Mathematica: t={};Do[t=Join[t,IntegerDigits[i,2]],{i,330,9705}];n=FromDigits[t,2];{PrimeQ[n],Length[IntegerDigits[n]]}
http://factordb.com/index.php?id=1100000000937316273
http://factordb.com/index.php?id=1100000000937484569

To be completed...