Bryan is correct, especially in his comment in the case of 0% true/prior prevalence
40/1000 = 4% positive. 1-2/40 = 2.5-5%.
But even in such a conditioned test scenario, in which the 2nd test is only applied to the positive-reporting sample of the first test, a decent test (e.g. 90% sensitivity, 95% specificity) will actually converge pretty quickly (i.e. "disagree with itself" a lot less).
E.g. if the true prevalence is 1% (instead of 0%) instead of t2:t1 positive reports ratio of 1:20 (i.e. 5%), you'll actually get (in the 1% prevalence case) just a 1:5 (t2:t1) ratio (more precisely 18.85%). Also this t2:t1 positive report ratio further drops to just 1:3 (29.18%) on just 2% true prevalence.
Here's a table of such calculations below, in which I assume the same test is repeated (as not to complicate this example with two sets of sensitivity/specificity.)
Furthermore, for a highly specific test, i.e. 99% (instead of 95%) specificity, the convergence is even faster, e.g. for just 1% true prevalence, the t2:t1 positive report ratio is now almost 1:2 (43.86%; up from 18.85% when the specificity was just 95%).
Ironically however, if the true prevalence is 0%, a more specific test (99% vs 95% specificity) will "disagree with itself" on a retest even more, i.e. 1:100 vs 1:20 concurrence.
Considering the specificities and sensitivities of the tests known (which is alas a bit iffy in "real world" situations as opposed to lab settings) you can basically find out what the true prevalence is, e.g. assuming 60% sensitivity and 95% specificity for the antigen test and 95% sensitivity and 99% specificity for the (t2) PCR test, from a range of t2:t1 like you reported (2:20 to 1:40), you can get somewhere between 0.1% and 1% true prevalence in the starting population... which is still a fairly large range. (Of some note, this doesn't depend on the initial population size anymore, i.e. having two tests allows us to "factor out" that.)
In reality (even for lab-settings tests) you only have confidence intervals for the sensitivity and specificity as opposed to their true number, which makes the above exercise a bit more involved... and as Bryan's numerical example showed, 0% (true) prevalence could well be in the solution interval. The specificity of the 2nd test (PCR) is actually critical in this regard, if you relax it to 95% (from 99%), then 0% true prevalence becomes a (realistic) solution.