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?

Because they're there.
Euclid called our attention to the fact after "because" in the third century BC, and Hillary called our attention to the appropriateness of "because" in the 20th century AD.
Also, large primes play a role in cryptography, which protects your bank P.I.N. number from thieves.
