A prime number is a number that has exactly two factors, or divisors - the number 1, and itself. So 2,3,5,7,11,13,17,.....are the first several prime numbers. As you can see, the larger they get the more spaced apart they are - which makes sense since larger numbers tend to have more factors. You can also see why it would be harder and harder to identify a number as prime the larger the numbers get. As a matter of fact, there are mathematicians and computer programmers who are devoting their whole career to the study of prime numbers, and to finding the "next" largest one.
Identifying prime numbers is such a formidable task that one method of developing an encryption code that is very difficult (nearly impossible) to break is by basing the code on the product of two very large prime numbers.
But, back to the question at hand. Co prime numbers are numbers that don't share any common factors other than 1. For example, while neither 8 nor 9 are prime numbers they are co prime numbers. The factors of 8 are 1,2, and 4, while the factors of 9 are 1 and 3 - no factors other than 1 in common. Another name for co prime is relatively prime.
Co-prime numbers are numbers that are relatively prime when compared to each other, as it were: they don't share any factors other than 1.
For example, 4 and 6 are not co-prime as they share common factors of 1 and 2.
7 and 12 are co-prime as they only share 1 as a factor, even though 12 isn't a prime number.
Hope this helps?
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