srj203
Nothing that has been done for his early education required lots of money. (Obviously, being in a developed country like Australia helped a lot --- but one can imagine something similar being done in almost any densely populated urban area in the world.)
However, almost everything in his very early age required large amounts of time, thinking, and attention by his parents.
If you have enough time, and your young children are interested in something, don't leave them to figure it out themselves.
One way to think about this, without any number theory requirements: if we keep throwing a coin with probability of heads p which is around 1/2 at the beginning, but then keeps decreasing on the rate of log n / n, we would expect (using undergraduate probability theory) that two heads indeed come up very close infinitely many times.
As primes up to n have the frequency of log n / n, this would be enough if the primes behaved like coin flip results. However, that is not the case, as primes are leftovers of some sieve, rather than totally independent and random.
The goal of some of the current methods is to establish a good ``probabilistic'' model of the primes, so that this intuition can be transformed to reality.