Why it is important to find largest prime numbers? It always takes a lot of effort and money to find the next largest prime number. Why is it so important to do this work and what is the application those numbers?

Just to add to the previous answers: Usually, part of the discovery of these mathematical curiosities is not the result itself, but the new or improved method for finding these new results. It's not just about finding the number which is meaningless in itself, but it's about showing that mathematical techniques have advanced so much that we can even show that these incredibly huge numbers are prime.
Similarly, who cares that we planted a flag on the moon, or that we sent people there at all? It's all about showing that we can do this.
