There are infinitely many Carmichael numbers

@article{Alford1994ThereAI,
  title={There are infinitely many Carmichael numbers},
  author={W. R. Alford and Andrew Granville and Carl Pomerance},
  journal={Annals of Mathematics},
  year={1994},
  volume={139},
  pages={703-722}
}
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FACTORS OF CARMICHAEL NUMBERS AND AN EVEN WEAKER $k$ -TUPLES CONJECTURE
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One of the open questions in the study of Carmichael numbers is whether, for a given $R\geq 3$ , there exist infinitely many Carmichael numbers with exactly $R$ prime factors. Chernick [‘On Fermat’s
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References

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On Distinguishing Prime Numbers from Composite Numbers
A new algorithm for testing primality is presented. The algorithm is distinguishable from the lovely algorithms of Solvay and Strassen [36], Miller [27] and Rabin [32] in that its assertions of
On Numbers Analogous to the Carmichael Numbers
A base a pseudoprime is an integer n such that 1 A Carmichael number is a composite integer n such that (1) is true for all a such that (a, n ) = l. It was shown by Carmichael [1] that, if n is a
On Linnik's constant.
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