11011...11011 (1013-digits)

This number is a prime.

                      1
                     101
                    10001
                   1000001
                  100000001
                 10000000001
                1000000000001
               100000000000001
              10000000000000001
             1000000000000000001
            100000000000000000001
           10000000000000000000001
          1000000000000000000000001
         100000000000000000000000001
        10000000000000000000000000001
       1000000000000000000000000000001
      100000000000000000000000000000001
     10000000000000000000000000000000001
    1000000000000000002000000000000000001
   100000000000000000202000000000000000001
  10000000000000000020802000000000000000001
 1000000000000000002084802000000000000000001
100000000000000000208464802000000000000000001
 1000000000000000002084802000000000000000001
  10000000000000000020802000000000000000001
   100000000000000000202000000000000000001
    1000000000000000002000000000000000001
     10000000000000000000000000000000001
      100000000000000000000000000000001
       1000000000000000000000000000001
        10000000000000000000000000001
         100000000000000000000000001
          1000000000000000000000001
           10000000000000000000001
            100000000000000000001
             1000000000000000001
              10000000000000001
               100000000000001
                1000000000001
                 10000000001
                  100000001
                   1000001
                    10001
                     101
                      1