[fernly]

Well I just had to try it on Claude 4.0, I mean somebody has to, right? and it did a clean, if rather terse, breakdown, concluding with:

Caesar's last breath: ~0.5 liters (typical final exhale)

Total atmospheric volume: Earth's atmosphere has a mass of about 5×10^18 kg. Using the ideal gas law with average molecular weight of air (~29 g/mol), this gives roughly 4×10^44 molecules total.

Molecules in Caesar's breath: 0.5 liters at standard conditions contains about 1.3×10^22 molecules.

Your inhale: ~0.5 liters also contains about 1.3×10^22 molecules.

The fraction: Caesar's molecules represent (1.3×10^22)/(4×10^44) = 3.25×10^-23 of all atmospheric molecules.

Final answer: (1.3×10^22) × (3.25×10^-23) ≈ 0.4 molecules

So statistically, you inhale less than one molecule from Caesar's last breath with each inhalation, but over the course of a day's breathing, you'd likely inhale several molecules that were once in his lungs as he died.