Consider three consecutive integers x, y = x+1, and z = x+2. When is the number xy+z prime? For example, if x = 3 or x = 5, then the results are 17 and 37, both prime, but if x = 7 or x = 11, the results are 65 and 145, which are composite.
Write a function to list prime numbers less than or equal to the input that can be written in the form . The function should also return the values of x (i.e., the smallest number of the triple) leading to the primes.
Optional: Prove that the number of primes of this form is infinite.
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Last Solution submitted on Apr 24, 2026

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