What Christian denominations/groups believe in biblical prophecies based on number of The Beast being 666? The actual Number of the beast is only mentioned in Revelation( 13:18).  In the Greek manuscripts, the  number is rendered in Greek numerical form as χξϛ, 666, or sometimes literally as "six hundred and sixty-six".

In 2005 Oxford University's Ashmolean Museum revealed the discovery of the oldest manuscript (about 1,700 years old) of Revelation 13 which gave the beast's number as 616 χιϛ.

Which Christian denominations/groups that believe in biblical prophecies based on number 666?
"Hexakosioihexekontahexaphobia" - the fear of the number 666.

The Bible Rev. 13:15-18 requires the reader to interpret: "Here is Wisdom, Let him that hath understanding count the number of the beast." and the questioner is asking about any possible interpretations, such as obtained by adding letter values or gematria. That includes the catholic church because in Quia Maior, the encyclical calling for the Fifth Crusade, Pope Innocent III identifies Muhammad with the beast of Revelation.


  Given enough time (and armed with the numerological tricks of the
  Hebrew, Greek, Aramaic, Latin, and English alphabets), one can make
  anyone's name add up to 666. . . .
  
  Likely candidates have been Martin Luther, Henry VIII, Robespierre, Napoleon
  Bonaparte, George Washington (and his alleged Illuminati double, Adam
  Weishaupt), Lenin, Adolf Hitler, Stalin, Chairman Mao, Franklin
  Roosevelt, Winston Churchill, Harry S. Truman, Prince Charles, King
  Juan Carlos of Spain, Mikhail Gorbachev, Bill Clinton, Osama Bin
  Laden, and both George Bushes - and, oh, I almost forgot, all the
  Popes.


Source: 666: What's in a Number?

The christian mystic Aleister Crowley claimed himself to represent 'the Beast 666' based on his interpretation of a Hebrew Kabbalah teaching (see link above).