## Rebuild Logarithm Tables

To keep what we have requires being able to repair and regenerate as needed.

There are at least two ways to rebuild the log tables if it ever becomes necessary.

The first way is kind of a reversed Sieve of Eratosthenes. Starting with the first four prime numbers larger than one, the logs of larger numbers that are not primes numbers can be easily generated.

The log of 16 is

Larger primes can be interpolated according to the instruction in any table of logs.

To increase precision, numbers can be used that are closer to the prime log being searched for.

The ratio of the prime to the lower boundary (6.4) to the entire interval (7.2 – 6.4) is roughly the same between logarithms and their powers of ten.

which is much closer to the logarithm of 7.

Or primes can be found by graphing from nearby numbers that can be easily factored.

The second way to rebuild log tables manually is with roots of ten.

This table shows up much better in its own tab.

The exponent of 10 is on the left-side column and the power to raise to is under the heading at the top.
The algorithm to generate the table is

for (q = 1; q < 9; q++) {
c = 10 ^ (10 ^ (-q))
for (i = 1; i < 11; i++) {
n = c ^ i
}}

Converting back and forth between common logs and natural logs only requires: