# table of factors of small Mersenne numbers

The following table lists the prime factors^{} for some small Mersenne numbers, specifically, numbers of the form ${2}^{p}-1$ where $p$ is a prime in the range $$ and ${2}^{p}-1$ is composite. Thus, the following values of $p$ have been left off the table: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127 and all primes greater than 199 (see table of Mersenne primes). The numbers get quite large, and correspondingly, so do their factors. All these numbers are squarefree^{} (given the Möbius function, $\mu ({2}^{p}-1)\ne 0$). Their factors are all of the form $2mp+1$, with $m$ in the range $$.

$p$ | Factors of ${2}^{p}-1$ |
---|---|

11 | 23, 89 |

23 | 47, 178481 |

29 | 233, 1103, 2089 |

37 | 223, 616318177 |

41 | 13367, 164511353 |

43 | 431, 9719, 2099863 |

47 | 2351, 4513, 13264529 |

53 | 6361, 69431, 20394401 |

59 | 179951, 3203431780337 |

67 | 193707721, 761838257287 |

71 | 228479, 48544121, 212885833 |

73 | 439, 2298041, 9361973132609 |

79 | 2687, 202029703, 1113491139767 |

83 | 167, 57912614113275649087721 |

97 | 11447, 13842607235828485645766393 |

101 | 7432339208719, 341117531003194129 |

103 | 2550183799, 3976656429941438590393 |

109 | 745988807, 870035986098720987332873 |

113 | 3391, 23279, 65993, 1868569, 1066818132868207 |

131 | 263, 10350794431055162386718619237468234569 |

137 | 32032215596496435569, 5439042183600204290159 |

139 | 5625767248687, 123876132205208335762278423601 |

149 | 86656268566282183151, 8235109336690846723986161 |

151 | 18121, 55871, 165799, 2332951, 7289088383388253664437433 |

157 | 852133201, 60726444167, 1654058017289, 2134387368610417 |

163 | 150287, 704161, 110211473, 27669118297, 36230454570129675721 |

167 | 2349023, 79638304766856507377778616296087448490695649 |

173 | 730753, 1505447, 70084436712553223, 155285743288572277679887 |

179 | 359, 1433, 1489459109360039866456940197095433721664951999121 |

181 | 43441, 1164193, 7648337, 7923871097285295625344647665764672671 |

191 | 383, 7068569257, 39940132241, 332584516519201, 87274497124602996457 |

193 | 13821503, 61654440233248340616559, 14732265321145317331353282383 |

197 | 7487, 26828803997912886929710867041891989490486893845712448833 |

199 | 164504919713, 4884164093883941177660049098586324302977543600799 |

Title | table of factors of small Mersenne numbers |
---|---|

Canonical name | TableOfFactorsOfSmallMersenneNumbers |

Date of creation | 2013-03-22 18:05:55 |

Last modified on | 2013-03-22 18:05:55 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |