Perl 5.24.1 64-bit, for reference:

use warnings;
use strict;

for(51..66){
    my $s = sprintf("%b", 2**$_-1);
    print "$_:" . length($s) . "\n";
}
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Output (* denotation is added after the fact to represent where it starts to "break").:

51:51
52:52
53:53
54:54
55:55
56:56
57:57
58:58
59:59
60:60
61:61
62:63 *
63:64 *
64:64 *
65:64 *
66:64 *
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