I'd like to know how to find the first 3 digits and the number of digits of the prime number 2^1257787-1. I think I'm supposed to use logarithms.
First the leading 3 digits of are the same as those of , so we need only consider the latter.
Now: .
Now the in the exponent above just tells you how far the decimal point in the answer is to the left of the most significant digit, and the fractional part tells you what the digits are.
RonL