If you pick any number, you have to go through all the possible divisors to see if they work.
A better way was invented by the ancient Greek, Eratosthenes. Write down all the numbers 3 to 999 (we know all primes are odd numbers). Then go through the 3x multiplication table crossing out all the multiples of 3 from the list. Do the same with 5, then 7, then 11 etc. After you have gone through all those up to 31, the numbers left in your list are all prime.
It isn't difficult to programme a pc to calculate Prime number with this method and my laptop calculated prime numbers up to 1 million in about 2 seconds :)
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There is a difference of 95 when the prime number 2 is subtracted from the prime number 97.
A mirror prime.
The number 63 is not a prime number as it can be divided by 3 to make 21 as well as it self and one
None. 251 is a prime number.
A prime number does not 'make' any other number. It may be a factor of a number., if so then there will be at least one other number.