What type of pseudoprime does the largest known pseudoprime tend to be?

There are some enormous Carmichael numbers (eg. 16+ million digits), pseudoprime to any coprime base, which can be generated by Löh & Niebuhr's method.

Update: this 2011 Hayman & Shallue poster reports the construction of a Carmichael number with more than 10 billion factors and around 295 billion decimal digits.

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Prime Numbers

Elementary Number Theory

Pseudoprimes

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