I know that the half life of a proton is more than $6.6\cdot 10^{33}$ years (antimuon decay). I have found this data on Wikipedia proton decay but I do not know the probability distribution that leads to this data.
Moreover I know that the universe life has been extimated $t_{univ}\simeq13\cdot10^9$ years.
The universe mass is quoted as $10^{53}$ kg [wikipedia]. And from the stable nuclides table I can extimate that the ratio between neutrons and protons in the universe is about $1.5$
Then assuming that the universe mass is principally given by neutron and protons we have that, approximating neutrons and protons' masses equal to $1.67\cdot10^{-27}$ kg there should be
$$1.5\cdot n_{p^+} +1 \cdot n_{p^+}=\frac{10^{53}}{1.67\cdot10^{-27}}\simeq 5.98\cdot10^{80}$$ so the number of $p^+$ in the universe ($n_{p^+}$) should be $$n_{p^+}\simeq 2.39\cdot 10^{80}$$
Now, applying to the proton's decay the radiactive decay law:
$$N(t) = N_0\,e^{-{\lambda}t}$$
where $N_0=2.39\cdot 10^{80}$ and $\lambda$ can be determined from the half life time:
$$ \lambda= \frac{\ln(2)}{t_{1/2}}$$
Since the exponent becomes
$$\frac{\ln(2)}{t_{1/2}}\cdot t_{univ}\simeq 1.36\cdot10^{-24}$$
and so I obtain a number of proton that decaded during universe life equal to $3.26\cdot10^{56}$
This number is about $1.36\cdot10^{-24}$ the number of $p^+$ in the universe so it should be not impossible for us to observe the $p^+$ decay during the total universe life.
This reasoning is very very primitive (too primitive). Has anyone a suggestion to improve it?