Not an expert on randomness, but thought this could be a fun little function to make.
A part of this answer is from the link in the comments above (C# A random BigInt generator), but extended to the requirement for them to be within a certain range.
This is what I came up with:
Public Function GenerateRandom(min as biginteger, max as biginteger) As BigInteger
Dim bigint As BigInteger
Do
' find the range of number (so we can generate #s from 0 --> diff)
Dim range as BigInteger = max - min
' create random bigint fitting for the range
Dim bytes As Byte() = range.ToByteArray()
Using rng As New RNGCryptoServiceProvider()
rng.GetBytes(bytes)
End Using
' ensure positive number (remember we're using 0 --> diff)
bytes(bytes.Length - 1) = bytes(bytes.Length - 1) And CByte(&H7f)
' add minimum to this positive number so that the number is now
' a candiate for being between min&max
bigint = min + New BigInteger(bytes)
' since we now only have a random number within a certain number of
' bytes it could be out of range. If so, just try again.
Loop While (bigint > max)
' we have a number in the given range!
return bigint
End Function