The correct answer is:
B.) Papyrus 52 (John Rylands University Library, Gr. P. 457)!
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From
Wikipedia:
The Rylands Library Papyrus P52, also known as the St John’s fragment, is a fragment from a papyrus codex, measuring only 3.5 by 2.5 inches (8.9 by 6 cm) at its widest; and conserved with the Rylands Papyri at the John Rylands University Library (Gr. P. 457), Manchester, UK. The front (recto) contains parts of seven lines from the Gospel of John 18:31-33, in Greek, and the back (verso) contains parts of seven lines from verses 37-38. Since 2007, the papyrus has been on permanent display in the library’s Deansgate building.
Although Rylands P52 is generally accepted as the earliest extant record of a canonical New Testament text, the dating of the papyrus is by no means the subject of consensus among critical scholars. The style of the script is strongly Hadrianic, which would suggest a most probable date somewhere between 117 CE and 138 CE. But the difficulty of fixing the date of a fragment based solely on paleographic evidence allows a much wider range, potentially extending from before 100 CE past 150 CE.
The fragment of papyrus was among a group acquired on the Egyptian market in 1920 by Bernard Grenfell. The original transcription and translation of the fragment of text was not done until 1934, by Colin H. Roberts. Roberts found comparator hands in papyri then dated between the mid 1st and mid 2nd centuries, with the closest match of Hadrianic date. Since this gospel text would be unlikely to have reached Egypt before c. 100 CE he proposed a date in the first half of the 2nd century. Over the 70 years since Roberts’ essay, the estimated ages of his comparator undated literary hands have been revised (in common with most other undated antique papyri) towards dates a couple of decades older; while other dated comparator hands have subsequently been suggested with dates ranging into the second half of the 2nd century.
So what about the other choices?
Papyrus 39 (P. Oxy. 1780): Oxyrhynchus, Egypt; 3rd century; contains John 8:14-22
Papyrus 66 (P. Bodmer II): Discovered 1952 (Jabal Abu Mana, Egypt); ca. AD 200; contains John 1:1-6:11; 6:35-14:26,29-30; 15:2-26; 16:2-4,6-7; 16:10-20:20,22-23; 20:25-21:9,12,17
Papyrus 1 (P. Oxy. 2): Discovered 1896-7 (Oxyrhychus, Egypt); ca. early 3rd century; contains Matthew 1:1-9,12,14-20
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