Just searched Wikipedia on Sabbatai Zevi and this is what it says:
“At age 22 in 1648, Sabbatai started declaring to his followers in Smyrna that he was the true Messianic redeemer. In order to prove this claim he started to pronounce the Tetragrammaton in Hebrew, an act which Judaism emphatically prohibited to all but the Jewish high priest in the Temple in Jerusalem on the Day of Atonement. For scholars acquainted with rabbinical, and kabbalistic literature, the act was highly symbolic. He revealed his Messiahship early on to Isaac Silveyra and Moses Pinheiro, the latter a brother-in-law of the Italian rabbi and kabbalist Joseph Ergas.”
Note that the year 1648 is 5408 according to Kaluach v. 3! That may be why he chose to reveal himself that year!