Factorization of Smarandache Concatenated Numbers, Sm-n (n < 84), noting four yet-to-be-factored composites

smfactors = {{}, {{2, 2}, {3, 1}}, {{3, 1}, {41, 1}}, {{2, 1}, {617, 1}}, {{3, 1}, {5, 1}, {823, 1}}, {{2, 6}, {3, 1}, {643, 1}}, {{127, 1}, {9721, 1}}, {{2, 1}, {3, 2}, {47, 1}, {14593, 1}}, {{3, 2}, {3607, 1}, {3803, 1}}, {{2, 1}, {5, 1}, {1234567891, 1}}, {{3, 1}, {7, 1}, {13, 1}, {67, 1}, {107, 1}, {630803, 1}}, {{2, 3}, {3, 1}, {2437, 1}, {2110805449, 1}}, {{113, 1}, {125693, 1}, {869211457, 1}}, {{2, 1}, {3, 1}, {205761315168520219, 1}}, {{3, 1}, {5, 1}, {8230452606740808761, 1}}, {{2, 2}, {2507191691, 1}, {1231026625769, 1}}, {{3, 2}, {47, 1}, {4993, 1}, {584538396786764503, 1}}, {{2, 1}, {3, 2}, {97, 1}, {88241, 1}, {801309546900123763, 1}}, {{13, 1}, {43, 1}, {79, 1}, {281, 1}, {1193, 1}, {833929457045867563, 1}}, {{2, 5}, {3, 1}, {5, 1}, {323339, 1}, {3347983, 1}, {2375923237887317, 1}}, {{3, 1}, {17, 1}, {37, 1}, {43, 1}, {103, 1}, {131, 1}, {140453, 1}, {802851238177109689, 1}}, {{2, 1}, {7, 1}, {1427, 1}, {3169, 1}, {85829, 1}, {2271991367799686681549, 1}}, {{3, 1}, {41, 1}, {769, 1}, {13052194181136110820214375991629, 1}}, {{2, 2}, {3, 1}, {7, 1}, {978770977394515241, 1}, {1501601205715706321, 1}}, {{5, 2}, {15461, 1}, {31309647077, 1}, {1020138683879280489689401, 1}}, {{2, 1}, {3, 4}, {21347, 1}, {2345807, 1}, {982658598563, 1}, {154870313069150249, 1}}, {{3, 3}, {19, 2}, {4547, 1}, {68891, 1}, {40434918154163992944412000742833, 1}}, {{2, 3}, {47, 1}, {409, 1}, {416603295903037, 1}, {192699737522238137890605091, 1}}, {{3, 1}, {859, 1}, {24526282862310130729, 1}, {19532994432886141889218213, 1}}, {{2, 1}, {3, 1}, {5, 1}, {13, 1}, {49269439, 1}, {370677592383442753, 1}, {17333107067824345178861, 1}}, {{29, 1}, {2597152967, 1}, {163915283880121143989433769727058554332117, 1}}, {{2, 2}, {3, 1}, {7, 1}, {45068391478912519182079, 1}, {326109637274901966196516045637, 1}}, {{3, 1}, {23, 1}, {269, 1}, {7547, 1}, {116620853190351161, 1}, {7557237004029029700530634132859, 1}}, {{2, 1}, {6172839455055606570758085909601061116212631364146515661667, 1}}, {{3, 2}, {5, 1}, {139, 1}, {151, 1}, {64279903, 1}, {4462548227, 1}, {4556722495899317991381926119681186927, 1}}, {{2, 4}, {3, 2}, {103, 1}, {211, 1}, {39448709943503776711542648338171477043440283875433388943, 1}}, {{71, 1}, {12379, 1}, {4616929, 1}, {3042410911077206144807069396988766146557218727107817, 1}}, {{2, 1}, {3, 1}, {86893956354189878775643, 1}, {2367958875411463048104007458352976869124861, 1}}, {{3, 1}, {67, 1}, {311, 1}, {1039, 1}, {6216157781332031799688469, 1}, {305788363093026251381516836994235539, 1}}, {{2, 2}, {5, 1}, {3169, 1}, {60757, 1}, {579779, 1}, {4362289433, 1}, {79501124416220680469, 1}, {15944694111943672435829023, 1}}, {{3, 1}, {487, 1}, {493127, 1}, {32002651, 1}, {53545135784961981058419604998638516483529257158438201753, 1}}, {{2, 1}, {3, 1}, {127, 1}, {421, 1}, {22555732187, 1}, {4562371492227327125110177, 1}, {3739644646350764691998599898592229, 1}}, {{7, 1}, {17, 1}, {449, 1}, {231058353953907153927797941629430896528705484237484443924582239474910453, 1}}, {{2, 3}, {3, 2}, {12797571009458074720816277, 1}, {1339846151380678925030581935625950075102697197563351, 1}}, {{3, 2}, {5, 1}, {7, 1}, {41, 1}, {727, 1}, {1291, 1}, {2634831682519, 1}, {379655178169650473, 1}, {10181639342830457495311038751840866580037, 1}}, {{2, 1}, {31, 1}, {103, 1}, {270408101, 1}, {374332796208406291, 1}, {3890951821355123413169209, 1}, {4908543378923330485082351119, 1}}, {{3, 1}, {4813, 1}, {679751, 1}, {4626659581180187993501, 1}, {27186948196033729596487563460186407241534572026740723, 1}}, {{2, 2}, {3, 1}, {179, 1}, {1493, 1}, {1894439, 1}, {15771940624188426710323588657, 1}, {1288413105003100659990273192963354903752853409, 1}}, {{23, 1}, {109, 1}, {3251653, 1}, {2191196713, 1}, {53481597817014258108937, 1}, {12923219128084505550382930974691083231834648599, 1}}, {{2, 1}, {3, 1}, {5, 2}, {13, 1}, {211, 1}, {20479, 1}, {160189818494829241, 1}, {46218039785302111919, 1}, {19789860528346995527543912534464764790909391, 1}}, {{3, 1}, {17708093685609923339, 1}, {2323923950500978408934946776574079545611397611995364705071565292612305003, 1}}, {{2, 7}, {43090793230759613, 1}, {2238311464092386636761884511894978048448617178182150344531477542781856216843, 1}}, {{3, 3}, {7, 3}, {127534541853151177, 1}, {1045271879581348729278017817925065799872257805888381045072615907010178634849, 1}}, {{2, 1}, {3, 6}, {79, 1}, {389, 1}, {3167, 1}, {13309, 1}, {69526661707, 1}, {8786705495566261913717, 1}, {107006417566370797549761092803112128112769421435739, 1}}, {{5, 1}, {768643901, 1}, {641559846437453, 1}, {1187847380143694126117, 1}, {4215236719202000513320239996510510828557825033460062191, 1}}, {{2, 2}, {3, 1}, {4324751743617631024407823, 1}, {23788800764365032854813369830458732886158417401021113465643479155975828316681, 1}}, {{3, 1}, {17, 1}, {36769067, 1}, {2205251248721, 1}, {2128126623795388466914401931224151279, 1}, {14028351843196901173601082244449305344230057319, 1}}, {{2, 1}, {13, 1}, {1448595612076564044790098185437, 1}, {327789067063631145720134335581588856152921479945230066396717484857630796759, 1}}, {{3, 1}, {340038104073949513, 1}, {324621819487091567830636828971096713, 1}, {3728107520554143574058126525447653708074390492098041537, 1}}, {{2, 3}, {3, 1}, {5, 1}, {97, 1}, {157, 1}, {67555753880267981819314968257940564232852139165917171861439543181780049107204700168947673874146559500327, 1}}, {{10386763, 1}, {35280457769357, 1}, {33689963756771087787406890988794422071942750389483226687410462898596940470571223420915460371, 1}}, {{2, 1}, {3, 2}, {1709, 1}, {329167, 1}, {1830733, 1}, {9703956232921821226401223348541281, 1}, {6862941251271421600892952202464376235224342144596167046191804311, 1}}, {{3, 2}, {17028095263, 1}, {2435984189933032657913735712547671618367909, 1}, {330698276590517405413770500371046766676563523569978590938716221, 1}}, {{2, 2}, {7, 1}, {17, 1}, {19, 1}, {197, 1}, {522673, 1}, {1072389445090071307, 1}, {20203723083803464811983788589, 1}, {611891180337745942599768541236768900814521123060392220304537, 1}}, {{3, 1}, {5, 1}, {31, 1}, {83719, 1}, {8018741962917674781000851595476715337223177, 1}, {3954865825608609239925917139441010044747553878722812487568124023324127, 1}}, {{2, 1}, {3, 1}, {7, 1}, {20143, 1}, {971077, 1}, {319873117219722504963051951872747251, 1}, {927600480728565729398211282118577179, 1}, {506464674142683362314480915373647544917, 1}}, {{397, 1}, {183783139772372071, 1}, {169207186381096030569641287629182352063847752831832860300985727686482291228260812667458777140342739211041, 1}}, {{2, 4}, {3, 1}, {23, 1}, {764558869, 1}, {1811890921, 1}, {16210201583355429120740178111425145802012035286597, 1}, {49798299077316075944525952275152868666920234906076151289, 1}}, {{3, 1}, {13, 1}, {23, 1}, {8684576204660284317187, 1}, {281259608597535749175083, 1}, {15490495288652004091050327089107, 1}, {3637485176043309178386946614318767365372143115591, 1}}, {{2, 1}, {5, 1}, {2411111, 1}, {109315518091391293936799, 1}, {11555516101313335177332236222295571524323, 1}, {405346669169620786437208619979711016226055320437594464205451, 1}}, {{3, 2}, {83, 1}, {2281, 1}, {7484379467407391660418419352839, 1}, {96808455591058960266687738381050176698103277406505724847082994829643349780363432993640165860627, 1}}, {{2, 2}, {3, 2}, {5119, 1}, {596176870295201674946617769, 1}, {1123704769960650101739921630151581054522510738566183226239911321871780637830758881774623162921434662407, 1}}, {{37907, 1}, {1612352371081094864112011094480307952600705089, 1}, {201992666185187831800817490810938117880341395186600971262233773863756955874363\ 353778851, 1}}, {{2, 1}, {3, 1}, {7, 1}, {1788313, 1}, {21565573, 1}, {99014155049267797799, 1}, {1634187291640507800518363, 1}, {1981231397449722872290863561307, 1}, {2377534541508613492655260491688014802698908815817, 1}}, {{3, 1}, {5, 2}, {193283, 1}, {8516478538454813678399839833613318110353048968468019310775290558323936344974946612980172082837107906069172212808249295700548030242851, 1}}, {{2, 3}, {828699354354766183, 1}, {213643895352490047310058981, 1}, {8716407028594814374740596028898426313034395366012872513707917231855753694435270081076237925828389, 1}}, {{3, 1}, {383481022289718079599637, 1}, {874911832937988998935021, 1}, {164811751226239402858361187055939797929, 1}, {7442132227048590901854639419294226672231934035068486536423, 1}}, {{2, 1}, {3, 1}, {31, 1}, {185897, 1}, {3570505053674714753162296261527331568459971771942918130965908811852725131532672806404601526406759603889145976969679985423963150530264526109, 1}}, {{73, 1}, {137, 1}, {22683534613064519783, 1}, {132316335833889742191773, 1}, {35488612864124533038957177977, 1}, {11589330059060921218833486882285427414280233987959540582909167514265308253, 1}}, {{2, 2}, {3, 3}, {5, 1}, {101, 1}, {10263751, 1}, {1295331340195453366408489, 1}, {1702600917839548328745392482587491026230318172323434581398602992701169952537157469971305061091390839579932352102383, 1}}, {{3, 3}, {509, 1}, {152873624211113444108313548197, 1}, {58762581888644185603361112342786137599799640821735382180404307223995625796855706598141292123658134092320545833186103011, 1}}, {{2, 1}, {29, 1}, {4703, 1}, {10091, 1}, {12295349967251726424104854676730107, 1}, {334523571229968373890203385137399026475051, 1}, {1090461105551993653223776199179348475393504023636425991597284018461539, 1}}, {{3, 1}, {53, 1}, {503, 1}, {177918442980303859, 1}, {86761868996529176338914746038472546147948566639206116156894174706616559488768497797981281542160938468741302182439934629484429635273281, 1}}};

Length[smfactors]

...that is, from FactorInteger[Sm1], which Mathematica equates to {}, to FactorInteger[Sm83]. But...

composites = Flatten[Position[Table[Count[PrimeQ[First[Transpose[smfactors[[i]]]]], False], {i, 1, 83}], 1]]

{75, 78, 83}

...so, Sm75, Sm78, & Sm83 have not (yet) been completely factored. Each contains one unfactored composite:

Table[sf = smfactors[[composites[[i]]]]; First[sf[[Length[sf]]]], {i, 1, Length[composites]}]

{8516478538454813678399839833613318110353048968468019310775290558323936344974946612980172082837107906069172212808249295700548030242851, 3570505053674714753162296261527331568459971771942918130965908811852725131532672806404601526406759603889145976969679985423963150530264526109, 86761868996529176338914746038472546147948566639206116156894174706616559488768497797981281542160938468741302182439934629484429635273281}

PrimeQ[%]

{False, False, False}