Logarithm tables... whats your preference?

Question

If you had to rely on a table of logarithms, what would you prefer? What would be more effective?

With a list consisting of 100 logarithm values...

1) A list of logarithms for the first 100 prime numbers
2) A list of logarithms for the the numbers 0 to 1 in increments of .01

Either list is just as long... but which would you rather have for accurate and effective mathematics?

Thanks, Ironduke, for not answering my question and pointing out an obvious, yet irrelevant, type-o.

The Maclaurin theorem is too much work, anyway, for any practical purpose. You will never be any more accurate than a pre-written list to whatever significant digits you wish.

Answer 1

List 2 is preferable. The prime numbers are not uniformly dense on the line, so interpolation precision is not going to be uniform.

I assume your table is decimal logarithms (otherwise what follows is not valid). Any number can be made to fall in the range (0, 1] to a suitable power of 10 factor. I.e. if you have a number X then you can always express X as X = S * 10^k for some k, so that S falls in (0, 1]. Then by applying the definition of logarithms

log X = log S + k

So using your mini-table in (0,1] and interpolation you can find a reasonable approximation to log X.

You can't do this with your table of logarithms of primes.

Answer 2

Log 0 is undefined.
I reall would not need a list because I could generate them using Maclauurin's theorem on ln(x+1)