From millimeter and optical observations of the Jupiter-family comet 17P/Holmes performed soon after its huge outburst of 2007 October 24, we derive super(14)N/ super(15)N = 139 plus or minus 26 in HCN and super(14)N/ super(15)N = 165 plus or minus 40 in CN, establishing that HCN has the same nonterrestrial isotopic composition as CN. The same conclusion is obtained for the long-period comet C/1995 01 (Hale-Bopp) after a reanalysis of previously published measurements. These results are compatible with HCN being the prime parent of CN in cometary atmospheres. The super(15)N excess relative to the Earth's atmospheric value indicates that N-bearing volatiles in the solar nebula underwent important N isotopic fractionation at some stage of solar system formation. HCN molecules never isotopically equilibrated with the main nitrogen reservoir in the solar nebula before being incorporated in Oort Cloud and Kuiper Belt comets. The super(12)C/ super(13)C ratios in HCN and CN are measured to be consistent with the terrestrial value.