> "Higgs detected 30000 times with 5 sigma meaning you'd have to repeat the proton smashing experiment several million times to get such a signal randomly"
> was actually performed by orders of magnitude more often

>>> 365*24*60*60*2*11245
709244640000 <- performed about this often in two years
>>> 709244640000/3500000
202641.32571428572 <- would have actually expected more than 30000 random "detection" events, but LHC probably wasn't operational at all times during these roughly 2 years...