Prime Sieve Method--spoj problem 2 prime Generator

Prime number is also known as prime numbers, except 1 and itself, cannot be divided into other natural numbers, in other words, the number except 1 and itself no longer have other factors; otherwise called composite. The smallest prime number is 2.

To determine whether an integer N is a prime number is simple, see if it can be divisible by an integer between 2 and sqrt (n).

def isprime (n):    if n%2==0:        return False    for i in Xrange (3,int (MATH.SQRT (n) +1), 2):        if n%i==0:            Return False    return True

But to find out all the prime numbers between 1 and N, one decision is clearly not a good idea. Since composite can be decomposed into a series of prime numbers, the composite between 1 and N is a multiple of a prime number between 1 and sqrt (n), excluding these composite, and the remainder being prime numbers:

Import Mathimport timeitdef findprime (n):    a=[true]* (n+1)    a[0]=false    a[1]=false for    i in Xrange (2,int (MATH.SQRT (n) +1)):        if a[i]:            k=i*i while            k<=n:                a[k]=false                k=k+i      if __name__== ' __ Main__ ':    T=timeit. Timer (' Findprime (2000000) ', ' from __main__ import findprime ')    print T.timeit (1)

The algorithm starts from 2 to determine whether it is prime and excludes multiples of prime numbers, and when 2 to I are judged, it is clear that i+1 is prime.

Spoj problem 2 Prime Generator requires finding prime numbers between N and M, of which 1 <= m <= n <= 1000000000, n-m<=100000.

In this case, a 1000000000-length sequence would be a waste of space, and a prime number between 1 and sqrt (n) would need to be found first, then the multiples of these primes between N and M would be excluded:

Import Mathdef findprime (n):    a=[true]* (n+1)    a[0]=false    a[1]=false for    i in Xrange (2,int (MATH.SQRT (n ) +1):        if a[i]:            k=i*i while            k<=n:                a[k]=false k=k+i for i in    xrange (2,n+1):        if A[i]:            yield idef findprimebyseed (n,m):    if n==1:        n=2    seed=findprime (int (math.sqrt (m)))    alist=[ 1]* (m-n+1) for    Prime in seed:           if prime<n:            k= (prime-n%prime)%prime        else:            k=2*prime-n While        k<=m-n:            alist[k]=false                        k+=prime for    i in Xrange (m-n+1):        if alist[i]:            Print I +n                if __name__== ' __main__ ':    line=int (Raw_input ()) for    I on Xrange (line):        n,m=raw_input (). Split ()        findprimebyseed (int (n), int (m))        print

　　

　　

Prime Sieve Method--spoj problem 2 prime Generator