2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66274In this paper, a random primality proving algorithm is proposed, which generates prime certificate of length O(log n). The certificate can be verified in deterministic time O(log^4 n). The algorithm runs in heuristical time tilde{O}(log^4 n), some supporting evidences are provided.10 pages, No figureNumber Theory11Y11text