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We present a sample of 1165 extreme emission-line galaxies (EELGs) at 45000 AA. JWST/NIRSpec spectroscopic observations of a subset (34) of the photometrically selected EELGs validate our selection method: all spectroscopically observed EELGs confirm our photometric identification of extreme emission, including some cases where the SED-derived photometric redshifts are incorrect. We find that the medium-band F410M filter in CEERS is particularly efficient at identifying EELGs, both in terms of including emission lines in the filter and in correctly identifying the continuum between Hb + [OIII] and Ha in the neighboring broad-band filters. We present examples of EELGs that could be incorrectly classified at ultra-high redshift (z>12) as a result of extreme Hb + [OIII] emission blended across the reddest photometric filters. We compare the EELGs to the broader (sub-extreme) galaxy population in the same redshift range and find that they are consistent with being the bluer, high equivalent width tail of a broader population of emission-line galaxies. The highest-EW EELGs tend to have more compact emission-line sizes than continuum sizes, suggesting that active galactic nuclei are responsible for at least some of the most extreme EELGs. Photometrically inferred emission-line ratios are consistent with ISM conditions with high ionization and moderately low metallicity, consistent with previous spectroscopic studies., Comment: 24 pages, 25 figures, submitted to ApJ