Question 84158: The Prime numbers between successive gaps of ten numbers are:
2, 3, 5, and 7.
11, 13, 17, and 19.
23 and 29.
31 and 37.
41, 43, 47, and (not 49 - square of 7)
53 and 59.
61 and 67.
71, 73, and 79 and (not 77)
83 and 89.
91 and 97.
Can you see a pattern forming? Despite of this I was not able to formulate a simple and general expression so that I could tell whether or not a number is prime by simply looking at the number and applying the above sequence. Can you help? Please! I am very excited about this project. It is my own thought and has not been assigned to me as a homework.
Thankyou.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! I think you are looking for something that doesn't exist!! Although the great mathematicians have been looking for one for centuries, there is NO pattern of prime numbers, and there is no way to recognize a prime number by looking at the sequence of primes around it. The only way to identify whether is number is prime is by the Sieve of Eratosthenes--that is, to test for divisibility by every prime number up to and including the square root of the number.
R^2 at SCC
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