Published online by Cambridge University Press: 17 November 2015
In light of the recent work by Maynard and Tao on the Dickson $k$-tuples conjecture, we show that with a small improvement in the known bounds for this conjecture, we would be able to prove that for some fixed
$R$, there are infinitely many Carmichael numbers with exactly
$R$ factors for some fixed
$R$. In fact, we show that there are infinitely many such
$R$.