Wow, Barbara, your twin pearls are lovely! There would have been 2 mop nucleus inserted at the same time in the oyster which then grew together instead of separately.
In PEARLS by Elizabeth Strack, describing part of the detailed Akoya grafting process:
"In most cases, two nuclei are inserted unless the nucleus is larger than 7mm. Sometimes 10 to 20 tiny nuclei are placed into one animal.........In earlier decades, it was often observed that two implanted nuclei would grow together and form a so-called twin pearl, but today's technology allows to prevent twinning." (pages 348-349)