The proton has never been observed to decay into other particles. So it is possible that it is an absolutely stable particle and will never decay. However, there are some grand unified theories that argue that the proton does decay and physicists have been carrying out experiments to detect them decaying. The catch is that these theories predict an extremely long lifetime for the proton, greater that 1031 years! How does one do such an experiment?
The way to do it is to take advantage of the probabilistic nature of quantum mechanics. When we say that the average lifetime of a particle is some value, what that means is that there is a range of times in which the particle can decay, starting with zero (i.e., immediately) as the lower bound and going up all the way to infinite times, and one can assign probabilities to any given time interval. Short-lived particles have probability distributions that peak at the low end, while those of long lived particles peak at higher values.
Of course the chance that any given proton will decay in the lifetime of an experimenter is extremely small. So what one does is observe a vast number of protons and thus increase the odds of seeing one decay. So if the proton lifetime is 1031 years, by observing a collection of 1031 protons, one could expect to see one decay per year. Of course, the technological challenges are immense.
A new paper reports on results of an experiment using a 50,000 ton tank of water surrounded by detectors that looked for proton decay predicted by one particular theoretical model. They looked for decays for 17 years but saw none. This null result means that the minimum lifetime of the proton has been nudged even more upwards and now stands at 5.9×1033 years for this particular decay pathway.