I think that a couple qualifications need to be established on the outset.  The first would be that the list of Indian Prime Ministers should probably start at Indian independence, so that a list could be generated from 1947.  Additionally, I think that one needs to look at the state in which the Prime Minister's representation arises from in terms of "what state has had the most Prime Ministers."  In this light, the question becomes from which representative state have Indian Prime Ministers hailed.  This is because the representative of constituency is of vital importance to the Prime Minister, perhaps even more important than state of birth.  With these in mind, it seems like the state of Uttar Pradesh in North Eastern India has generated the most Prime Ministers.  Uttar Pradesh has generated eight of the 13 Prime Ministers since 1947.  Names like Nehru, Indira Gandhi, Vajpayee, and Charan Singh have come from constituencies rooted in Uttar Pradesh.  Considered by many to be a center of Indian politics, the State of Uttar Pradesh has generated the most Prime Ministers of any other state in Modern India.