标签:手机 The time 应用 存在 generate tin hal app
素数(prime)也称为质数,就是除了1和它本身没有其他约数。素数的研究一直是数学界热点,人们一直在寻找素数的规律,以及是否存在一个最大的素数。当然,这不仅仅是一个纯数学问题,素数在计算机加密学中有很广泛的应用。# Primality Testing with the Rabin-Miller Algorithm
# http://inventwithpython.com/hacking (BSD Licensed)
import random
def rabinMiller(num):
# Returns True if num is a prime number.
s = num - 1
t = 0
while s % 2 == 0:
# keep halving s while it is even (and use t
# to count how many times we halve s)
s = s // 2
t += 1
for trials in range(5): # try to falsify num‘s primality 5 times
a = random.randrange(2, num - 1)
v = pow(a, s, num)
if v != 1: # this test does not apply if v is 1.
i = 0
while v != (num - 1):
if i == t - 1:
return False
else:
i = i + 1
v = (v ** 2) % num
return True
def isPrime(num):
# Return True if num is a prime number. This function does a quicker
# prime number check before calling rabinMiller().
if (num < 2):
return False # 0, 1, and negative numbers are not prime
# About 1/3 of the time we can quickly determine if num is not prime
# by dividing by the first few dozen prime numbers. This is quicker
# than rabinMiller(), but unlike rabinMiller() is not guaranteed to
# prove that a number is prime.
lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
if num in lowPrimes:
return True
# See if any of the low prime numbers can divide num
for prime in lowPrimes:
if (num % prime == 0):
return False
# If all else fails, call rabinMiller() to determine if num is a prime.
return rabinMiller(num)
def generateLargePrime(keysize=1024):
# Return a random prime number of keysize bits in size.
while True:
num = random.randrange(2**(keysize-1), 2**(keysize))
if isPrime(num):
return num
(代码块可左右滑动)
如果我们要判断一个数是不是素数,可以直接调用其中的isPrime()函数。
isPrime(2)
# True
isPrime(71)
# True
isPrime(99)
# False
对于一个11位的手机号码,如果你的尾数是0,2,4,5,6,8,那么你可以放弃了,根本不可能是素数。
比如我们要寻找以1881308****开头的1万个手机号码中的素数的个数:
my_prime = []
for i in range(18813080000,18813089999):
if isPrime(i):
my_prime.append(i)
print(my_prime)
# [18813080003,18813080021, 18813080029, 18813080059,
# ....
# 18813089921, 18813089983, 18813089987]
我们可以找到403个是素数的幸运数字。
值得注意的是,Rabin-Miller算法并不是逐一进行验证,因而用它判断一个数是不是素数存在一定的风险,如果该算法认为一个数是素数,那么这个数”极有可能“是素数,如果认为一个数不是素数,那么该数”绝对“不是素数。当然,这种算法的优点就是速度,几乎不需要耗费额外的时间。
所以,下次选手机号码的时候一定看一下它是不是素数,当别人说我的手机号码是”XX的生日“,”有4个8“的时候,你的手机号码是一个素数,深藏功与名!
而且运营商绝对不会把它当作靓号加价卖给你!
===== THE END ====
参考资料:参见代码备注
标签:手机 The time 应用 存在 generate tin hal app
原文地址:https://blog.51cto.com/15069450/2577352