No, there is no pattern to prime numbers in the sense that you mean. If someone wants to know the next Prime number in the list, a computer must calculate that number, checking to see if the number is divisible by anything other than 1 and itself.
As of October 2010, computers have been able to list primes all the way out to 13 digits! As you read this, computers are still calculating more prime numbers.
Prime numbers do have a variety of interesting properties, and an entire branch of mathematics (Number Theory) spends a lot of effort exploring those properties, but none of those properties makes it possible to just quickly figure out "the next number."
Property: Except for 2 and 5, all primes end in 1, 3, 7, and 9.
Property: If you divide a prime number by another prime number, other than 2 and 5, you always get a repeating decimal.
(In case you haven't already guessed, 2 and 5 are special prime numbers in our decimal number system, since 2 x 5 = 10.)
Property: If 2n + 1 is prime, and n > 0, it can be shown that n must be a power of two. After extensive study, only 5 such primes have been found.
Property: After 2 and 3, all primes must be of the form 6n + 1 or 6n - 1.
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.
Yes
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
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.
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
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.
The factors of any prime numbers are 1 and the numbers themselves.
There is no simple way. The difficulty wit prime numbers is that there is no pattern.