Trident brand gum was not named in honor of the weapon wielded by Poseidon. It was named for the three plaque-softening enzymes in its original formula that were designed to help promote dental health.
Trident was first introduced by the American Chicle Company in 1960 in response to studies linking sugar to tooth decay. The original Trident gum contained sugar along with three enzymes believed to soften dental tartar. In 1964, sugar-free Trident with saccharin was introduced using the slogan "The great taste that is good for your teeth." Trident was the first national brand of sugar-free gum in the United States. Over the years, Trident continued to emphasize the cavity-fighting benefits of sugar-free gum in its advertisements, including their long-running slogan, "Four out of five dentists recommend sugar-free gum for their patients who chew gum."