The number of verses in the Qor'an depends on the way you count them. As in the Bible, edition may show minor differences in that respect.
Many Muslims say the qor'an has 6666 verses, whether there is an edition with 6666 verses, I don't know. Perhaps the best way to look at this issue is to call 6666 the "popular" number of verses in the Qor'an.
Numbers mentioned besides 6666 as the total of Qor'anic verses are 6214, 6236, 6348, and 6616.