python練手好例子：驗證哥德巴赫猜想

哥德巴赫猜想是一個謎，但十分適合用來作爲編程練習
涉及的幾個問題：
1、如何驗證一個數是素數 def prime(n)
一個整數n不能被2 到 $\sqrt{n}$整除，則爲素數
2、產生N以內的素數列表
本文中N取100，可以取更大
3、對於大於6的偶數，從素數表中取得素數和的計算

import math

def prime(n):
    retBool = True
    # print("n=",n,int(math.sqrt(n)))
    for num in range(2, int(math.sqrt(n))+1):
        # print("\nnum=",n,num,n%num)
        if n % num == 0:
            retBool = False
            break
        else:
            retBool = True
    return retBool

if __name__ == '__main__':
    su = []
    for i in range(3, 100):   # 100可改成100000或更大，自然需要時間更長
        if i % 2 != 0 or i==2:
            if prime(i):
                su.append(i)
    # print(su)
    num = len(su)
    p = 6
    # with open("test.txt","w") as f:
    f = open("test.txt","w")
    f.write(str(p)+"=")
    while(p<su[num-1]+su[0]):
        for k in range(1,num):
            if p<su[k-1]*2 :
                break
            else:
                p1=su[k-1]
                p2=p-p1
                if(p2 in su):
                    print("p=",p,p1,p2)
                    f.write(str(p1)+"+"+str(p2)+"; ")
        p=p+2
        f.write("\n"+str(p)+"=")

    f.close()

計算結果如下：

6=3+3;
8=3+5;
10=3+7; 5+5;
12=5+7;
14=3+11; 7+7;
16=3+13; 5+11;
18=5+13; 7+11;
20=3+17; 7+13;
22=3+19; 5+17; 11+11;
24=5+19; 7+17; 11+13;
26=3+23; 7+19; 13+13;
28=5+23; 11+17;
30=7+23; 11+19; 13+17;
32=3+29; 13+19;
34=3+31; 5+29; 11+23; 17+17;
36=5+31; 7+29; 13+23; 17+19;
38=7+31; 19+19;
40=3+37; 11+29; 17+23;
42=5+37; 11+31; 13+29; 19+23;
44=3+41; 7+37; 13+31;
46=3+43; 5+41; 17+29; 23+23;
48=5+43; 7+41; 11+37; 17+31; 19+29;
50=3+47; 7+43; 13+37; 19+31;
52=5+47; 11+41; 23+29;
54=7+47; 11+43; 13+41; 17+37; 23+31;
56=3+53; 13+43; 19+37;
58=5+53; 11+47; 17+41; 29+29;
60=7+53; 13+47; 17+43; 19+41; 23+37; 29+31;
62=3+59; 19+43; 31+31;
64=3+61; 5+59; 11+53; 17+47; 23+41;
66=5+61; 7+59; 13+53; 19+47; 23+43; 29+37;
68=7+61; 31+37;
70=3+67; 11+59; 17+53; 23+47; 29+41;
72=5+67; 11+61; 13+59; 19+53; 29+43; 31+41;
74=3+71; 7+67; 13+61; 31+43; 37+37;
76=3+73; 5+71; 17+59; 23+53; 29+47;
78=5+73; 7+71; 11+67; 17+61; 19+59; 31+47; 37+41;
80=7+73; 13+67; 19+61; 37+43;
82=3+79; 11+71; 23+59; 29+53; 41+41;
84=5+79; 11+73; 13+71; 17+67; 23+61; 31+53; 37+47; 41+43;
86=3+83; 7+79; 13+73; 19+67; 43+43;
88=5+83; 17+71; 29+59; 41+47;
90=7+83; 11+79; 17+73; 19+71; 23+67; 29+61; 31+59; 37+53; 43+47;
92=3+89; 13+79; 19+73; 31+61;
94=5+89; 11+83; 23+71; 41+53; 47+47;
96=7+89; 13+83; 17+79; 23+73; 29+67; 37+59; 43+53;
98=19+79; 31+67; 37+61;
100=3+97; 11+89; 17+83; 29+71; 41+59; 47+53;