Protons are the most stable composite particles in nature. Protons never decay.
There are experiments designed to catch decaying protons but proton decay has never been observed.
Latest experimental lower limit on proton lifetime is 1.6^34 years (16 followed by 33 zeros) as reported by the Super-K experiment in Japan. This result rules out some of the grand unification theories (see the nice article by Natalie Wolchover)
One of the predicted (hypothetical) proton decay modes according to GUT (Grand Unified Theory): a proton decays to a positron and a neutral pion and a neutral pion immediately decays into two gamma rays as shown in the figure below.
Reminder: protons do not decay naturally but they can be broken. We can split the protons by smashing them against each other with tremendous force. This is what they do in the Large Hadron Collider (LHC) at CERN.