Akatalytos (G179) appears only once in the NT — in Hebrews 7:16, describing the nature of Christ's priesthood. He is a priest 'not according to a legal requirement concerning bodily descent but by the power of an indestructible life.' The word is the negative of katalyō (to dissolve, destroy, dismantle).
The entire argument of Hebrews 7 hinges on this word: Jesus' priesthood is permanent because his life is indestructible. The Levitical priests died — their priesthood ended at death. Melchizedek appears without recorded beginning or end as a type. But Christ's actual, physical resurrection means his life is literally akatalytos — nothing can end it. An undying priest makes continual, effective intercession.