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{36096800156828895568286578224818258719817914995401933354161, 1}}, {{41, 1}, {271, 1}, {35121409, 1}, {518203357921, 1}, {190893195970004711, 1}, {1589908647339072250321, 1}, {316362908763458525001406154038726382279, 1}, {605431706028029946531059199512572282414786250085768871, 1}, {94518941227657738924275388203289075281658118450062185929972854243729690463660471, 1}}, {{11, 1}, {101, 1}, {1889, 1}, {430148941, 1}, {2559647034361, 1}, {1090805842068098677837, 1}, {4411922770996074109644535362851087, 1}, {4340876285657460212144534289928559826755746751, 1}, {230175856669373992253976277974612031182496625023886807386072581333871027940087154579555293851089822885094561, 1}}, {{3, 1}, {37, 1}, {317, 1}, {6163, 1}, {10271, 1}, {307627, 1}, {90758677, 1}, {49172195536083790769, 1}, {1603873536486496162414778277997333003, 1}, {3660574762725521461527140564875080461079917, 1}, {6188975208492505209268886608725598925166783728988042084791755874926952500431775685466135397158979759267737179161, 1}}, {{11, 1}, {103, 1}, {239, 1}, {4013, 1}, {4649, 1}, {909091, 1}, {923441, 1}, {2071723, 1}, {1868879293, 1}, {5363222357, 1}, {21993833369, 1}, {3924966376871, 1}, {5673320472670315859129, 1}, {768736559421401249042753476963, 1}, {323012942148562751650814544437350454640448842187, 1}, {103746647830421551242486430622636901002236971549990724717454338463, 1}}, {{479, 1}, {142847911, 1}, {162385812809900583261295597372983559948698484946321658540735656202018003505845104737134070357362269119992033891923896707742660065148483572244656969761256208962241824944638737217461295395400432531624931235045560966776497496089919, 1}}, {{3, 1}, {7, 1}, {11, 1}, {13, 1}, {17, 1}, {31, 1}, {37, 1}, {41, 1}, {61, 1}, {73, 1}, {101, 1}, {137, 1}, {211, 1}, {241, 1}, {271, 1}, {2161, 1}, {3541, 1}, {9091, 1}, {9901, 1}, {27961, 1}, {1676321, 1}, {2906161, 1}, {4188901, 1}, {5070721, 1}, {5882353, 1}, {39526741, 1}, {99990001, 1}, {1132716961, 1}, {5964848081, 1}, {9999999900000001, 1}, {19721061166646717498359681, 1}, {281259985248437790051014401, 1}, {31388506438433752927908678241, 1}, {100009999999899989999000000010001, 1}}, {{125997820213, 1}, {8818494710724135843992143485822092387241346180661731882584652814791399260404212300220860100310211000039811546760342771415871328563704658755540522813656456530773991725065170759876875165438074252973593473504031270181916247141124747, 1}}};
Length[repfactors]
241
...that is, from FactorInteger[R1], which Mathematica equates to {}, to FactorInteger[R241]. But...
composites = Flatten[Position[Table[Count[PrimeQ[First[Transpose[repfactors[[i]]]]], False], {i, 1, 241}], 1]]
{239, 241}
...so, R239, & R241 have not (yet) been completely factored. Each contains one unfactored composite:
Table[rf = repfactors[[composites[[i]]]]; First[rf[[Length[rf]]]], {i, 1, Length[composites]}]
{162385812809900583261295597372983559948698484946321658540735656202018003505845104737134070357362269119992033891923896707742660065148483572244656969761256208962241824944638737217461295395400432531624931235045560966776497496089919, 8818494710724135843992143485822092387241346180661731882584652814791399260404212300220860100310211000039811546760342771415871328563704658755540522813656456530773991725065170759876875165438074252973593473504031270181916247141124747}
PrimeQ[%]
{False, False}
22 June 2006 © Rarebit Dreams