THE LAST SUPPER EXPLAINED – HOMILY OF HIS HOLINESS BENEDICT XVI
In the meantime, the discovery of the [Dead Sea] Scrolls at Qumran has led us to a possible and convincing solution which, although it is not yet accepted by everyone, is a highly plausible hypothesis. We can now say that John’s account is historically precise. Jesus truly shed his blood on the eve of Easter at the time of the immolation of the lambs. In all likelihood, however, he celebrated the Passover with his disciples in accordance with the Qumran calendar, hence, at least one day earlier; he celebrated it without a lamb, like the Qumran community which did not recognize Herod’s temple and was waiting for the new temple
It does not tell you that Qumram always celebreated the Passover on a Tuesday evening, which is exactly when it was