For no particularly good reason I had to make a notebook with the best known solutions for the ABC conjecture.

Rad[n_] := Times@@(First/@FactorInteger[n]);
quality[{a_,b_,c_}]:= N[Log[c]/Log[Rad[a b c]]];
Text@Grid[Reverse[Sort[
{quality[#], Row[Drop[Flatten[Transpose[{Riffle[ToString[#[[1]]]^#[[2]]&/@FactorInteger[#],"*"]&/@#,{" + "," = ","0"}}]],-1]]}&/@{
{2,6436341,6436343},{121,48234375,48234496},{24833,5020969537415167,5020969537440000},
{283,8251953125,8251953408},{1,4374,4375},{343,59049,59392},
{2477678547239,613474843408551921511,613474845886230468750},
{125,11174240024064,11174240024189},{611596453,5368709120,5980305573},
{20218313059443,121517356341481357,121537574654540800},
{188728275341281,30687043271724658719,30687232000000000000},
{10023806115968,236997656946088771,237007680752204739},
{239,1919140625,1919140864},{198425,96889010407,96889208832},
{44,14087010572580078081,14087010572580078125},
{73,5973865915867136,5973865915867209},{16777216,311385505409,311402282625},
{121,255879,256000},{37,32768,32805},{115966796875,9301344999072,9417311795947},
{8654525279998779296875,229727166528260169448321941,229735821053540168227618816},
{1,301327047,301327048},{49,31640576,31640625},{16119,214358881,214375000},
{5595907,184693744467968,184693750063875},{13841287201,2271670157312,2285511444513},
{110330191652531040475,3651621299988620198933,3761951491641151239408},{3200,4823609,4826809},
{464743623105438551,6045120559074418176746593449,6045120559539161799852032000}}]]]