In order to calculate the first few digits, consider:

2ⁿ - 1 = antilog(log2ⁿ) - antilog (log 1)

of course for the first 6,320,428 of its 6,320,430 digits, the
[-antilog (log1)] doesn't really figure

so first few digits may be found by:

antilog log(2ⁿ)=antilog(nlog2)

= antilog(20,996,011*log2)

=antilog6320429.1002909014785008091847663
(using the scientific calculator provided by Microsoft windows)

=10^6320429 * 10^{0.1002909014785008091847663}

=1.2597689545033010502 * 10^6320429

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