We present 4 new measurements of nitrogen abundances and one upper limit in damped Lyman alpha absorbers (DLAs) obtained by means of high resolution (FWHM \~ 7 km/s) UVES/VLT spectra. In addition to these measurements we have compiled data from all DLAs with measurements of nitrogen and alpha-capture elements (O, S or Si) available in the literature, including all HIRES/Keck and UVES/VLT data for a total of 33 systems, i.e. the largest sample investigated so far. We find that [N/alpha] ratios

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... e distributed in two groups: 75% of the DLAs show a mean value of [N/alpha] = -0.87 with a scatter of 0.16 dex, while the remaining 25% shows ratios clustered at [N/alpha] = -1.45 with an even lower dispersion of 0.05 dex. The high [N/alpha] plateau is consistent with the one observed in metal-poor HII regions of blue compact dwarf (BCD) galaxies ([N/alpha] = -0.73 +/- 0.13), while the [N/alpha] ~ -1.5 values are the lowest ever observed in any astrophysical site. These low [N/alpha] ratios are real and not due to ionization effects. They provide a crucial evidence against the primary production of N by massive stars as responsible for the plateau at -0.9/-0.7 dex observed in DLAs and BCD galaxies. The transition between the low-N ([N/alpha] ~ -1.5) and high-N ([N/alpha] ~ -0.9) DLAs occurs at a nitrogen abundance of [N/H] ~ -2.8, suggesting that the separation may result from some peculiarity of the nitrogen enrichment history. The [N/alpha] ~ -1.5 values and their low dispersion are consistent with a modest production of primary N in massive stars; however, due to the limited sample, specially for the low-N DLAs, we cannot exclude a primary origin in intermediate mass stars as responsible for the low N abundances observed.