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This article is the fifth version of proposed proofs of Goldbach's conjecture et al. It includes also new proposed proofs such the Twin Prime Conjecture. The proofs of Andrica and Goldbach are enhanced.Error in proof theorem 5 is solved.Main ideas for the proof of the Riemann Hypothesis is worked out.Modification theorem 3: Cramer-Granville.Small modification Goldbach.doi:10.6084/m9.figshare.14204396.v11 fatcat:b2qk3kgpabeprmpd46s7lw2mn4