For the first reason but not for the second

I’m having some trouble understanding “for the first reason but not for the second” from a sentence in a programming textbook called The Structure and Interpretation of the Computer Science(emphasis mine):

Numbers that fool the Fermat test are called Carmichael numbers, and
little is known about them other than that they are extremely rare.
There are 255 Carmichael numbers below 100,000,000. The smallest few
are 561, 1105, 1729, 2465, 2821, and 6601. In testing primality of
very large numbers chosen at random, the chance of stumbling upon a
value that fools the Fermat test is less than the chance that cosmic
radiation will cause the computer to make an error in carrying out a
“correct” algorithm. Considering an algorithm to be inadequate for
the first reason but not for the second illustrates the difference
between mathematics and engineering.

Here is some context: the Fermat test is a test for primality. The answer it gives is only probably correct, although it would be correct in most cases.

From my understanding, the italicized sentence mainly talks about the fact that preciseness is vital in mathematics, but is not extremely important in engineering. However, I don’t know what “the first reason” and “the second” refers to. Please explain it to me.