Catalyzes the ATP- and formate-dependent formylation of 5-aminoimidazole-4-carboxamide-1-beta-d-ribofuranosyl 5'-monophosphate (AICAR) to 5-formaminoimidazole-4-carboxamide-1-beta-d-ribofuranosyl 5'-monophosphate (FAICAR) in the absence of folates. 5-amino-1-(5-phospho-beta-D-ribosyl)imidazole-4-carboxamide + ATP + formate = 5-formamido-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide + ADP + phosphate Binds 1 Mg(2+) or Mn(2+) ion per subunit. Purine metabolism; IMP biosynthesis via de novo pathway; 5-formamido-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide from 5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide (formate route): step 1/1. Belongs to the phosphohexose mutase family.