Prime power triples The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way: 28 = 22 + 23 + 2433 = 32 + 23 + 2449…

The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way: 28 = 22 + 23 + 24 33 = 32 + 23 + 24 49 = 52 + 23 + 24 47…

>>> sum([int(i) for i in str(2**1000)]) 1366 >>>…

通过替换*3这样一个两位数的第一位,我们可以发现形成的九个数字有六个是质数,即13, 23,43,53,73,83.类似的,如果我们用同样的数字替换56**3这样一个五位数的第三位和第四位,会生成56003, 56113, 56333, 56443, 56663, 56773, 56993七个质数,事实是56003是拥有这个性质的最小质数.已知对于一个质数,可以通过使用相同的数字替换这个质数的一部分(不一定是相邻的数位),可以生成八个质数,求满足这个条件的最小质数. 分析:欧拉工程的前五十题都是…

素数3, 7, 109, 673很有意思,从中任取两个素数以任意顺序拼接起来形成的仍然是素数.例如,取出7和109,7109和1097都是素数.这四个素数的和是792,是具有这样性质的四个素数的最小的和.求满足以上性质的五个素数的最小的和. 分析:这道题的解法非常让人出人意料,这个问题实际上和图论中的的分团问题有关.要理解这个问题,我们需要知道一点图论中的基础知识.如果你已经对图论比较了解了,这一段可以跳过.图论属于组合数学的一个分支,图是图论的主要研究对象.所谓图是指由若干给定的顶点及连接两顶…

本题来自 Project Euler 第9题:https://projecteuler.net/problem=9 # Project Euler: Problem 9: Special Pythagorean triplet # A Pythagorean triplet is a set of three natural numbers, # a < b < c, for which, a**2 + b**2 = c**2 # For example, 3**2 + 4**2 = 9 +…

本题来自 Project Euler 第16题:https://projecteuler.net/problem=16 ''' Project Euler 16: Power digit sum 2**15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 2**1000? Answer: 1366 ''' print(sum(int(i…

本题来自 Project Euler 第11题:https://projecteuler.net/problem=11 # Project Euler: Problem 10: Largest product in a grid # In the 20×20 grid below, four numbers along a diagonal line have been marked in red. # The product of these numbers is 26 × 63 × 78 ×…

本题来自 Project Euler 第7题:https://projecteuler.net/problem=7 # Project Euler: Problem 7: 10001st prime # By listing the first six prime numbers: # 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. # What is the 10 001st prime number? # Answer…

本题来自 Project Euler 第3题:https://projecteuler.net/problem=3 # Project Euler: Problem 3: Largest prime factor # The prime factors of 13195 are 5, 7, 13 and 29. # What is the largest prime factor of the number 600851475143 ? # Answer: 6857 a = 6008514751…