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The first two consecutive numbers to have two distinct prime factors are:14 = 27 15 = 35The first three consecutive numbers to have three distinct prime factors are:644 = 2²723 645 = 3543 646 = 21719.Find the first four consecutive integers to have four distinct prime factors. What is the first 阅读全文
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The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.Find the sum of the only eleven primes that are both 阅读全文
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The decimal number, 585 = 10010010012(binary), is palindromic in both bases.Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.(Please note that the palindromic number, in either base, may not include leading zeros.)题目大意：十进制数字585 = 10010010012(二进制),可以看出在十 阅读全文
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The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.How many circular primes are there below one million?题目大意：我们称197为一个循环质数，因为它的所有轮转形式: 19 阅读全文
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145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.Find the sum of all numbers which are equal to the sum of the factorial of their digits.Note: as 1! = 1 and 2! = 2 are not sums they are not included.题目大意：145 是一个奇怪的数字, 因为 1! + 4! + 5! = 1 + 24 + 120 = 145.找出所有等于各位数字阶乘之和的数字之和。注意: 因为 1! = 阅读全文
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The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that49/98 = 4/8, which is correct, is obtained by cancelling the 9s.We shall consider fractions like, 30/50 = 3/5, to be trivial examples.There are exactly four non-trivia 阅读全文
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Consider all integer combinations ofabfor 2a5 and 2b5:22=4, 23=8, 24=16, 25=3232=9, 33=27, 34=81, 35=24342=16, 43=64, 44=256, 45=102452=25, 53=125, 54=625, 55=3125If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:4, 8, 9, 16, 25, 阅读全文
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Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:2122 23 242520 7 89 1019 6 1 2 1118 5 4 3 121716 15 1413It can be verified that the sum of the numbers on the diagonals is 101.What is the sum of the numbers on the diagonals in a 1001 .. 阅读全文
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Usingnames.txt(right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a na 阅读全文
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It is possible to show that the square root of two can be expressed as an infinite continued fraction.2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...By expanding this for the first four iterations, we get:1 + 1/2 = 3/2 = 1.51 + 1/(2 + 1/2) = 7/5 = 1.41 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...1 阅读全文
