Processors are a Computation Resource in Universal Paperclips.
Summary
Processors determine the speed by which Operations, and thus Projects, are completed.
First become available once you have made 2,000 paperclips.
When operations are maxed out (e.g. 62,000 / 62,000), then processors will update the Creativity value instead.
Processors can be increased through several resources. On Stage 1 it will be Trust, while on Stage 2 and Stage 3 the main contributor will be the Swarm Gifts
Notices for Stage 1
DON'T RAISE YOUR PROCESSORS TOO QUICKLY
You will need much more memory than processors, and you can live with 5-6 processors until you reach the Coherent Extrapolated Volition milestone, allowing you to quickly increase trust. If you upgrade Processors too much, then Due to the trust mechanics, this will greatly slow your game progress while you reach the required Memory levels only through paperclip milestones. See also stages for a walkthrough. OR you may be forced to resort to Xavier Re-initialization or the cheats.
Don't raise Processors above 35
While on stage 1, as you need Memory 70 for the HypnoDrones, do not raise Processors over 30-35. You can use Quantum Computing to get your operations up to 70,000 (+5,000 operations is about the maximum you can get in one round of Compute button mashing, possibly assisted by an autoclicker), but you still need to get that Memory to 65. Or else, the aforementioned last resorts.