Java Program to find Prime Number : Prime Number is a positive integer number that is divisible by only two numbers, that is 1 and the number itself. Note: 1 is not a prime number as it isn’t divisible by two number. The prime numbers are 2, 3, 5, 7, 11……. Prime Numbers Java Program

The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a unique product of prime numbers. So, for instance, 6936=2*2*2*3*17*17. A method named encodeNumber will encode a number n as an array that contains the prime numbers that, when multipled together, will equal n. So encodeNumber(6936) would return

A number n>0 is called cube-powerful if it is equal to the sum of the cubes of its digits. Examples: if n is return because 153 1 because 153 = 13 + 53 + 33 370 1 because 370 = 33 + 73 + 03 371 1 because 371 = 33 + 73 + 13

A factor that is a prime number is prime factor. A function named largestPrimeFactor that will return the largest prime factor of a number. If the number is <=1 it should return 0. Recall that a prime number is a number > 1 that is divisible only by 1 and itself, e.g., 13 is prime

A function named largestAdjacentSum that iterates through an array computing the sum of adjacent elements and returning the largest such sum. Examples: if a is return {1, 2, 3, 4} 7 because 3+4 is larger than either 1+2 or 2+3 {18, -12, 9, -10} 6 because 18-12 is larger than -12+9 or 9-10 {1,1,1,1,1,1,1,1,1} 2

A method named getExponent(n, p) that returns the largest exponent x such that px evenly divides n. If p is <= 1 the method should return -1. For example, getExponent(162, 3) returns 4 because 162 = 21 * 34, therefore the value of x here is 4. Examples: if n is and p is return

The fullness quotient of an integer n > 0 to be the number of representations of n in bases 2 through 9 that have no zeroes anywhere after the most significant digit. For example, to see why the fullness quotient of 94 is 6 examine the following table which shows the representations of 94 in

A cluster in an integer array to be a maximum sequence of elements that are all the same value. For example, in the array {3, 3, 3, 4, 4, 3, 2, 2, 2, 2, 4} there are 5 clusters, {3, 3, 3}, {4, 4}, {3}, {2, 2, 2, 2} and {4}. A cluster-compression of an array

An array to be trivalent if all its elements are one of three different values. For example, {22, 19, 10, 10, 19, 22, 22, 10} is trivalent because all elements are either 10, 22, or 19. However, the array {1, 2, 2, 2, 2, 2, 2} is not trivalent because it contains only two different

A stacked number is a number that is the sum of the first n positive integers for some n. The first 5 stacked numbers are 1 = 1 3 = 1 + 2 6 = 1 + 2 + 3 10 = 1 + 2 + 3+ 4 15 = 1 + 2 + 3