109 lines
2.6 KiB
Python
109 lines
2.6 KiB
Python
''' mbinary
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#########################################################################
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# File : isPrime.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-03-04 21:34
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# Description:
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#########################################################################
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'''
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from random import randint
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def quickMulMod(a,b,m):
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'''a*b%m, quick'''
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ret = 0
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while b:
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if b&1:
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ret = (a+ret)%m
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b//=2
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a = (a+a)%m
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return ret
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def quickPowMod(a,b,m):
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'''a^b %m, quick, O(logn)'''
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ret =1
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while b:
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if b&1:
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ret =quickMulMod(ret,a,m)
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b//=2
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a = quickMulMod(a,a,m)
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return ret
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def isPrime(n,t=5):
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'''miller rabin primality test, a probability result
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t is the number of iteration(witness)
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'''
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t = min(n-3,t)
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if n<2:
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print('[Error]: {} can\'t be classed with prime or composite'.format(n))
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return
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if n==2: return True
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d = n-1
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r = 0
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while d%2==0:
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r+=1
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d//=2
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tested=set()
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for i in range(t):
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a = randint(2,n-2)
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while a in tested:
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a = randint(2,n-2)
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tested.add(a)
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x= quickPowMod(a,d,n)
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if x==1 or x==n-1: continue #success,
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for j in range(r-1):
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x= quickMulMod(x,x,n)
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if x==n-1:break
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else:
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return False
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return True
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'''
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we shouldn't use Fermat's little theory
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Namyly:
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For a prime p, and any number a where (a,n)=1
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a ^(p-1) \equiv 1 (mod p)
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The inverse theorem of it is not True.
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a counter-example: 2^340 \equiv 1 (mod 341), but 341 is a composite
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'''
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class primeSieve:
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'''sieve of Eratosthenes, It will be more efficient when judging many times'''
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primes = [2,3,5,7,11,13]
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def isPrime(self,x):
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if x<=primes[-1]:
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return twoDivideFind(x,self.primes)
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while x>self.primes[-1]:
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left = self.primes[-1]
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right = (left+1)**2
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lst = []
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for i in range(left,right):
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for j in self.primes:
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if i%j==0:break
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else:lst.append(i)
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self.primes+=lst
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return twoDivideFind(x,lst)
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def twoDivideFind(x,li):
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a,b = 0, len(li)
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while a<=b:
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mid = (a+b)//2
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if li[mid]<x:a=mid+1
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elif li[mid]>x: b= mid-1
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else:return mid
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return -1
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if __name__=='__main__':
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n = 100
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print('prime numbers below',n)
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print([i for i in range(n) if isPrime(i)])
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while 1:
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n = int(input('n: '))
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print(isPrime(n))
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