List the numbers from 2 to 100. Rows of 10 work well. Cross out all the multiples of 2 that are greater than 2. This will be the rest of the even numbers. Go to the next number that isn't crossed out (3) and cross out all of its greater multiples. Proceed in this fashion. Next up will be 5. You can stop when you get to fifty. The numbers that aren't crossed out are prime.
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by finding the prime numbers up to 100
In part because the problem of finding large prime numbers isn't exactly trivial.
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.