The cosmic age is an important physical quantity in cosmology. Based on the radiometric method, a reliable lower limit of the cosmic age is derived to be $15.68± 1.95$ Gyr by using the $r$-process abundances inferred for the solar system and observations in metal-poor stars. This value is larger than the latest cosmic age $13.813± 0.058$ Gyr from Planck 2013 results, while they still agree with each other within the uncertainties. The uncertainty of $1.95$ Gyr mainly originates from the error on thorium abundance observed in metal-poor star CS 22892-052, so future high-precision abundance observations on CS 22892-052 are needed to understand this age deviation. ; Comment: 4 pages, 3 figures