Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).
Carmichael's Conjecture
See also
Carmichael Number, Carmichael's Totient Function ConjectureExplore with Wolfram|Alpha
References
Alford, W. R.; Granville, A.; and Pomerance, C. "There Are Infinitely Many Carmichael Numbers." Ann. Math. 139, 703-722, 1994.Cipra, B. What's Happening in the Mathematical Sciences, Vol. 1. Providence, RI: Amer. Math. Soc., 1993.Guy, R. K. "Carmichael's Conjecture." §B39 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 94, 1994.Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. "The Pseudoprimes to
." Math. Comput. 35, 1003-1026,
1980.Ribenboim, P. The
New Book of Prime Number Records. New York: Springer-Verlag, pp. 29-31,
1989.Schlafly, A. and Wagon, S. "Carmichael's Conjecture on the
Euler Function is Valid Below 
." Math. Comput. 63, 415-419,
1994.Referenced on Wolfram|Alpha
Carmichael's ConjectureCite this as:
Weisstein, Eric W. "Carmichael's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CarmichaelsConjecture.html