# Does a Carmichael number with $k$ prime factors exist for every $k\ge 3$?

Here

https://oeis.org/search?q=carmichael+number+factors&language=german&go=Suche

the smallest Carmichael numbers with $k=3,...,35$ prime factors are shown. In Wikipdia, it is stated, that a Carmichael number with over $1,000,000$ prime factors has been constructed.

Is there a Carmichael number with $k$ prime factors for every $k\ge 3$ ?

• The Wikipedia article says a Carmichael number with over 16 million digits and $1,101,518$ factors was found. It also states that there are at least $n^{2/7}$ Carmichael numbers less than $n$ I would expect that this means there are Carmichael numbers with arbitrarily many factors. That certainly leaves open the possibility that there is some number of factors not represented. – Ross Millikan Oct 15 '15 at 16:22