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Generating prime numbers in poly-time

To show that I can generate a list of the first J primes in time polynomial in J, I need to work out the cost of however I am generating the list.

If I am generating the list by checking numbers one after the other and discarding non-primes, there are two parts to the cost of generating the list - how long it takes to check each number, and how many numbers I need to check.

If primes were vanishingly rare, then I couldn't afford to check every number from 2 on, because simply listing all those numbers would be too expensive. But if I know that the Jth prime is no larger than 2j*ln(j) I can at least list them all in polynomial time.

In fact, if I have to generate J primes, and I start by taking the first 2J*ln(J) numbers, and I decide to check each number for being prime by test dividing it by every prime found so far, I never have more than J primes on hand at any time, so I cannot end up doing more than 2J^2*ln(J) trial divisions. This won't win me any prize for efficiency or clever algorithms, or even sharp bounds for computational cost, but it is no worse than polynomial.

Categories : Algorithm

Related to : Generating prime numbers in poly-time
Print prime numbers in an interval
I don't see what your strange while loop has do to with finding if a number is prime. You should be checking if n is divisible by any number i between 2 and sqrt(n). You check that with the condition if (n%i==0).

Categories : Java
Why it doesn't generate me first n prime numbers?
Your condition for printing is not correct. (prim);cout<<i<<","; should be if(prim) cout<<i<<","; Note that your logic prints primes <= n, not the first n prime numbers.

Categories : C++
Use sort method and JOptionPane to have user input 10 numbers and output be the 10 numbers sorted
Plenty of errors in the main method. What you should do to fix: JOptionPane returns String so you should enter your numbers so that it can be converted to numbers, with some sort of delimiter Split and convert to numbers Assemble and int array and call the method Something like public static void main(String[] args) { // Request for user to enter 10 numbers int[] numbers = new int[10

Categories : Java
Python: prime test
It looks like you're tring to use the trivial (aka slow) method of computing primes: for a prime candidate p, try dividing all integers from 2 to floor(sqrt(p)). eps = 1e-9 def isprime(p): int_p = int(p) # only integers are prime, accounting for floating point rounding error if abs(int_p - p) < eps: return False else: # a number is prime only if it cannot be eve

Categories : Python
How to count same numbers and return muximum counted numbers value from each column
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Categories : Sql Server
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