Prime Number Checker

Our Prime Number Checker is a complete prime number toolkit with five specialized modes for students, educators, and math enthusiasts. Mode 1: Check if a Number is Prime Enter any positive integer and get an instant verdict. The tool displays whether it's prime or composite, its complete prime factorization (e.g., 360 = 2³ × 3² × 5), the count of divisors, the next prime above it, and the nearest prime below it. Bonus facts include whether it's a twin prime (differs from a prime by 2), a Fibonacci prime, a palindrome prime, or a perfect square. Mode 2: First N Primes Generate the first N prime numbers (up to 1,000). Results display in a grid with the count, their sum, and the largest prime in the set. Useful for understanding prime density and distribution. Mode 3: Primes in a Range Find all prime numbers between any two values (up to a range of 100,000). Results include the complete list, count, sum of primes in range, the largest prime found, and the largest gap between consecutive primes — a fascinating measure of prime distribution. Mode 4: GCD & LCM Calculator Enter two numbers to calculate their Greatest Common Divisor (GCD) and Least Common Multiple (LCM). The tool shows step-by-step work using the Euclidean algorithm for GCD and the relationship LCM = (a × b) ÷ GCD(a, b). Also indicates whether the numbers are coprime (GCD = 1). Mode 5: Goldbach Conjecture Explore one of mathematics' most famous unsolved problems. Enter any even number and find all pairs of primes that sum to it. Goldbach's conjecture (1742) states every even integer greater than 2 is the sum of two primes — proven true for all tested numbers up to 4 × 10¹⁸ but never formally proven for all numbers.