I know there are several variants of proofs for the Prime Number Theorem.

Which one is the easiest one to study and then re-teach?

By easiest, I mean those that assume minimal knowledge beyond secondary school mathematics.

For example, most school leavers having done maths will have calculus, and could stretch to understand concepts like asymptotic equivalence and integration in the complex plane, but won't have concepts like group theory.

  • 3
    $\begingroup$ "Minimal knowledge beyond secondary school mathematics" will most likely not be the simplest proof by far. Learning concepts that are missing and then checking a simpler proof with stronger requirements might be overall easier. $\endgroup$
    – gnasher729
    Commented Jun 28, 2020 at 23:44
  • $\begingroup$ I agree wiith gnasher729. $\endgroup$ Commented Jun 28, 2020 at 23:53
  • $\begingroup$ @gnasher729 - I understand your point. If you have suggestions for such a simple proof I would appreciate it. I am looking at an "analytic" proof and an 'elementary" proof and the analytic one s of course simpler as the concepts are more powerful. $\endgroup$
    – Penelope
    Commented Jun 29, 2020 at 21:42

1 Answer 1


You might check out

D. Zagier, Newman's Short Proof of the Prime Number Theorem,

which appears in

The American Mathematical Monthly, Vol. 104, No. 8 (Oct., 1997), pp. 705-708

and is available online at


This is the easiest proof of which I am aware, but its challenging nevertheless. But an undergrad with a solid background in analysis should be able to hack it.


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