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In part because the problem of finding large prime numbers isn't exactly trivial.

Q: Why are people so fascinated by finding new prime numbers?

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by finding the prime numbers up to 100

yes

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.

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There is no known system for finding prime numbers.

by finding the prime numbers up to 100

yes

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.

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

1 Prime numbers have only 2 factors which are themselves and one 2 Prime numbers can't be composite numbers which have more than 2 factors 3 Prime numbers are odd except for two which is the only even prime number 4 Prime numbers are used in finding the LCM of 2 or more numbers 5 Prime numbers are used in finding the HCF of 2 or more numbers 6 Prime numbers are used in finding the LCD of fractions 7 Prime numbers are used in reducing fraction to their lowest terms 8 Prime numbers are rational because they can be expressed as fractions 9 Prime numbers are infinite 10 Prime numbers are irrational when square rooted 11 Prime numbers can't be 0 or 1 which are also not composite numbers 12 Prime numbers don't follow a forecasted numerical pattern 13 Prime numbers make up 25% of the first 100 integers or whole numbers 14 Prime numbers have a code amongst themselves that has never been cracked