As it seems to depend on more than machine bits I'm curious what $MaxNumber
various Mathematica installs have.
If your setup is different please fill in system information and Log2 @ Log2 @ $MaxNumber // Round
in the table below:
$$\begin{array}{r|c|c|l|c} \text{OS} & \text{Bits} & \text{Version} & \text{\\\$MaxNumber} & \log_2\log_2\\ \hline \\ % v7 \text{Windows} & 32 & 7.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Linux} & 64 & 7.0.1 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{Windows} & 64 & 7.0.1 & 1.233433712981650\times 10^{323228458} & 30 \\ % v8 \text{Windows} & 32 & 8.0.4 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Windows} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{OS X} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{Linux} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ % v9 \text{Windows} & 32 & 9.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Windows} & 64 & 9.0.1 & 2.174188391646043\times 10^{20686623745} & 36 \\ \text{OS X} & 64 & 9.0.1 & 8.768126706828697\times 10^{2711437152599256} & 53 \\ \text{Linux} & 64 & 9.0.1 & 8.768126706828697\times 10^{2711437152599256} & 53 \\ \text{Windows} & 64 & 10.1.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 10.2.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 10.3.1 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{OS X} & 64 & 10.4.1 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 11.0.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{OS X} & 64 & 12.1.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Linux ARM} & 32 & 12.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ % Your data here \end{array}$$$$\begin{array}{r|c|c|l|c} \text{OS} & \text{Bits} & \text{Version} & \text{\\\$MaxNumber} & \log_2\log_2\\ \hline \\ % v7 \text{Windows} & 32 & 7.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Linux} & 64 & 7.0.1 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{Windows} & 64 & 7.0.1 & 1.233433712981650\times 10^{323228458} & 30 \\ % v8 \text{Windows} & 32 & 8.0.4 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Windows} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{OS X} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ \text{Linux} & 64 & 8.0.4 & 1.233433712981650\times 10^{323228458} & 30 \\ % v9 \text{Windows} & 32 & 9.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ \text{Windows} & 64 & 9.0.1 & 2.174188391646043\times 10^{20686623745} & 36 \\ \text{OS X} & 64 & 9.0.1 & 8.768126706828697\times 10^{2711437152599256} & 53 \\ \text{Linux} & 64 & 9.0.1 & 8.768126706828697\times 10^{2711437152599256} & 53 \\ \text{Windows} & 64 & 10.1.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 10.2.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 10.3.1 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{OS X} & 64 & 10.4.1 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 11.0.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Windows} & 64 & 11.3.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{OS X} & 64 & 12.1.0 & 1.605216761933662\times 10^{1355718576299609} & 52 \\ \text{Linux ARM} & 32 & 12.0.1 & 5.297557459040040\times 10^{323228467} & 30 \\ % Your data here \end{array}$$