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It is generally known that under the generalized Riemann hypothesis one could establish the twin primes conjecture by the circle method, provided one could obtain the estimate o (nlog-2 n) for the integral of the representation function over the minor arcs. One of the new results here is that the assumption of GRH can be removed. We compare this and other such sufficiency results with similar results for the Goldbach conjecture.

A Comparison of Sufficiency Condtions for the Goldbach and the Twin Primes Conjectures