Landau's problem

Landau's problem asks whether there are infinitely many prime numbers that are exactly three steps apart, known as prime pairs separated by a gap of 4 (like 3 and 7, 7 and 11). In simple terms, it questions if such prime pairs keep appearing forever or if they eventually stop. While mathematicians know many results about the distribution of primes and related gaps, the specific question of whether infinitely many prime pairs differ by four remains unproven, representing a subtle and intriguing challenge in understanding prime number patterns.