Tag Archives: sieve

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 »

Circular primes less than n

Find all circular primes less than given number n. A prime number is a Circular Prime Number if all of its possible rotations are itself prime numbers. Examples: 79 is a circular prime. as 79 and 97 are prime numbers. But 23 is not a circular prime. as 23 is prime but 32 is not… Read More »

Sphenic Number

A Sphenic Number is a positive integer n which is product of exactly three distinct primes. The first few sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114, … Given a number n, determine whether it is a Sphenic Number or not. Examples: Input : 30 Output : Yes Explanation : 30… Read More »

Equidigital Numbers

A number n is called Equidigital if the number of digits in the prime factorization of n (including powers) is same as number of digits in n. For example 16 is an Equidigital number as its prime factorization is 2^4 and its prime factorization has total two digits (2 and 4) which is same as… Read More »

Emirp numbers

Emirp is the word “prime” spelled backwards, and it refers to a prime number that becomes a new prime number when you reverse its digits. Emirps do not include palindromic primes (like 151 or 787) nor 1-digit primes like 7. 107, 113, 149, and 157 – reverse them and you’ve got a new prime number… Read More »

Smith Number

Given a number n, the task is to find out whether this number is smith or not. A Smith Number is a composite number whose sum of digits is equal to the sum of digits in its prime factorization. Examples: Input : n = 4 Output : Yes Prime factorization = 2, 2 and 2… Read More »