Boiling raw eggs in hot spring water produces black eggs (kuro tamago) through a chemical reaction with geothermal heat and volcanic gas as iron properties (an ingredient of the hot spring water) adhere to the porous shells. The black color of iron sulfide is a result of a reaction with hydrogen sulfide, and it produces boiled eggs with black shells.
There is a jizo (guardian deity of children) in Owakudani known as Enmei Jizo Bosatsu, who promotes longevity and child-raising, and it is said to have been carved by Kobo Daishi during the Heian Period (794-1185). This jizo became known as a good luck symbol for extending lifespans if kuro tamago are consumed (hot spring waters for making kuro tamago used to be located near this jizo). The figure  in the legend of extending longevity by seven years is a lucky number associated with the Seven Deities of Good Fortune, etc., and over the course of time it began to be associated with kuro tamago.
As well as being popular in their own right, the staid design of the bags containing kuro tamago also enjoy their own popularity in the background. Many people even paste them into scrapbooks as a momentum from their vacation. Actually, however, this bag is the second design. Do you prefer the second design or the third design?