of all the proof methods I had never seen the Heuristic proof method before, I came across this http://oddperfect.org/pomerance.html , seemed too complicated to be used for understanding the method itself, proof by contradiction uses irrationality of square root of 2 as an example, so every other method of proof has a simple example to understand the method, what is a simple example for Heuristic proof? is there a list of proof methods and some simple examples/applications?
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3I think you're confused. A heuristic argument such as this is not a proof. – Robert Israel Jul 31 '16 at 23:28
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@RobertIsrael : Is there such a thing as heuristic proof? – jimjim Jul 31 '16 at 23:38
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Here is a simple example for the Twin Primes conjecture. The Prime Number Theorem can be viewed as saying that the "probability" that a positive integer $n$ is prime is approximately $1/\log(n)$. Assuming independence, this would make the probability that $n$ and $n+2$ are both prime approximately $1/\log(n)^2$. Since $\sum_{n=2}^\infty 1/\log(n)^2 = \infty$, that would indicate that there should be infinitely many twin primes.
Of course, this is not a proof, and can't be made into a proof as far as we know: Twin Primes is still a conjecture!
Robert Israel
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