Twin primes are a pair of prime numbers that differ by 2. Forexample, 3 and 5 are twin primes, 5 and 7 are twin primes, and 11 and 13 aretwin primes. Write a program to find all twin primes less than 1,200. Display theoutput as follows:(3, 5)(5, 7)...
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Twin primes are a pair of prime numbers that differ by 2. For
example, 3 and 5 are twin primes, 5 and 7 are twin primes, and 11 and 13 are
twin primes. Write a
output as follows:
(3, 5)
(5, 7)
...
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- Description A mathmatician Goldbach's conjecture: any even number(larger than 2) can divide into two prime number’s sum.But some even numbers can divide into many pairs of two prime numbers’ sum. Example:10 =3+7, 10=5+5, 10 can divide into two pairs of two prime number. Input Input consist a positive even number n(4<=n<=32766). Output Print the value of how many pairs are this even number can be divided into. Sample Input 1 1234 Sample Output 1 25use JAVA to write the code. : Euclid’s algorithm for finding the greatest common divisor (gdc) of two numbers The algorithm: given two numbers, n1 and n2: Divide n1 by n2 and let r be the remainder. If the remainder r is 0, the algorithm is finished and the answer is n2. (If the remainder is 1, the numbers are mutually prime and we are done-see below.) Set n1 to the value of n2, set n2 to the value of r, and go back to step 1. Entering 0 for one of the values is bad. It should work for the other value, but you have to figure out which is OK and which is bad. Catch this problem as it happens and make the user enter another value until they enter an acceptable one. Give an appropriate error message if this happens.Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…
- Problem-1: Check if an integer is Prime An integer greater than 1 is prime if its only positive divisor is 1 or itself. For example, 2, 3, 5, and 7 are prime numbers, but 4, 6, 8, and 9 are not. Key idea: To test whether a number is prime, check whether it is divisible by 2, 3, 4, and so on up to number/2. If a divisor is found, the number is not a prime. The algorithm can be described as follows: Use a boolean variable isPrime to denote whether the number is prime; Set isPrime to true initially; for (int divisor = 2; divisor <= number / 2; divisor++) { if (number % divisor == 0) { Set isPrime to false Exit the loop; } }JAVA Coding Problem Holi is celebrated in India as a festival of colours and your friend Khan from India has gifted you X packets of colours. Now you are planning to make a beautiful rangoli, to make it you need to map all colours pairwise distinct, so that they look attractive. To do so, you can mix the colours zero or more times: Pick any two random colours. Let's denote their weight by t and u. Mix the colour with second colour. After the process, the value of the first colour remains t, but the weight of the second colour changes to t+ u. Now you have to develop the code to find the minimum number of mixing operations you needs to perform to make a beautiful Rangoli. Sample Test Case Scenario: 1 3 321 Output:Java Assignment: Mathematics is the very interesting subject and for the India it is also a point of pride because Mr. Brahmagupta gives the 0 to world. So, in this series want to be great mathematician like Brahmagupta. He is keep practicing for her goal achievement. Once He knew about the Vector dot Product So He asked his friend Sammer the problem. He gave her two vectors A and B length N. He asked him to reduce the dot output of these two vectors. Sammer has the option to change the order of the objects of these two carriers i.e., in any two objects I and j at any vector can change the shape of these objects. Since Sammer is new to the program, he has asked you to resolve the issue using C++ Programming language. Input: 1 4 142-5 3 -8 5 2 Output: -50
- " Given positive integers n and r, list all the r-permutations, withrepetition allowed, of the set {1, 2, 3, . . . , n} " Develop a mini calculator that could allow a user to enter the input r and n and the calculator would shows the output. Your calculator must based on questions above Example if user input n = 3 and r = 2. the answer will display the list 1,1 1,2 1,3 2,1 2,2 2,3 3,1 3,2Problem specification: There is a grid of NXN squares. We can easily determines how many different rectangles (squares are excluded) there are in the grid. For example, in a 3X3 grid, you can find 22 different rectangles, marked as the green rectangles. You can see that we did not count the red ones as they are squares. In this assignment, you will write a Java program that takes the value of N as input and determines the total area of all the rectangles in the grid. Assume that the smallest squares in the grid have length 1. So a 3X2 rectangle will have an area of 6. For example, the total area of all the rectangles in the 3X3 grid is 66.…Three numbersa. Write a program that reads three numbers and prints “all the same” if they are allthe same, “all different” if they are all different, and “neither” otherwise.b. Write a program that reads three numbers and prints “increasing” if they are inincreasing order, “decreasing” if they are in decreasing order, and “neither”otherwise. Here, “increasing” means “strictly increasing”, with each value largerthan its predecessor. The sequence 3 4 4 would not be considered increasing.c. Repeat part b. but before reading the numbers, ask the user whetherincreasing/decreasing should be “strict” or “lenient”. In lenient mode, thesequence 3 4 4 is increasing and the sequence 4 4 4 is both increasing anddecreasing
- Please written by computer source Both 169 and 961 are the square of a prime. 169 is the reverse of 961. We call a number a reversible prime square if: It is not a palindrome, and It is the square of a prime, and Its reverse is also the square of a prime. 169 and 961 are not palindromes, so both are reversible prime squares. Find the sum of the first 50 reversible prime squares. in java[Python Language] Using loops of any kind, lists, or is not allowed. Angela loves reading books. She recently started reading an AI generated series called “Harry Trotter”. Angela is collecting books from the series at her nearest bookstore. Since the series is AI generated, the publishers have produced an infinite collection of the books where each book is identified by a unique integer. The bookstore has exactly one copy of each book. Angela wants to buy the books in the range [l,r], where l ≤ r. As an example, the range [−3,3] means that Angela wants to buy the books − 3, − 2, − 1, 0, 1, 2, and 3. Dan also loves the series (or maybe annoying Angela – who knows, really), and he manages to sneak into the bookstore very early to buy all of the books in the range [d,u], where d ≤ u. When Angela later visits, sadly she will not find those books there anymore. For example, if Angela tries to buy books [−2,3] and Dan has bought books [0,2], Angela would only receive books − 2, − 1,…Practicing Loops. Einstein Private Elementary school has three classes in each of its 9 grades. 27 classes in total. It has kindergarten (grade 0) though 8th grade. The school allows parents to pay tuition over the nine-month school year. Tuition for kindergarten is $90 dollars every month. Tuition for the other grades is $50 times the grade level every month. (1st grade is $50 a month, second grade is $100 a month, etc.) Design a programming solution that outputs nine tuition payment bills for each of the 27 classrooms. Each bill must contain the grade number (0 through 8), the classroom number (1 through 3), the month (1 through 9) and the amount of the tuition due. Your output should look something like: Grade Classroom Month Tuition 0 1 1 90 0 1 2 90 0 1 3 90 0 1 4 90 ... 8 3 7 400 8 3…
