Yes, this is the Magdalene Papyrus, known as P64.  The latest on this is that scholars are in disagreement on this one.  My friend James Greig wrote an article on this manuscript, although I do not have a copy on my computer right now.  Unlike the Rylands Papyrus, which is almost universally thought to be from about AD 125, the evidence for the early date of the Magdalene Manuscript is of a more dabatable sort.  If it were me, I would not use this date or would only mention it in passing being sure to point out that this is a controversial date.  In my next edition of RFB, I probably will change this one.  Here is a little something from good old Wikipedia:

P ⁶⁴ was originally given a 3rd century date by Charles Huleatt, the one who donated the Manuscript to Magdalen College, and then papyrologist A. S. Hunt studied the manuscript and dated it to the early 4th century. But in reaction to what he thought was far too late a dating for the manuscript, Colin Roberts published the manuscript and gave it a dating of ca. 200, which was confirmed by three other leading papyrologists: Harold Bell, T. C. Skeat and E. G. Turner,^[1] and this has been the general accepted date of the Magdalen since.

But in late 1994, considerable publicity surrounded Carsten Peter Thiede‘s redating of the Magdalen papyrus to the last third of the 1st century, optimistically interpreted by journalists. His official article appeared in Zeitschrift für Papyrologie und Epigraphik the following year. The text for the layman was cowritten with Matthew d’Ancona and presented as The Jesus Papyrus, Weidenfeld & Nicolson, London, 1996. (also published as: Eyewitness to Jesus, 1996, New York: Doubleday). Thiede’s re-dating has generally been viewed with skepticism by established Biblical scholars.

Philip Comfort and David Barret in their book Text of the Earliest NT Greek Manuscripts argue for a more general date of 150-175 for the manuscript, and also for P⁴ and P67, which they argue came from the same code..  P⁴ was used as stuffing for the binding of “a codex of Philo, written in the later third century and found in a jar which had been walled up in a house at Coptos [in 250].”^[2] If P⁴ was part of this codex, then the codex may have been written roughly 100 year’s prior or earlier.^[3] Comfort and Barret also show that this P^4/64/67 has affinities with a number of the late 2nd century papyri.^[4]

Comfort and Barret "tend to claim an earlier date for many manuscripts included in their volume than might be allowed by other palaeographers."^[5] The Novum Testamentum Graece, a standard reference for the Greek witnesses, lists P⁴ and P^64/67 separately giving the former a date of the 3rd century, while the latter is assigned ca. 200.^[6] Most recently Charlesworth has concluded ‘that P⁶⁴⁺⁶⁷ and P⁴, though written by the same scribe, are not from the same … codex.’^[7]

John Oakes