How many receptors do we have on our fingertipps per square centimeters? I found 2500 but do not find the source. Is this correct?
I'll assume you're only asking about mechanoreceptors, else it gets too murky.
Humans have four types of mechanoreceptors.
Meissner corpuscle, innervated by RA1 (rapidly adapting type 1) nerve fibers. There are 2 of the fibers per square millimeter in the monkey finger (my source does not list it for humans), with 10 to 20 Meissner corpuscles per axon, so 1000 to 2000 per square centimeter.
Merkel cell, at the end of SA1 (slowly adapting type 1) nerve fibres. I did not find a source for the adult human, but Kandell says that RA1 fibres are the "most numerous". So 2000 would be the upper limit for Merkel cells too. But here it gets complicated, because the actual mechanoreceptor is not a single Merkel cell, but a cluster of them.
and 4., Pacinian corpuscles and Ruffini endings (corresponding to RA2 and SA2 fibres) are much rarer. The whole hand has 2400 Pacinian corpuscles in the young and 300 in the elderly. Both of them only have one receptor per nerve fibre.
Given this information, 2500 is certainly in the right ballpark. I would trust that number.
Note that this doesn't mean that you can sense 2500 separate locations of pressure in a square centimeter of fingertip. The different mechanoreceptors sense different types and frequency of pressure, and the sensory fields overlap even within a single type of receptor.
Kandel, Eric R., James H. Schwartz, and Thomas M. Jessell, eds. Principles of neural science. Vol. 4. New York: McGraw-hill, 2000.