Zhenwan can be read as 'for Precious Enjoyment.' The marks to the narrow sides read Hong fu Wan dai which can be translated as 'Good luck for 10,000 generations' and Yi Zi Yi Sun which can be translated as 'Good for sons - Good for grandsons'.
For a banded agate bottle similarly carved to imitate a purse, but unmarked, see Xia Gengqi and Zhang Rong (chief compilers), Masterpieces of Snuff Bottles in the Palace Museum, Beijing, 1995, p. 142, no. 138. Another is illustrated by Bob C. Stevens, The Collector's Book of Snuff Bottles, New York and Tokyo, 1980, pp. 140-141, no. 533. Another bottle also from the Gerry P. Mack Collection with slightly differing inscriptions was sold by Sotheby's, New York, 25 October 1997, lot 55.
For a banded agate example formerly in the Bob C. Stevens Collection with Zhenwan mark to the base, see Rachelle R. Holden, Rivers and Mountains Far from the World, Hong Kong, 1994, p. 381, no. 178.
For a simple banded agate bottle, see Robert Kleiner, Chinese Snuff Bottles from the Collection of Mary and George Bloch, British Museum, London, 1995, Catalogue, p. 397, no. 259, where the author discusses the status symbol of the purses in a man's wardrobe