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I noticed the new Faq has been changed from exponents to digits.
Also below;
->
-> Your calculations are fine. Just one slight detail you forgot:
->
-> 10^2 is the smallest number with *3* digits;
-> 10^3 is the smallest with *4* digits;
-> and so on.
->
-> INT[ Log10 [ N] + 1 ] always gives the number of digits in N. Here, that
-> is INT [ exponent * log10[2] +1 ], or INT [ exponent / 3.32etc + 1]
->
So INT [ exponent / 3.32etc + 1] = number of decimal digits in
2^exponent-1?
Right?
The part of the FAQ states:
-> > >we can work similarly to come up with how many digits are in a
Mersenne
-> > >number:
-> >
-> > >10^(d-1)-1 < 2^n-1 <= 10^d-1
-> > >10^(d-1) < 2^n <= 10^d
-> > >log_2(10^(d-1)) < n <= log_2(10^d)
-> > >(d-1)*log_2(10) < n <= d*log_2(10)
-> > >d-1 < n/log_2(10) <= d
-> >
-> > >2^n-1 has d digits.
Well 2^127-1 has 39 digits and 127/3.321928094887 = 38.2308094493297819.
The above states n/log_2(10) <= d. Does this not mean less than or equal to
d? This seems either in error or misleading.
I am surprised that this explanation is a answer to the original question
of the FAQ which was "How many digits are in a given Mp?".
The simple formula;
INT [ exponent / 3.321928094887 + 1] = number of decimal digits in
2^exponent-1
would have been more straight forward to us novices.
Thanks for your help.
Dan
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