Problem 60581. List primes of the form xy+z
Consider three consecutive integers x,
, and
. When is the number
prime? For example, if
or
, then the results are 17 and 37, both prime, but if
or
, 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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