What organization has 17 separate institutes and is the world's premier medical research organization that supports some 35,000 research projects nationwide?

National Institute of Health (NIH)

Explanation:

The National Institute of Health is the world's premier medical research organization, it is responsible for biomedical and public health research. There are about 17 institutes under NIH, they include; National Cancer Institute, National Eye Institute, National Human Genome Research Institute, National Institute of Aging among others.