Catalyzes the formation of 2-amino-5-formylamino-6-ribofuranosylamino-4(3H)-pyrimidinone ribonucleotide monophosphate and inorganic phosphate from GTP. Also has an independent pyrophosphate phosphohydrolase activity. GTP + 3 H2O = 2-amino-5-formylamino-6-(5-phospho-D-ribosylamino)pyrimidin-4(3H)-one + 2 H(+) + 2 phosphate Belongs to the archaeal-type GTP cyclohydrolase family.