On my computer, the calculation of all invalid numbers in the given input file, rather than just the first one, takes between 2000 and 4000 microseconds.
Welcome to Number Associative Mining and Trading Inc, or NAMT for short! Your duties are to make sure our turtles, working in difficult environments, are making correct associations, and stopping their operations when the tunnel is about to crumble. For that, our mathematicians finally found with absolute certainty the pattern the numbers mined follow before going too far.
Here's how the mathematicians have written the solution, they did write it in understandable words for once: "The first 100 numbers of the mine are always secure, but after that, the next number is only safe if it is the sum of 2 numbers in the previous 100."