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 $1 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, $\mu(2^{p}-1)\neq 0$). Their factors are all of the form $2mp+1$, with $m$ in the range $0.

$p$ 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 TableOfFactorsOfSmallMersenneNumbers 2013-03-22 18:05:55 2013-03-22 18:05:55 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 11A41