素数判定

素数判定

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 7 Accepted Submission(s) : 3

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Problem Description

对于表达式n^2+n+41，当n在（x,y）范围内取整数值时（包括x,y）(-39<=x

Input

输入数据有多组，每组占一行，由两个整数x，y组成，当x=0,y=0时，表示输入结束，该行不做处理。

Output

对于每个给定范围内的取值，如果表达式的值都为素数，则输出\否则请输出“Sorry”,每组输出占一行。

Sample Input

0 1 0 0

Sample Output

OK

Author

lcy

分拆素数和

Time Limit : 1000/1000ms (Java/Other) Memory Limit : 32768/32768K (Java/Other)

Total Submission(s) : 4 Accepted Submission(s) : 3

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Problem Description

把一个偶数拆成两个不同素数的和，有几种拆法呢？

Input

输入包含一些正的偶数，其值不会超过10000，个数不会超过500，若遇0，则结束。

Output

对应每个偶数，输出其拆成不同素数的个数，每个结果占一行。

Sample Input

30 26 0

Sample Output

3 2

Source

2007省赛集训队练习赛（2）

How many prime numbers

Time Limit : 3000/1000ms (Java/Other) Memory Limit : 32768/32768K (Java/Other)

Total Submission(s) : 24 Accepted Submission(s) : 7

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Problem Description

Give you a lot of positive integers, just to find out how many prime numbers there are.

Input

There are a lot of cases. In each case, there is an integer N representing the number of integers to find. Each integer won’t exceed 32-bit signed integer, and each of them won’t be less than 2.

Output

For each case, print the number of prime numbers you have found out.

Sample Input

3

2 3 4

Sample Output

2

Author

wangye

Source

素数回文

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 0 Accepted Submission(s) : 0

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Problem Description

xiaoou33对既是素数又是回文的数特别感兴趣。比如说151既是素数又是个回文。现在xiaoou333想要你帮助他找出某个范围内的素数回文数，请你写个程序找出 a 跟b 之间满足条件的数。(5 <= a < b <= 100,000,000);

Input

这里有许多组数据，每组包括两组数据a跟b。

Output

对每一组数据,按从小到大输出a，b之间所有满足条件的素数回文数（包括a跟b）每组数据之后空一行。

Sample Input

5 500

Sample Output

5 7 11 101 131 151 181 191 313 353 373 383

Author

xiaoou333

Source

Largest prime factor

Time Limit : 5000/1000ms (Java/Other) Memory Limit : 32768/32768K (Java/Other)

Total Submission(s) : 3 Accepted Submission(s) : 3

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Problem Description

Everybody knows any number can be combined by the prime number. Now, your task is telling me what position of the largest prime factor. The position of prime 2 is 1, prime 3 is 2, and prime 5 is 3, etc. Specially, LPF(1) = 0.

Input

Each line will contain one integer n(0 < n < 1000000).

Output

Output the LPF(n).

Sample Input

1 2 3 4 5

Sample Output

0 1 2 1 3

Author

Wiskey

Source

HDU 2007-11 Programming Contest_WarmUp

Deciphering Password

Time Limit : 5000/1000ms (Java/Other) Memory Limit : 32768/32768K (Java/Other)

Total Submission(s) : 0 Accepted Submission(s) : 0

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Problem Description

Xiaoming has just come up with a new way for encryption, by calculating the key from a publicly viewable number in the following way:

Let the public key N = AB, where 1 <= A, B <= 1000000, and a0, a1, a2, …, ak-1 be the factors of N, then the private key M is calculated by summing the cube of number of factors of all ais. For example, if A is 2 and B is 3, then N = A = 8, a0 = 1, a1 = 2, a2 = 4, a3 = 8, so the value of M is 1 + 8 + 27 + 64 = 100. However, contrary to what Xiaoming believes, this encryption scheme is extremely vulnerable. Can you write a program to prove it?

B

Input

There are multiple test cases in the input file. Each test case starts with two integers A, and B. (1 <= A, B <= 1000000). Input ends with End-of-File. Note: There are about 50000 test cases in the input file. Please optimize your algorithm to ensure that it can finish within the given time limit.

Output

For each test case, output the value of M (mod 10007) in the format as indicated in the sample output.

Sample Input

2 2 1 1 4 7

Sample Output

Case 1: 36 Case 2: 1 Case 3: 4393

Source

Humble Numbers

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 0 Accepted Submission(s) : 0

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Problem Description

A number whose only prime factors are 2,3,5 or 7 is called a humble number. The sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, ... shows the first 20 humble numbers.

Write a program to find and print the nth element in this sequence

Input

The input consists of one or more test cases. Each test case consists of one integer n with 1 <= n <= 5842. Input is terminated by a value of zero (0) for n.

Output

For each test case, print one line saying \Depending on the value of n, the correct suffix \ordinal number nth has to be used like it is shown in the sample output.

Sample Input

1 2 3 4 11 12 13 21 22 23 100 1000 5842 0

Sample Output

The 1st humble number is 1. The 2nd humble number is 2. The 3rd humble number is 3. The 4th humble number is 4. The 11th humble number is 12. The 12th humble number is 14. The 13th humble number is 15. The 21st humble number is 28. The 22nd humble number is 30. The 23rd humble number is 32. The 100th humble number is 450.

The 1000th humble number is 385875.

The 5842nd humble number is 2000000000.

The Euler function

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 32768/32768K (Java/Other)

Total Submission(s) : 0 Accepted Submission(s) : 0

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Problem Description

The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: suppose you are given a, b, try to calculate (a)+ (a+1)+....+ (b)

Input

There are several test cases. Each line has two integers a, b (2

Output

Output the result of (a)+ (a+1)+....+ (b)

Sample Input

3 100

Sample Output

3042

Source

2009 Multi-University Training Contest 1 - Host by TJU

Product of coprimes

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 5 Accepted Submission(s) : 3

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Problem Description

You are given a positive integer m. Calculate the product of all positive integers less then or equal to m and coprime with m, and give the answer modulo m.

Input

There are multiple tests end with EOF, each test contains only a positive integer m ≤ 10^9 in a line. The number of tests is no more than 5000.

Output

In the output file you should write the answer to the task.

Sample Input

1 2 3 4 5 6 7

Sample Output

0 1 2 3 4 5 6

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