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Medhaṅkara Buddha
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Medhaṅkara Buddha, is briefly mentioned in the Buddhavamsa. He is mentioned along with the first four Buddhas.

"Inneumarable aeons ago, Taṇhaṅkara Buddha (1st Buddha), Medhaṅkara Buddha (2nd Buddha - the Buddha we are talking about), Saraṇaṅkara Buddha (3rd Buddha) and Dīpaṃkara Buddha (4th Buddha) were born in the Sāramaṇḍa kalpa."

Kalpa generally gets translated as Aeon (time period for a particular World). Sāramaṇḍa is the name of that time period and is the World where the first four Buddhas were born.

The one who would later be known as Gotama Buddha, became a disciple of Medhaṅkara Buddha. He asked for a wish to be granted, but the wish was not granted. The one who would later be known as Gotama Buddha asked the same wish to the 1st, 3rd and 4th Buddha. The 2nd and 3rd Buddha did not grant him his wish but the 4th Buddha did. The wish was that in the future, the one who would later be known as Gotama Buddha would become a Buddha.

Medhaṅkara Buddha went on and lived a long life, about 90,000 years.
Contrast this with Taṇhaṅkara Buddha who had a life span of about 100,000 years.