To paint with a primer, a kind of paint formulated to help stick another coat of paint (top coat) onto the surface which you are painting. Presumably, the chemisty which makes for ideal top coat paint is not the same as the chemistry for ideal primer paint.
In bicycle racing, a prime (pronounced "preem") is a special prize for the winner of the next lap, usually in the middle of the race somewhere. This is used mainly in criterium races, which involve the riders going around a short (less than a few miles) course. If the races are long (20-50 or more laps), the winning strategy may be to hide in the pack, waiting for the sprint finish. To discourage such boring race tactics, organizers put in prime laps. They are usually (but not always) randomly selected, non-previously announced laps in which a bell is rung. The winner of the next lap is given the prime prize. Racers are usually told there will be a prime lap, but not told which lap they will be.
Sometimes, the prizes for the prime are collected from the spectators. Sometimes, spectators give out money in order to have the prime when they want. Frequently, primes are given out when the race organizer is noticing that the race is looking boring.
Racers get really angry and tired when a diabolical race organizer sets up three primes consecutively near the end of the race. This wrecks any sneaky race tactics, and insures that the really, really strong will win the race.