$ perl -e 'print sprintf("%b",2**53-1),"\n"'
11111111111111111111111111111111111111111111111111111
$ perl -e 'print sprintf("%b",2**54-1),"\n"'
1000000000000000000000000000000000000000000000000000000
$ perl -e 'print sprintf("%b",2**(53-1)),"\n"'
10000000000000000000000000000000000000000000000000000