Mersenne primes: Difference between revisions
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Welcome to the Wikiversity '''Mersenne Primes Learning Project'''. |
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Marin Mersenne's name is widely known because of his interest in prime numbers that are one less than a power of two. Mersenne also did research in the area of the theory of music and musical instruments (see [[w:Marin Mersenne|Wikipedia]]). Participants in this learning project are encouraged to join the distributed computing project that allows the computing power of personal computers to help search for Mersenne prime numbers (see [[#Research Project|Research Project]], below). |
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==Mersenne prime numbers== |
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In [[School:Mathematics|Mathematics]], Mersenne prime numbers are those [[prime numbers]] which are one less than a power of two. |
In [[School:Mathematics|Mathematics]], Mersenne prime numbers are those [[prime numbers]] which are one less than a power of two. |
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<math>Mn=2^n - 1\,\ </math> |
<math>Mn=2^n - 1\,\ </math> |
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if <math>n\,\ </math> is not a prime number then |
if <math>n\,\ </math> is not a prime number, then <math>n\,\ </math> can be written as, <math>n=a\cdot b\,\ </math> |
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<math>Mn=2^n-1=2^{ab}-1=(2^a-1)\cdot \left(1+2^a+2^{2a}+2^{3a}+\dots+2^{(b-1)a}\right)\,\ </math> |
<math>Mn=2^n-1=2^{ab}-1=(2^a-1)\cdot \left(1+2^a+2^{2a}+2^{3a}+\dots+2^{(b-1)a}\right)\,\ </math> |
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|5 |
|5 |
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|31 |
|31 |
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|'''Third |
|'''Third Mersenne prime''' |
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|7 |
|7 |
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|127 |
|127 |
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|''' |
|'''Fourth Mersenne prime''' |
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|11 |
|11 |
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|41 |
|41 |
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|2199023255551 |
|2199023255551 |
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|13367, 164511353 |
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|43 |
|43 |
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|8796093022207 |
|8796093022207 |
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|431, 9719, 2099863 |
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|47 |
|47 |
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|140737488355327 |
|140737488355327 |
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|2351, 4513, 13264529 |
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|53 |
|53 |
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|9007199254740991 |
|9007199254740991 |
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|6361, 69431, 20394401 |
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|- |
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|59 |
|59 |
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|576460752303423487 |
|576460752303423487 |
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|179951, 3203431780337 |
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|61 |
|61 |
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|67 |
|67 |
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|147573952589676412927 |
|147573952589676412927 |
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|193707721, 761838257287 |
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|71 |
|71 |
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|2361183241434822606847 |
|2361183241434822606847 |
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|228479, 48544121, 212885833 |
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|73 |
|73 |
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|9444732965739290427391 |
|9444732965739290427391 |
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|439, 2298041, 9361973132609 |
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|79 |
|79 |
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|604462909807314587353087 |
|604462909807314587353087 |
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|2687, 202029703, 1113491139767 |
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|83 |
|83 |
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|9671406556917033397649407 |
|9671406556917033397649407 |
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|167, 57912614113275649187721 |
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|89 |
|89 |
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|97 |
|97 |
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|158456325028528675187087900671 |
|158456325028528675187087900671 |
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|11447, 13842607235828485645766393 |
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|- |
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|101 |
|101 |
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|2535301200456458802993406410751 |
|2535301200456458802993406410751 |
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|7432339208719, 341117531003194129 |
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|103 |
|103 |
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|10141204801825835211973625643007 |
|10141204801825835211973625643007 |
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|2550183799, 3976656429941438590393 |
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|107 |
|107 |
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|162259276829213363391578010288127 |
|162259276829213363391578010288127 |
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|'''Eleventh Mersenne prime''' |
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|109 |
|109 |
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|649037107316853453566312041152511 |
|649037107316853453566312041152511 |
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|745988807, 870035986098720987332873 |
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|113 |
|113 |
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|10384593717069655257060992658440191 |
|10384593717069655257060992658440191 |
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|3391, 23279, 65993, 1868569, 1066818132868207 |
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|127 |
|127 |
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|170141183460469231731687303715884105727 |
|170141183460469231731687303715884105727 |
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|''' |
|'''Twelfth Mersenne prime''' |
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|131 |
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|2722258935367507707706996859454145691647 |
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|263, 10350794431055162386718619237468234569 |
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|137 |
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|174224571863520493293247799005065324265471 |
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|32032215596496435569, 5439042183600204290159 |
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|139 |
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|696898287454081973172991196020261297061887 |
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|5625767248687, 123876132205208335762278423601 |
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|149 |
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|713623846352979940529142984724747568191373311 |
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|86656268566282183151, 8235109336690846723986161 |
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|151 |
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|2854495385411919762116571938898990272765493247 |
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|18121, 55871, 165799, 2332951, 7289088383388253664437433 |
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|157 |
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|182687704666362864775460604089535377456991567871 |
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|852133201, 60726444167, 1654058017289, 2134387368610417 |
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|163 |
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|11692013098647223345629478661730264157247460343807 |
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|150287, 704161, 110211473, 27669118297, 36230454570129675721 |
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|167 |
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|187072209578355573530071658587684226515959365500927 |
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|2349023, 79638304766856507377778616296087448490695649 |
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|173 |
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|11972621413014756705924586149611790497021399392059391 |
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|730753, 1505447, 70084436712553223, 155285743288572277679887 |
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|179 |
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|766247770432944429179173513575154591809369561091801087 |
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|359, 1433, 1489459109360039866456940197095433721664951999121 |
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|181 |
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|3064991081731777716716694054300618367237478244367204351 |
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|43441, 1164193, 7648337, 7923871097285295625344647665764672671 |
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|191 |
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|3138550867693340381917894711603833208051177722232017256447 |
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|383, 7068569257, 39940132241, 332584516519201, 87274497124602996457 |
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|193 |
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|12554203470773361527671578846415332832204710888928069025791 |
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|13821503, 61654440233248340616559, 14732265321145317331353282383 |
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|197 |
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|200867255532373784442745261542645325315275374222849104412671 |
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|7487, 26828803997912886929710867041891989490486893845712448833 |
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|199 |
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|803469022129495137770981046170581301261101496891396417650687 |
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|164504919713, 4884164093883941177660049098586324302977543600799 |
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|211 |
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|3291009114642412084309938365114701009965471731267159726697218047 |
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|15193, 60272956433838849161, 3593875704495823757388199894268773153439 |
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==See also== |
==See also== |
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*[http://mersennewiki.org/index.php/Main_Page Mersenne wiki] |
*[http://mersennewiki.org/index.php/Main_Page Mersenne wiki] |
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[[Category: |
[[Category:Prime numbers]] |
Latest revision as of 07:40, 25 February 2024
Welcome to the Wikiversity Mersenne Primes Learning Project.
Marin Mersenne's name is widely known because of his interest in prime numbers that are one less than a power of two. Mersenne also did research in the area of the theory of music and musical instruments (see Wikipedia). Participants in this learning project are encouraged to join the distributed computing project that allows the computing power of personal computers to help search for Mersenne prime numbers (see Research Project, below).
Mersenne prime numbers
[edit | edit source]In Mathematics, Mersenne prime numbers are those prime numbers which are one less than a power of two.
if is not a prime number, then can be written as,
- This implies, the Mersenne number is not a prime number if n is not prime.
To find Mersenne primes
[edit | edit source]Prime factors | ||
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2 | 3 | First Mersenne prime |
3 | 7 | Second Mersenne prime |
5 | 31 | Third Mersenne prime |
7 | 127 | Fourth Mersenne prime |
11 | 2047 | 23, 89 |
13 | 8191 | Fifth Mersenne prime |
17 | 131071 | Sixth Mersenne prime |
19 | 524287 | Seventh Mersenne prime |
23 | 8388607 | 47, 178481 |
29 | 536870911 | 233, 1103, 2089 |
31 | 2147483647 | Eighth Mersenne prime |
37 | 137438953471 | 223, 616318177 |
41 | 2199023255551 | 13367, 164511353 |
43 | 8796093022207 | 431, 9719, 2099863 |
47 | 140737488355327 | 2351, 4513, 13264529 |
53 | 9007199254740991 | 6361, 69431, 20394401 |
59 | 576460752303423487 | 179951, 3203431780337 |
61 | 2305843009213693951 | Ninth Mersenne prime |
67 | 147573952589676412927 | 193707721, 761838257287 |
71 | 2361183241434822606847 | 228479, 48544121, 212885833 |
73 | 9444732965739290427391 | 439, 2298041, 9361973132609 |
79 | 604462909807314587353087 | 2687, 202029703, 1113491139767 |
83 | 9671406556917033397649407 | 167, 57912614113275649187721 |
89 | 618970019642690137449562111 | Tenth Mersenne prime |
97 | 158456325028528675187087900671 | 11447, 13842607235828485645766393 |
101 | 2535301200456458802993406410751 | 7432339208719, 341117531003194129 |
103 | 10141204801825835211973625643007 | 2550183799, 3976656429941438590393 |
107 | 162259276829213363391578010288127 | Eleventh Mersenne prime |
109 | 649037107316853453566312041152511 | 745988807, 870035986098720987332873 |
113 | 10384593717069655257060992658440191 | 3391, 23279, 65993, 1868569, 1066818132868207 |
127 | 170141183460469231731687303715884105727 | Twelfth Mersenne prime |
131 | 2722258935367507707706996859454145691647 | 263, 10350794431055162386718619237468234569 |
137 | 174224571863520493293247799005065324265471 | 32032215596496435569, 5439042183600204290159 |
139 | 696898287454081973172991196020261297061887 | 5625767248687, 123876132205208335762278423601 |
149 | 713623846352979940529142984724747568191373311 | 86656268566282183151, 8235109336690846723986161 |
151 | 2854495385411919762116571938898990272765493247 | 18121, 55871, 165799, 2332951, 7289088383388253664437433 |
157 | 182687704666362864775460604089535377456991567871 | 852133201, 60726444167, 1654058017289, 2134387368610417 |
163 | 11692013098647223345629478661730264157247460343807 | 150287, 704161, 110211473, 27669118297, 36230454570129675721 |
167 | 187072209578355573530071658587684226515959365500927 | 2349023, 79638304766856507377778616296087448490695649 |
173 | 11972621413014756705924586149611790497021399392059391 | 730753, 1505447, 70084436712553223, 155285743288572277679887 |
179 | 766247770432944429179173513575154591809369561091801087 | 359, 1433, 1489459109360039866456940197095433721664951999121 |
181 | 3064991081731777716716694054300618367237478244367204351 | 43441, 1164193, 7648337, 7923871097285295625344647665764672671 |
191 | 3138550867693340381917894711603833208051177722232017256447 | 383, 7068569257, 39940132241, 332584516519201, 87274497124602996457 |
193 | 12554203470773361527671578846415332832204710888928069025791 | 13821503, 61654440233248340616559, 14732265321145317331353282383 |
197 | 200867255532373784442745261542645325315275374222849104412671 | 7487, 26828803997912886929710867041891989490486893845712448833 |
199 | 803469022129495137770981046170581301261101496891396417650687 | 164504919713, 4884164093883941177660049098586324302977543600799 |
211 | 3291009114642412084309938365114701009965471731267159726697218047 | 15193, 60272956433838849161, 3593875704495823757388199894268773153439 |
Research Project
[edit | edit source]Join the Great Internet Mersenne Prime Search. Describe your experience below.