Try skipping over the adding and just picking a new random number.
Generates a number coprime to 2, 3, 5, 7, 11. Speed: Trial div (add) : trial div (retry) : coprime 1 : 0.42 : 0.84
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Generates a number coprime to 2, 3, 5, 7, 11. Speed: Trial div (add) : trial div (retry) : coprime 1 : 0.42 : 0.84