I’m not sure whats going on with the small numbers though. When I use the formula to try and get the probability of goldbachs conjecture holding for all numbers >2 , I get around 10^-15.
More sophisticated formulae that take into account the even odd pattern still get around 10^-6. Of course, this is sensitively dependant on exactly where you start. But it seems that this probabilistic reasoning showing so strongly that a small even number shouldn’t be a sum of primes indicates a problem with the probabilistic model.
Yes, I got that result too. The problem is that the prime number theorem isn’t a very good approximation for small numbers. So we’d need a slightly more sophisticated model that has more low numbers.
I suspect that moving from “sampling with replacement” to “sampling without replacement” might be enough for low numbers, though.
I’m not sure whats going on with the small numbers though. When I use the formula to try and get the probability of goldbachs conjecture holding for all numbers >2 , I get around 10^-15.
More sophisticated formulae that take into account the even odd pattern still get around 10^-6. Of course, this is sensitively dependant on exactly where you start. But it seems that this probabilistic reasoning showing so strongly that a small even number shouldn’t be a sum of primes indicates a problem with the probabilistic model.
Yes, I got that result too. The problem is that the prime number theorem isn’t a very good approximation for small numbers. So we’d need a slightly more sophisticated model that has more low numbers.
I suspect that moving from “sampling with replacement” to “sampling without replacement” might be enough for low numbers, though.