Black holes with masses below approximately 10 ^ { 15 } g are expected to emit gamma rays with energies above a few tens of MeV , which can be detected by the Fermi Large Area Telescope ( LAT ) .
Although black holes with these masses can not be formed as a result of stellar evolution , they may have formed in the early Universe and are therefore called Primordial Black Holes ( PBHs ) .
Previous searches for PBHs have focused on either short timescale bursts or the contribution of PBHs to the isotropic gamma-ray emission .
We show that , in case of individual PBHs , the Fermi LAT is most sensitive to PBHs with temperatures above approximately 16 GeV and masses 6 \times 10 ^ { 11 } g , which it can detect out to a distance of about 0.03 pc .
These PBHs have a remaining lifetime of months to years at the start of the Fermi mission .
They would appear as potentially moving point sources with gamma-ray emission that becomes spectrally harder and brighter with time until the PBH completely evaporates .
In this paper , we develop a new algorithm to detect the proper motion of a gamma-ray point sources , and apply it to 318 unassociated point sources at high galactic latitude in the third Fermi -LAT source catalog ( 3FGL ) .
None of unassociated point sources with spectra consistent with PBH evaporation show significant proper motion .
Using the non-detection of PBH candidates , we derive a 99 % confidence limit on PBH evaporation rate in the vicinity of the Earth \dot { \rho } _ { PBH } < 7.2 \times 10 ^ { 3 } \ > { pc ^ { -3 } { yr } ^ { -1 } } .
This limit is similar to the limits obtained with ground-based gamma-ray observatories .