Abraxas (Abrasax) is the name at the centre of the Basilidian system reported by Irenaeus (Against Heresies 1.24): the Greek letters of Abrasax sum to 365, the number of the days of the year and of the heavens in that system, so that the name is the name of the whole year and of the power that governs it. From the second century the name crowds the Graeco-Egyptian magical gems, engraved on amulets beside a cock-headed, serpent-legged figure with a whip and shield and invoked with IAO and Sabaoth as a protective name of power. Carl Jung took Abraxas up in the Seven Sermons to the Dead (1916) as the god beyond good and evil, and through Hermann Hesse's Demian the figure entered modern occultism.
Modern Practice
Worked with as an amuletic and talismanic name rather than as a god with a cult: engraved, drawn or vibrated for protection and for solar-year timing, while Jungian readers use it as an image of the whole beyond the split of good and evil.
α 1 + β 2 + ρ 100 + α 1 + σ 200 + α 1 + ξ 60 = 365. The letters may be written ΑΒΡΑΞΑΣ or ΑΒΡΑΣΑΞ; addition is commutative, so both give 365.
Meaning
Abrasax is the name the Basilidian tradition gives the ruler of the 365 heavens, and the 365 of the name is the number of the days: one heaven for each day of the year, which is the whole system inside a word. The name is carved on stones and spoken in the magical papyri as a name of power, and it survives into modern occultism in the Latin form Abraxas. It is the one isopsephy in this file whose number and doctrine are reported together by an ancient source.