The Large Hadron Collider is the largest particle accelerator in the world. It is located in Switzerland and is 17 miles in circumference. It was built to try to answer some of the most fundamental questions of particle physics and discover new types of subatomic particles. Protons are able to be accelerated to speeds only about 3 meters per second slower than the speed of light. But you should know that no particles at this facility are being accelerated at or above the speed of light. As you stated, it is impossible to exceed the speed of light by all known laws of physics.
The particles going around the Large Hadron Collider do NOT travel faster than the speed of light, c, at a value of 299,792,458 m/s. However, they do get very close to it, something like 0.9999c, which is still smaller than the speed of light :D