EularProject 47：具有相同个数因子的连续数字

Distinct primes factors

Problem 47

The first two consecutive numbers to have two distinct prime factors are:

14 = 2 × 7

15 = 3 × 5

The first three consecutive numbers to have three distinct prime factors are:

644 = 22 × 7 × 23

645 = 3 × 5 × 43

646 = 2 × 17 × 19.

Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?

Answer:

134043

__author__ = ‘zhengyi‘
primeNum=4
consecutiveNum=4

from math import sqrt
def IsPrime(x):
    k=int(sqrt(x))+1
    for i in range(2,k):
        if x%i==0:
            return False
    return True

def primeCount(x):
    result=0
    for i in range(0,len(primeSet)):
        if x%primeSet[i]==0:
            result+=1
            while x%primeSet[i]==0:
                x//=primeSet[i]
            if x==1:
                return result

primeSet=[]
p=1
consecutive=0
while True:
    p+=1
    if IsPrime(p):
        primeSet.append(p)
        consecutive=0
    else:
        if primeCount(p)==primeNum:
            consecutive+=1
            if consecutive==consecutiveNum:
                print(p-consecutiveNum+1)
                break
        else:
            consecutive=0

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