01-1998) – Roland Clarkson (GIMPS)
M6972593 (01-06-1999) – Nayan Hajratwala (GIMPS)
M13466917 (14-11-2001) – Michael Cameron (GIMPS)
M20996011 (17-11-2003) – Michael Shafer (GIMPS)
M24036583 (15-05-2004) – Josh Findley (GIMPS)
M25964951 (18-02-2005) – Martin Nowak (GIMPS)
M30402457 (15-12-2005) – Curtis Cooper, Steven Boone (GIMPS)
M32582657 (04-09-2006) – Curtis Cooper, Steven Boone (GIMPS)
M37156667 (06-09-2008) – Hans-Michael Elvenich (GIMPS)
M42643801 (12-04-2009) – Odd M. Strindmo (GIMPS)
M43112609 (23-08-2008) – Edson Smith (GIMPS)
M57885161 (25-01-2013) – Curtis Cooper (GIMPS)

Share this!
Share on Facebook0Share on Tumblr0Tweet about this on TwitterShare on Reddit0Share on StumbleUpon0Share on Google+0Email this to someone