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Zhang has shown there are infinitely many intervals of bounded lengthcontaining two primes. It appears that the current techniques cannot prove thatthere are infinitely many intervals of bounded length containing three primes,even if strong conjectures such as the Elliott-Halberstam conjecture areassumed. We show that there are infinitely many intervals of length at most$10^8$ which contain two primes and a number with at most 31 prime factors.

Bounded length intervals containing two primes and an almost-prime II