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Step 4 of 4: Historical footnote: 1966 announcement, 1973 details, 1975 simplification
In plain words

Chen first announced this theorem in 1966 as an outline, but political turmoil in China during the Cultural Revolution delayed the publication of full technical details until 1973, in Scientia Sinica. The original proof was extremely intricate, packing the weighted sieve, the switching principle, and delicate numerical constant-chasing into a dense argument. Two years later, P. M. Ross published a substantially simplified exposition of the same result, which is now the standard reference route taught in sieve-theory courses, though the switching principle at its heart remains Chen's central idea.

W(N)>0 ⟹ ∃ p≤N prime with N−p=P2,N even and sufficiently largeW(N) > 0 \ \Longrightarrow\ \exists\, p \le N \text{ prime with } N-p = P_2,\qquad N \text{ even and sufficiently large}
Detailed analysis

Chen's 1973 paper actually proves two closely related theorems with nearly identical methods: Theorem I is the Goldbach-type statement proved here; Theorem II is the analogous twin-prime statement that for any positive even hh, there are infinitely many primes pp such that p+hp+h is either prime or a P2P_2. Subsequent work (Wu 2004, and explicit versions by Yamada 2015 and Johnston–Bordignon–Starichkova 2022) has made the 'sufficiently large' threshold and sieve constants fully explicit, but the exponent '2' in P2P_2 has not been improved since Chen's original 1973 paper — it remains the sharpest unconditional approach to Goldbach's conjecture known as of 2026.