0.00000 04559 23795 07319 6286;
dividing this by 2 × 2,193,349 we obtain
0.00000 00000 00103 93325 3457,
and the third term is
0.00000 00000 00000 00003 1590,
so that the series =
0.00000 04559 23691 13997 4419;
whence, taking out the logarithms from Wolfram’s table,
loge 43,867 = 10.68891 76079 60568 10191 3661.
The principle of the method is to multiply the given prime (supposed to consist of 4, 5 or 6 figures) by such a factor that the product may be a number within the range of the factor tables, and such that, when it is increased by 1 or 2, the prime factors may all be within the range of the logarithmic tables. The logarithm is then obtained by use of the formula