2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65345In 1737 Leonard Euler gave what we often now think of as a new proof, based on infinite series, of Euclid's theorem that there are infinitely many prime numbers. Our short paper uses a simple modification of Euler's argument to obtain new results about the distribution of prime factors of sets of integers, including a weak one-sided Tschebyshev inequality. An example shows that there cannot be a prime number theorem in this situation, or even a pair of Tschebyshev inequalities, but it would be very interesting to know if a one-sided Tschebyshev inequality holds.Revision 1, Plain Tex, 7 pages. Revision 1 corrects history, references and non-computability exampleNumber Theorytext