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c.1200, pilegrim, from Old French pelerin, peregrin "pilgrim, crusader; foreigner, stranger" (11c., Modern French pèlerin), from Late Latin pelegrinus, dissimilated from Latin peregrinus "foreigner" (source of Italian pellegrino, Spanish peregrino), from peregre (adv.) "from abroad," from per- "beyond" + agri, locative case of ager "country" (see acre).
Change of first -r- to -l- in most Romance languages by dissimilation; the -m appears to be a Germanic modification. Pilgrim Fathers "English Puritans who founded Plymouth colony" is first found 1799 (they called themselves Pilgrims from c.1630, in reference to Hebrew xi:13).