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