Expansion of Carmichael's theorem

For a couple of years, I had the pleasure to work (e.g., try to contribute) to Professor Stein Erik Johansen's exploration of prime numbers.

Mathematicians have tried in vain to discover some order in the
sequence of prime numbers but we have every reason to believe that
there are some mysteries which the human mind will never penetrate."
(Leonhard Euler, 1707-83)

"It will be another million years, at least, before we understand the
primes." (Paul Erdos, 1913-96)

The article can be read here, and downloaded below.
You don't have a pdf plugin, but you can download the pdf file.

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