The user wants me to do some quick napkin math / estimation to calculate the energy required by a Proof-of-Work (PoW) check running on-device instead of a CAPTCHA, considering world traffic and estimating energy wasted per year.

Let me first do a web search to find relevant data points:

Let me search for these data points.

Good, I have some useful data points. Let me search for more specific data on energy consumption per hash, global web request volume, and CAPTCHA frequency to make the napkin math more grounded.

I have good data now. Let me search for a couple more specific data points — global HTTP requests per day and energy per hash on typical CPUs (not ASICs, since we're talking about on-device PoW running on laptops/phones).

I now have enough data to build a comprehensive napkin math model. Let me organize the key data points:

Let me do the calculations properly using Python to make sure I get the math right.

The 1% and 5% challenge rates are way too high — they produce absurd numbers (388 billion to 2 trillion challenges per day). The literature estimate of 200M CAPTCHAs/day is much more realistic. Let me reconsider the model.

The issue is that "challenges" include invisible challenges that happen on every page load (like reCAPTCHA v3 scoring, Turnstile managed mode). But most of those are invisible and lightweight. The question is specifically about PoW checks that would run on-device.

Let me reconsider: the question asks about replacing CAPTCHA with PoW checks. So the relevant number is how many CAPTCHA-equivalent challenges happen daily. The 200M figure from literature is about visible CAPTCHAs. But invisible challenges (Turnstile, reCAPTCHA v3) happen much more frequently.

Let me look at it differently: if we replaced ALL bot-detection challenges with PoW, how many would that be?

Cloudflare Turnstile alone protects millions of sites. reCAPTCHA is on 1.8M websites. If each protected site gets even 1000 visits/day, that's billions of challenges.

Let me recalibrate and use the 500M midpoint, but also consider that many "invisible" challenges are very lightweight and don't require PoW. The question seems to be about PoW as a CAPTCHA replacement — so let's focus on the scenario where PoW replaces CAPTCHA on all sites that currently use it.

Actually, let me re-read the question: "calculate the amount of energy required by a PoW check running on-device instead of a captcha. Consider the world traffic and estimate the amount of energy wasted per year."

This is asking: if we replaced CAPTCHAs with on-device PoW checks, how much energy would that consume? Let me recalibrate to more realistic numbers.

The math looks more reasonable now. Let me continue building the model with the energy calculations.

Good progress. Now let me scale this up to daily and yearly energy consumption, and also consider the key insight: most of this energy is "wasted" in the sense that it's spent on proving work rather than doing useful computation. Let me also consider that devices are heterogeneous (phones vs laptops) and the actual incremental energy matters (not total system power, but the delta from baseline).

The numbers seem quite low (sub-1 TWh). This is because I'm calculating with single-core full load but the energy per challenge is small. However, I need to reconsider — the 15W is the INCREMENTAL power from hashing, not total system power. Let me also consider that:

Let me also consider that on mobile devices, the power draw is different and battery impact matters. Let me recalculate with more realistic heterogeneous device distribution and also compute what this means in practical terms (household equivalents, etc.).

Actually wait — 0.6 TWh in the highest scenario is still a lot of energy! Let me put this in perspective and also consider a wider range where most of the world's traffic goes through some form of challenge. Let me also reconsider the model.

Actually, I think there's a modeling issue. Let me reconsider: Cloudflare Turnstile and similar services run on a HUGE portion of the web. If we replaced ALL of these with PoW, and every single HTTP request (not just pageview) required a PoW... that would be very different. But that's not realistic.

Let me also look at this from another angle: what if EVERY website that currently uses any form of bot protection switched to PoW? And what if the difficulty was set high enough to actually deter bots? Let me model this more carefully.

The TWh numbers are printing as 0.0000 due to formatting. Let me fix the display and also recalculate. The energy numbers are coming out quite small. Let me reconsider the model — I think there's an issue with the difficulty level. Let me think about this more carefully.

Actually, wait. The issue might be that I'm underestimating the impact. Let me recalculate more carefully. The formula should be:

energy_per_challenge = hashes_per_challenge * joules_per_hash daily_energy = challenges_per_day * energy_per_challenge yearly_kwh = daily_energy * 365 / 3600 / 1000

Let me recalculate step by step.

The numbers are still quite small (sub-1 TWh even in aggressive scenarios). Let me reconsider the model. I think the key issue is that CAPTCHA challenges are relatively infrequent in the grand scheme of things, and each individual PoW challenge is quite small.

But wait — I think I need to reconsider the core question. The user is asking about the energy cost of PoW checks as a replacement for CAPTCHA. Let me think about whether there are scenarios where this is much larger.

Actually, I think the more interesting comparison is: what if we used PoW not just for "are you human" checks, but as a rate-limiting mechanism for ALL web requests? That's what some proposals suggest — using PoW as a DDoS prevention mechanism where every request must include a PoW solution. In that case, the numbers get much larger.

Let me also consider that my energy-per-hash estimate might be too low. Let me recalculate using a different approach: instead of calculating from hash rate and power, let me use known CPU energy efficiency data.

For a modern CPU:

But for a phone:

My 1.8 µJ/hash weighted average seems reasonable.

But actually, I think the more important point is that even at large scale, the energy is relatively modest compared to other things. Let me put this in perspective against:

And also consider that I may have been too conservative on challenge volume. Let me look at this from a different angle: what if we consider ALL bot management challenges, including those that are invisible?

Cloudflare alone:

Let me recalculate with this.

The numbers are quite small even in aggressive scenarios. Let me reconsider whether I'm approaching this right. Maybe I should think about it differently.

One key issue: the user asked about "PoW check running on-device instead of a captcha." The key insight is that this is specifically about client-side PoW. But maybe the scale is much larger than I think?

Let me reconsider:

But even then, the energy per challenge is tiny (fraction of a joule). So the total remains small UNLESS we make the difficulty very high.

Wait — I think the real question might be about something different. Let me re-read: "calculate the amount of energy required by a PoW check running on-device instead of a captcha. Consider the world traffic and estimate the amount of energy wasted per year."

Maybe the user wants me to consider a hypothetical where PoW replaces CAPTCHA globally, and think about what that means. Let me present the model as-is but also discuss what it would take for the numbers to get large.

Actually, I think there might be an angle I'm missing. Let me think about this from the perspective of the user's likely intent. They probably heard about PoW CAPTCHAs and want to know: "would this waste a lot of energy?" The answer my model gives is: surprisingly little, because:

But let me also model a worst-case scenario: what if every single page load on the entire internet required a PoW? And what if the difficulty was set to make it actually effective against bot farms (which would require a meaningful time investment, say 5-10 seconds)?

Let me also verify my energy-per-hash calculation by computing it a different way.

Now I'm getting more meaningful numbers in the worst-case scenarios. But these are still quite small compared to Bitcoin mining. Let me now synthesize all this into a coherent napkin math analysis and create a nice summary. The key finding is:

The interesting conclusion: PoW CAPTCHA is surprisingly energy-efficient compared to what people might think, because the volume of challenges is tiny compared to the continuous mining in Bitcoin.

Let me also think about what the user likely cares about: is PoW a good replacement for CAPTCHA from an energy perspective? The answer seems to be: yes, the energy cost is tiny. But there's another angle: user experience. Even 200ms of CPU burn per page load (diff 20) would be noticeable and annoying on mobile devices (battery drain, heat).

Let me create a comprehensive summary now.

The home calculation seems off in some cases — 934 GWh should be ~93,000 homes, not 93. Let me fix that and produce the final summary. Also I want to add a couple more perspectives:

Let me add these and produce the final output.

Now let me create one more calculation — comparing to the server-side energy currently used by CAPTCHA systems. This adds important context because CAPTCHA isn't free today — Google runs ML models, serves images, does behavioral analysis on their servers. Let me estimate that and also produce a final, clean summary table.

Now I have a comprehensive model. Let me produce a final, clean summary of all the napkin math. The key conclusions are:

Let me present this cleanly to the user.