September 2023 - Solution
September 2023 Solution:
The solutions are 79820644 and 202373481820525416280764330407686074634 (\pm 1, depending on how you're counting).
The paper ["A Natural Prime-Generating Recurrence"] by Eric S. Rowland gives a good overview of this this nice prime-generation method. While the main solution can be reached by rather naive programming, the bonus one requires additional tricks, and Rowland gives a nice trick allowing to bypass the "1" elements of the sequence, with the price being the need to factor numbers (or rather, find the smallest factor)