In part because the problem of finding large prime numbers isn't exactly trivial.
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by finding the prime numbers up to 100
Nobody. That is because there is no pattern to prime numbers. There are various methods to find some classes of prime numbers but none that will find all of them.
Not really. You just have to try different numbers. As to patterns, the probability of finding a prime goes down for higher numbers. The number of prime numbers up to a number "n" is roughly equal to n / ln(n), where ln() is the natural logarithm function.
One method for finding prime numbers is called the "Sieve of Eratosthenes" because it basically "sifts" through the numbers looking for numbers that are not not prime.
The prime factors of 42 are 2, 3 and 7