首先我们要明确质数（素数）的含义：
所谓质数（素数），是它的因数只有1与它本身，例如2。
所以我们可以这样判断一个数是否为质数：
# -*- coding: UTF-8 -*-
# 用户输入数字
num = int(input("请输入一个数字: "))
# 质数大于 1
if num > 1:
# 查看因子
for i in range(2,num):
if (num % i) == 0:
print(num,"不是质数")
print(i,"乘",num//i,"是",num)
break
else:
print(num,"是质数")
# 如果输入的数字小于或等于 1，不是质数
else:
print(num,"不是质数")
这样子是不是很简单？
那么有可能有人要问了：我要做质数表怎么办呢？
其实就是上面的程序在加一个for循环就好了：
# -*- coding: UTF-8 -*-
def prime(num):
for i in range(2,num):
if (num % i) == 0:
break
else:
print(num,"是质数")
for i in range(2,100002):
prime(i)
input()
为了便于以后查看，我们把它写入到文件中：
# -*- coding: UTF-8 -*-
def prime(num):
a = open('prime.txt','a')
for i in range(2,num):
if (num % i) == 0:
break
else:
print(num,"是质数")
a.write(str(num)+"是质数"+'\n')
for i in range(2,100002):
prime(i)
input()
所谓完全数，就是一个数的因子之和（不包括它本身）等于它，例如6。
要用Python计算完全数，还要了解梅森素数。即
如果这个数为素数，则称之为 “梅森素数”）。
这是一个梅森素数列表：
lst = [2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011,24036583,25964951,30402457,32582657,37156667,42643801,43112609,57885161,74207281,77232917,82589933]
完全数公式：
其中
为梅森素数。
寻找完全数程序：
import time
c = 0
lst = [2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011,24036583,25964951,30402457,32582657,37156667,42643801,43112609,57885161,74207281,77232917,82589933]
xx = open('perfect.docx','w')
time_start=time.time()
for i in lst:
c += 1
a = (2**(i-1))*(2**i-1)
xx.write(str(c)+':'+str(a)+'\n')
time_end=time.time()
print(str(c)+' complete numbers have been calculated, it takes %s seconds.'%str(time_end-time_start)+'This m is '+str(i)+',it has '+str(len(str(a)))+' digits.')
input()
