You are correct in one sense.My paternal grandmother left a family tree in my father's baby book stating that we are directly related to the Pereguine White born on the Mayflower.At some point White and Ludden came together as my great grandfather's uncle was named after Pereguine. As of this date I have been unable to make the exact connection but the name Phoebe White is written in my family tree as being wed to Jacob Ludden born in 1760.I have been searching to verify this data but so far can't fine anyone who really knows the facts. Most of these Luddens are from Massachusetts and Maine.My grandfather's name was Willliam Robinson Ludden, his father was Forest Edwin Ludden who married Elizabeth Robinson.Forest's father was John Mandeville Ludden married Elevene Carver. The tree goes back further but this will give you an ideal of where we are from and who is who. Hope this helps.