"Daran" <[EMAIL PROTECTED]> asks
> Is M751 now the smallest unfactorised composite Mersenne? What is the
> smallest Mersenne not completely factorised?
M751 and M809 are the first Mersennes with no known factor.
The first holes in the 2^n - 1 table are 2,673- c151 and 2,683- c203.
This means, for example, that 2^673 - 1 is partially factored,
but it has a 151-digit composite cofactor.
The first holes in the 2^n + 1 table are 2,647+ c169 and 2,653+ c154.
The first holes in the 2LM table are 2,1238L c160 and 2,1238M c145.
These denote cofactors of 2^619 - 2^310 + 1 and 2^619 + 2^310 + 1,
both of which divide 2^1238 + 1.
Below are ten recently found factorizations.
Algebraic factors, such as the factors 23 and 89 of 2^671 - 1
(these divide 2^11 - 1, which in turn divides 2^671 - 1) do not appear.
Factors above the * lines were previously known.
Peter Montgomery
[EMAIL PROTECTED]
September, 2001
C(2,619+)
* c186 = p91.p96
1257388159910804265763446600825278256318012249697661907431303034629811311740864601663325811
576735513593459498091224888775105070536100466874272552892992673568274909599171018374973329229033
C(2,632+)
286297736737
* c177 = p66.p111
471211668918301561515489208246219513333426679953187468148445645729
514032034228747931945571962470228019101894473686825197910636442532520433593399910044880487939432413264840902977
C(2,641+)
1283 32051 139739 353833 1078163
* c169 = p59.p110
73819843823154749726309925820314356063695778208135055585507
18795947089943685289042850201861326689719641302766796883477502913493254840480457593719603600834006204492522841
C(2,641-)
35897 49999 1173835097 2401258891949526685926151441
* c148 = p69.p79
745276300734440606226386924312213175677903182797334854064486587296999
2420161564200739329410254310444778820196576654139080232429544162649795567983079
C(2,643-)
3189281
* c188 = p71.p117
22532429052605670225026391054393428833168207234802434915090881303620353
507909591297683949138862971271266635431758872031092542127980551589004038646657157217329569167343063743426799521984799
C(2,671-)
116356769 33491655209 64110547427930873
* c145 = p68.p78
13646560594525825890627182668772241639702837721889959372317451952089
608833519146176962786346063898868909094632504100539398786357475514441579020823
C(2,727-)
* c219 = p98.p122
17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927
40099499726183758517891939428601665707063794593443940689888526556802581529262728143398959743444150539520890742947533452401
C(2,1202L)
7213
* c178 = p87.p91
322191336498946329196503049475322564558677154558189688098324958943433876457693205092709
3571063752373727959434120513220011301363863161567383982128636656862221716975343445451820353
C(2,1222L)
1363753
* c161 = p69.p92
390941529316414655423854492083019690148253103500590794058313678419233
70215922956051621713037377195110638684576079957295845924735328290270267776117780526372201309
C(2,1234M)
86381 7367588575848411802768597653205046693
* c144 = p56.p88
25030363534817185101957125006047751030454874478028239473
6828519750766734356393222104746037438762841641726469993132504189166732581463128027874013
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