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Bilangan prima Mersenne

Bilangan prima Mersenne adalah sebuah bilangan prima dengan rumus:

Mn = 2n − 1.

Di antara semua bilangan prima Mersenne yang sudah ditemukan, sepuluh bilangan terbesarnya ditemukan dengan menggunakan GIMPS. Bilangan prima Mersenne terbesar, sekaligus bilangan prima terbesar yang diketahui saat ini memiliki 17,425,170 digit angka. Kebanyakan bilangan-bilangan prima terbesar yang diketahui merupakan bilangan prima Mersenne.

Belum diketahui apakah jumlah bilangan prima Mersenne benar-benar tak terhingga.

Berikut adalah tabel daftar bilangan prima Mersenne yang sudah ditemukan.

# n Mn Jumlah angka dalam Mn Tanggal ditemukan Penemu
1 2 3 1
2 3 7 1
3 5 31 2
4 7 127 3
5 13 8191 4 1456
6 17 131071 6 1588 Cataldi
7 19 524287 6 1588 Cataldi
8 31 2147483647 10 1772 Euler
9 61 2305843009213693951 19 1883 Pervushin
10 89 618970019…449562111 27 1911 Powers
11 107 162259276…010288127 33 1914 Powers
12 127 170141183…884105727 39 1876 Lucas
13 521 686479766…115057151 157 30 Januari 1952 Robinson
14 607 531137992…031728127 183 30 Januari 1952 Robinson
15 1,279 104079321…168729087 386 25 Juni 1952 Robinson
16 2,203 147597991…697771007 664 7 Oktober 1952 Robinson
17 2,281 446087557…132836351 687 9 Oktober 1952 Robinson
18 3,217 259117086…909315071 969 8 September 1957 Riesel
19 4,253 190797007…350484991 1.281 3 November 1961 Hurwitz
20 4,423 285542542…608580607 1.332 3 November 1961 Hurwitz
21 9,689 478220278…225754111 2.917 11 Mei 1963 Gillies
22 9,941 346088282…789463551 2.993 16 Mei 1963 Gillies
23 11,213 281411201…696392191 3.376 2 Juni 1963 Gillies
24 19,937 431542479…968041471 6.002 4 Maret 1971 Tuckerman
25 21,701 448679166…511882751 6.533 30 Oktober 1978 Noll & Nickel
26 23,209 402874115…779264511 6.987 9 Februari 1979 Noll
27 44.497 854509824…011228671 13,395 8 April 1979 Nelson & Slowinski
28 86.243 536927995…433438207 25,962 25 September 1982 Slowinski
29 110.503 521928313…465515007 33,265 28 Januari 1988 Colquitt & Welsh
30 132,049 512740276…730061311 39.751 20 September 1983 Slowinski
31 216,091 746093103…815528447 65.050 6 September 1985 Slowinski
32 756,839 174135906…544677887 227.832 19 Februari 1992 Slowinski & Gage
33 859,433 129498125…500142591 258.716 10 Januari 1994 Slowinski & Gage
34 1,257,787 412245773…089366527 378.632 3 September 1996 Slowinski & Gage
35 1,398,269 814717564…451315711 420.921 13 November 1996 GIMPS / Joel Armengaud
36 2,976,221 623340076…729201151 895.932 24 Agustus 1997 GIMPS / Gordon Spence
37 3,021,377 127411683…024694271 909.526 27 Januari 1998 GIMPS / Roland Clarkson
38 6,972,593 437075744…924193791 2.098.960 1 Juni 1999 GIMPS / Nayan Hajratwala
39 13,466,917 924947738…256259071 4.053.946 14 November 2001 GIMPS / Michael Cameron
40* 20,996,011 125976895…855682047 6.320.430 17 November 2003 GIMPS / Michael Shafer
41* 24,036,583 299410429…733969407 7.235.733 15 Mei 2004 GIMPS / Josh Findley
42* 25,964,951 122164630…577077247 7.816.230 18 Februari 2005 GIMPS / Martin Nowak
43* 30,402,457 315416475…652943871 9.152.052 15 Desember 2005 GIMPS / Curtis Cooper dan Steven Boone
44* 32,582,657 124575026…053967871 9.808.358 4 September 2006 GIMPS / Curtis Cooper dan Steven Boone [1]
45* 37,156,667 202254406…308220927 11.185.272 6 September 2008 GIMPS / Hans-Michael Elvenich[1]
46* 42,643,801 169873516…562314751 12.837.064 12 April 2009 GIMPS / Odd M. Strindmo[2]
47* 43,112,609 316470269…697152511 12.978.189 23 Agustus 2008 GIMPS / Edson Smith[1]
48* 57,885,161 581887266…724285951 17,425,170 25 Januari 2013 GIMPS / Curtis Cooper[3][4]

Keterangan:
*Belum diketahui apakah ada bilangan prima Mersenne yang berada di antara bilangan ke-39 (M13,466,917) dan bilangan ke-44 (M32,582,657) yang belum ditemukan, sehingga posisi-posisi ini dapat saja berubah.

Pranala luar

Wikisumber memiliki naskah asli yang berkaitan dengan artikel ini:

Referensi

  1. ^ a b Titanic Primes Raced to Win $100,000 Research Award. Retrieved on 2008-09-16.
  2. ^ "On April 12th [2009], the 47th known Mersenne prime, 242,643,801-1, 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 last August.", The List of Largest Known Primes Home Page, http://primes.utm.edu/primes/page.php?id=88847 [retrieved 2012-09-18]
  3. ^ Utomo, Yunanto Wiji. yunan, ed. "Eureka! Bilangan Prima Terbesar Ditemukan". Kompas.com. Diakses tanggal 7 Februari 2013. 
  4. ^ Woltman, George. "NEW MERSENNE PRIME! TOTALLY MERSENNE THIS TIME! thread". mersenneforum. Diakses tanggal 5 February 2013. 

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