Mark rutte is PM since when Willem Alexander was Prince of Orange
That's not true; while he was prime minister at the day of the abdication/inauguration, Willem-Alexander became prince of Orange in 1980:
30 April 1980 (inauguration of his mother) - 4 November 1982: Dries van Agt (CDA)
4 November 1982 - 22 August 1994: Ruud Lubbers (CDA)
22 August 1994 - 22 July 2002: Wim Kok (PvdA)
22 July 2002 - 14 October 2010: Jan Peter Balkenende (CDA)
14 October 2010 - now: Mark Rutte (VVD)
So, during his mother's reign (while the current king was the heir), there were 5 different prime ministers (from 3 different parties) of which Mark Rutte was the last. One prime minister that was very important for him personally was Wim Kok who was prime minister when he asked Máxima to marry him while there were serious issues related to her father that needed to be managed. Had that not been properly managed by PM Wim Kok he might have given up the throne for her...
Since his birth while his grandmother was queen, in addition to Van Agt, there were three other prime ministers:
5 April 1967 - 6 July 1971: Piet de Jong (KVP --> merged into CDA in 1980)
6 July 1971 - 11 May 1973: Barend Biesheuvel (ARP --> merged into CDA in 1980)
11 May 1973 - 19 December 1977: Joop den Uyl (PvdA)
After him Dries van Agt (see above; then KVP) took over.