Vinogradov's Three Primes Theorem with Primes from Special Sets

on YouTube ↗01h 02m

" summary

Shows that the only genuine obstruction to Vinogradov’s three‑prime conclusion for a subset of primes is concentration on small Bohr sets (a Boset obstruction), proves a transference principle reducing the problem to dense models, and uses exponential‑sum bounds plus sieve majorants/minorants and Baker–Harman–Pintz short‑interval estimates to get concrete improvements: recovers Zhao’s sharp 5/8 density barrier example, handles sieve‑controlled sets like the “Zen” primes, and pushes the almost‑equal‑primes exponent to theta = 0.55, with effective arguments and explicit Fourier/control bounds.

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" chapters (12)

1. 0:00Vinogradov's three primes theorem
2. 3:25Generalizing prime subsets
3. 7:49Congruence obstructions
4. 11:55Boset obstructions beyond congruence
5. 18:18Only possible obstruction
6. 21:44Almost equal primes results
7. 27:30Refining Boset intuition
8. 31:02Majorant and minorant bounds
9. 42:50Transference principle
10. 51:18Majorant function construction
11. 56:02Identity majorant reduction
12. 1:00:37Q&A