Tag Archives: sieve

Count all perfect divisors of a number

Given a number n, count total perfect divisors of n. Perfect divisors are those divisors which are square of some integer. For example a perfect divisor of 8 is 4. Input : n = 16 Output : 3 Explanation : There are only 5 divisor of 16: 1, 2, 4, 8, 16. Only three of… Read More »

Sieve of Eratosthenes in 0(n) time complexity

The classical Sieve of Eratosthenes algorithm takes O(N log (log N)) time to find all prime numbers less than N. In this article, a modified Sieve is discussed that works in O(N) time. Example : Given a number N, print all prime numbers smaller than N Input : int N = 15 Output : 2… Read More »

Find two prime numbers with given sum

Given an even number (greater than 2 ), print two prime numbers whose sum will be equal to given number. There may be several combinations possible. Print only first such pair. An interesting point is, a solution always exist according to Goldbach’s conjecture. Examples: Input: n = 74 Output: 3 71 Input : n =… Read More »

Super Prime

Super-prime numbers (also known as higher order primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. First few Super-Primes are 3, 5, 11 and 17. The task is to print all the Super-Primes less than or equal to the given positive integer N. Examples: Input: 7… Read More »

Mersenne Prime

Mersenne Prime is a prime number that is one less than a power of two. In other words, any prime is Mersenne Prime if it is of the form 2k-1 where k is an integer greater than or equal to 2. First few Mersenne Primes are 3, 7, 31 and 127. The task is print… Read More »