It depends on the requirement and how you want to use Bahmni and how you choose your server architecture. If you want all the modules and configurations in Bahmni, replication switched on from master to slave machines etc… then you need 8GB and quad core processor.
Bahmni (with all the modules) has lot of features irrespective of the hospital usage (though it doesn’t have huge data). For example, the 3 main modules in bahmni elis, mrs, erp talk to each other continuously and each of them have their own databases. Pacs Integration (integration between emr and Digital X-Ray Machines) gives the ability to view Dicom Images. This needs DCM4CHEE server.
For example ELIS, ERP and PACS are on postgresql… Minimum requirements for postgres MRS is on Mysql Database and the memory usages are mentioned here Dc4chee minimum requirements are mentioned here Openerp / odoo system requirements
You can also refer to the survey summary of openmrs implementations
The recommended requirements are mentioned considering all the modules and integrations and also the usage. If you want to use FULL Bahmni with all the configuration along with the data being generated(by hospital) , then you need the server with more resources to support all of the features.
You can choose to switch off unnecessary modules and still run on 4GB server. Please let us know what all modules you want to use from Bahmni, then we can help you turn off other modules that are not needed.