Yes
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Prime numbers do not have a specific geometric pattern. They are determined by whether they are divisible only by 1 and themselves. Prime numbers are distributed seemingly randomly and do not exhibit any predictable geometric pattern.
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.
There is no simple way. The difficulty wit prime numbers is that there is no pattern.
Prime numbers have only 2 factors and their set is not well defined because they do not follow an orderly mathematical pattern.
If you notice something, it is [most likely] a false impression. There is no known pattern to prime numbers.