Excuse me for butting in, but your math is all wrong.
Your number, 4**1953, is the number of possible genes of length 1953. But what you should be counting is the number of single point mutations. That is as very much smaller number, because you can't access all of the sequences by a single point mutation from a given sequence. The number of single point mutations in a gene of 1953 b.p. is 3 * 1953: three possible changes at every site, times 1953 sites. Of course, many of these mutations will be neutral, and many others will be redundant, so the actual number is still less.
js1138 is correct.
On the contrary, 3^1953 is greater than 20 million.
By orders of magnitude.