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The primary function of sugar polymers, particularly polysaccharides such as starch and glycogen, is indeed to serve as long-term energy storage. These polymers are made up of long chains of sugar molecules (monosaccharides) linked together. When energy is needed, these sugar polymers can be broken down into their constituent sugars, providing a readily available source of energy for cellular functions.

While sugar polymers might have roles in signaling and structural support in certain contexts (as seen in cell walls and certain cell recognition processes), their most prominent and essential function across various organisms is related to energy storage. For example, starch serves as an energy reserve for plants, while glycogen plays a similar role in animals. This energy storage capability allows organisms to maintain metabolic processes during times when immediate supplies of glucose are not available.

In summary, the primary function of sugar polymers revolves around their capacity to store energy efficiently, which is crucial for the survival and metabolic activities of organisms.