No.
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.
There are infinitely many such numbers and they do not form any systematic pattern.
Any two prime numbers will be relatively prime. Numbers are relatively prime if they do not have any prime factors in common. Prime numbers have only themselves as prime factors, so all prime numbers are relatively prime to the others.
Yes
There is no pattern.
Co-prime numbers, relatively prime numbers and any set of prime numbers.
Prime numbers are divisible because any numbers that are divisible are prime. If a number isn't divisible, it isn't prime. Prime numbers have to be divisible by at least one pair of numbers to be prime.
Any number that is not a prime number.. . .Prime numbers: 1,3,5 and 7
The factors of any prime numbers are 1 and the numbers themselves.
Perhaps the fact that they are prime numbers!
The multiples of any number cannot be prime numbers because such numbers are the product of at least two numbers. Prime numbers, but definition, cannot be cannot be the product of any numbers except itself and one.
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.