Under Elliott-Halberstam conjecture, infinitely many twin almost-primes exist with explicit asymptotic via improved localized sieve.
An Elementary Proof of the Prime Number Theorem with a Remainder Term.Inventiones math., 11:199–258
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Twins almost prime under a Elliott-Halberstam's conjecture
Under Elliott-Halberstam conjecture, infinitely many twin almost-primes exist with explicit asymptotic via improved localized sieve.