We don't have synonyms for big 4 yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are big d, big o and big c.
(n) :
Alternative form of Big Four. [(historical) The four top Allied powers of World War I and their leaders: David Lloyd George of Britain, Georges Clemenceau of France, Vittorio Emanuele Orlando of Italy and Woodrow Wilson of the United States, who met at the Paris Peace Conference in 1919 at Versailles.]
(n) :
Alternative form of Big Four. [(historical) The four top Allied powers of World War I and their leaders: David Lloyd George of Britain, Georges Clemenceau of France, Vittorio Emanuele Orlando of Italy and Woodrow Wilson of the United States, who met at the Paris Peace Conference in 1919 at Versailles.]