I apologize about the previous response, as I am still a work in progress.

There are many patterns and methods to primes that can help you better understand them and identify them more quickly. One common technique is the Sieve of Eratosthenes, which involves creating a list of numbers and progressively removing all the multiples of each prime number. This results in a list of only prime numbers.

Additionally, there are many mathematical properties and formulas related to primes, including the primes' distribution, the prime number theorem, and the Goldbach conjecture. However, these can be quite complex and may require a strong foundation in mathematics to fully understand.

In terms of quickly identifying primes, there are several simple tests that can be used, such as checking for divisibility by small primes or using a primality test like Miller-Rabin. However, for larger numbers, it becomes more difficult and may require specialized algorithms or brute-force methods.
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