ClearAll[PrimeFactorCounts, U]
PrimeFactorCounts[n_Integer] := Total[FactorInteger[n][[All, 2]]]
U[n_, m_] := (6 m + 1) (12 m + 1) Product[2^i 9 m + 1, {i, 1, n - 2}]
FindFirstChernickCarmichaelNumber[n_Integer?Positive] :=
 Module[{step, i, m, formula, value},
  step = Ceiling[2^(n - 4)];
  If[n > 5, step *= 5];
  i = step;
  formula = U[n, m];
  PrintTemporary[Dynamic[i]];
  While[True,
   value = formula /. m -> i;
   If[PrimeFactorCounts[value] == n,
    Break[];
    ];
   i += step
   ];
  {i, value}
  ]
FindFirstChernickCarmichaelNumber[3]
FindFirstChernickCarmichaelNumber[4]
FindFirstChernickCarmichaelNumber[5]
FindFirstChernickCarmichaelNumber[6]
FindFirstChernickCarmichaelNumber[7]
FindFirstChernickCarmichaelNumber[8]
FindFirstChernickCarmichaelNumber[9]