Seeing how long it takes to iterate to 1 in 3x+1 Problem

number = 27378675654323346464096990095909090234289295774747302;

iteratingtofixedpoint[numb_,option_] := Module[{},
count = 0;
num = numb;
If[Mod[numb,2] == 0, num = numb + 1];
(*If[Mod[numb,3] == 0, num = numb + 2];*)

initialnum = num;
While[num > 1,
{
num = 3 num + 1;
While[Mod[num,2] == 0, num = num/2];
count = count + 1;
}];
If[option == 1,
{
Print["Number of iterations to reach 1 is ", count, "."];
Print["Expected number of iterations is ",  Log[initialnum] / Log[4./3], "."];
Print["Number has roughly ", Floor[Log[10,initialnum]], " digits."];
}, Return[count]];
];

iteratingtofixedpoint[number 10^200,1]

histogramiterates[start_,numdo_] := Module[{},
output = {};
For[n = 1, n ≤ numdo, n++, output = AppendTo[output, iteratingtofixedpoint[ start + Floor[ n Sqrt[start ]],0]]];
Print[Histogram[output,Automatic, "Probability"]];
];

histogramiterates[123424989089080980989089089098989898988980984523523543535353535435444444444444444444444444444444555555555555555555555555555555555544444444444444444444449089898989898989929,1000]