Is there any pattern in prime numbers?

Answer 1

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.