It would be impossible to write such a program because there are an infinite number of prime numbers. Even if we limit ourselves to the "known" primes, there are currently in excess of 7.853e11,185,263 primes. However, there is no list of these known primes in existence because, weirdly, some of them are actually unknown (we know they exist we simply do not know their value).
If we consider the top 10 largest known primes alone, the current largest known prime (discovered in January 2013) has 17,425,170 decimal digits. However, the second largest known prime (discovered in August 2008) only has 12,978,189 digits. Nobody knows exactly how many primes exist between these two known primes because not every value was tested. Any that were tested prior to January 2013 were obviously found to be composite numbers otherwise they would now be listed somewhere between the current 1st and 2nd largest known primes.
Prime number enthusiasts are simply not interested in listing every prime; their goal is to find the largest known prime and if that means missing out some of the smaller primes along the way then so be it. However, if you examine the top 10 and look at the dates that each was discovered, you will find that we do occasionally find one of the missing primes. But unless someone actually tests every potential prime between any two largest known primes, the list will never be complete.
Even if complete list of all known primes could be created, it would be impossible to even store it. The top 10 alone would require nearly 1 GB of storage if the digits were listed in full using plain ASCII text. But we're talking about just 10 numbers that have an average of 9.8 million digits each. There are roughly 7.853e11,185,263 primes less than the current largest prime and there simply isn't enough storage on the planet to cater for all that data, let alone the infinite number of primes that have yet to be discovered.
Ultimately, the task in question is impossible to fulfil, so there's simply no point in even trying.
There is no known system for finding prime numbers.
by finding the prime numbers up to 100
In part because the problem of finding large prime numbers isn't exactly trivial.
All numbers have factors. Some factors are prime numbers, some are composite numbers, one is neither. When finding the factors of a number, you find all the factors. The prime factorization is a multiplication string of just prime factors that will total the given number.
VBnet program to find the prime numbers between 100 to 200?
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.
Prime Factorization is finding which prime numbers multiply together to make the original number.
There are no mathematical patterns to prime numbers. That is why finding prime numbers is so difficult and that leads to their use in cryptography.
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.
finding the prime factors of a composite number
The prime factors of 42 are 2, 3 and 7