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In the paper [On the sum of the reciprocals of the differences between consecutive primes, Ramanujan J., 47,427–433(2018)] by me, I proved under the Hardy–Littlewood prime-pair conjecture that $$\sum_{n\le X}\frac{1}{p_{n+1}-p_n}\sim \frac{X\log\log\log X}{\log X},$$ and without the Hardy–Littlewood prime-pair conjecture, then one has $$ \sum_{n\le X}\frac{1}{p_{n+1}-p_n}\ll \frac{X\log\log\log X}{\log X}. $$ Therefore, by using the standard Abel’s summation formula one prove that the conjecture is true unconditionally.