16 Also he compels all, the small and the great, and the rich and the poor, and the free men and the slaves, to be given a mark on their right hand or on their forehead [signifying allegiance to the beast], 17 and that no one will be able to buy or sell, except the one who has the mark, either the name of the beast or the number of his name. 18 Here is wisdom. Let the person who has enough insight calculate the number of the beast, for it is the [imperfect] number of a man; [a]and his number is [b]six hundred and sixty-six.

Footnotes:
Revelation 13:18 Regardless of the earthly power of the two beasts (the demonically controlled Antichrist/dictator and his false prophet) described in these verses, they and their mentor, Satan, fall far short of the power, perfection, and majesty of God the Father, God the Son, and God the Holy Spirit, whose perfection is represented biblically by the number seven.
Revelation 13:18 This is not actually three sixes (or the equivalent in Greek or Hebrew letters), as commonly represented. Such a combination would not be used; and if it were, the sum would then be only eighteen, because in alphabet-based numbering systems like ancient Hebrew and Greek, place values are not used (10’s, 100’s etc.), but the letters are treated more like Roman numerals. What John is most likely indicating is that the letters of the name will add up to 666 (the best Greek manuscripts have the number spelled out), and there could be many different combinations of letters that would do so. Determining the values of the individual letters is another matter. John probably assumed that the name would be Hebrew or Greek, and in Hebrew vowels for the most part are not represented as letters. Further complications arise when names from other nationalities are considered, and are converted for valuation. For example, at various times it has been argued that the name “Nero Caesar” adds up to 666 when transliterated to Hebrew as NRWN QSR (according to the Greek form); but in the Talmud, the name is transliterated as NYRWN QYSR, which totals 686. Also, the original Latin form of the name (without the second “n”), if converted directly to Hebrew, adds up to 616, and a few ancient manuscripts had that number.