Toomey theorem

Toomey's theorem addresses a specific problem in number theory involving how certain collections of prime numbers relate to each other through their multiples. Essentially, it states that if you have two sets of primes where the multiples of the primes in one set are contained within the multiples of the primes in the other, then these prime sets are closely connected—either they are the same set or one is a subset of the other, with some additional conditions. This theorem helps mathematicians understand the structure of prime numbers and their relationships within larger sets.