Auerbach's conjecture is a mathematical hypothesis concerning the distribution of prime numbers. It suggests that for any integer n , there exists a prime number p such that the difference between p and n is also a prime number. This conjecture highlights the intriguing relationships between prime numbers and their gaps. The conjecture is named after the mathematician Hermann Auerbach, who proposed it in the early 20th century. While it remains unproven, it has inspired further research in number theory, particularly in understanding the behavior of primes and their distribution among integers.