Abstract
The purpose of this paper is to give the absolute mathematics for the prime set. Absolute mathematics was introduced by N.Kurokawa in order to solve the Riemann conjecture. One of the idea for absolute mathematics is the prime differential on the rational integer Z. We analyze all possible arithmetic generalizations of symplectic and contact structures on a prime set. There are two different types of structures according to the Lagrangian subspace and Legendrian subspace. Main result is that the prime set is characterized by the Lagrangian subspace of absolute symplectic space (T*P, ω). We also define a notion of the absolute Weyl algebra.
