April 6 1830 is recognized as the official first day of TCOJCOLDS. This is the day the Church was organized and formalized with the state of New York. On this day there was 6 official members as that was the requirement of the state at that time. There had been groups meeting before that time and there was also more than 6 people in attendence at the first official meeting of the church. But for all intents and purposes April 6 1830 was the begining of TCOJCOLDS,which was a Tuesday,BTW.
CTR
http://www.lds.org/churchhistory/history
http://scriptures.lds.org/chchrono/contents