We describe an algorithm for constructing Carmichael numbers
N
N
with a large number of prime factors
p
1
,
p
2
,
…
,
p
k
p_{1}, p_{2}, \dots , p_{k}
. This algorithm starts with a given number
Λ
=
lcm
(
p
1
−
1
,
p
2
−
1
,
…
,
p
k
−
1
)
\Lambda =\operatorname {lcm} (p_{1}-1, p_{2}-1, \dots ,p_{k}-1)
, representing the value of the Carmichael function
λ
(
N
)
\lambda (N)
. We found Carmichael numbers with up to
1101518
1101518
factors.