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Question: Can training-induced changes be maintained long term and can they be extended to other related but untrained skills? Method: We (i) measured the independent and combined contribution of intensive, 5-day cognitive training and brain stimulation applied to critical and control brain region using transcranial random noise stimulation, tRNS; (ii) tested whether any improvement in a trained cognitive skill transferred onto non-trained skills; and (iii) tested the possible long-term effects of any cognitive improvement. Participants were trained on a well-known, parametrically-designed numerosity discrimination task, requiring them to judge the most numerous of two sets i.e. the set containing more dots (see Fig. 1). Results: [•] There was a significant improvement (on average about 18%) in performing a numerosity discrimination task following intensive and continuous repetition of the task. However, there was an even larger improvement (about 37%) when this repetition was accompanied by tRNS to brain areas that are critical for numerosity discrimination, i.e. the left and right parietal lobes. The improvement was much smaller when stimulation was not associated to cognitive training or when tRNS was applied to brain regions irrelevant for the trained task, i.e. the motor areas. [•] Improvements in numerosity discrimination following cognitive training combined to parietal tRNS were maintained up to 16weeks post-training. In contrast, the other experimental conditions showed no such steadiness of learning. [•] When intense cognitive training was associated to parietal tRNS, improvement in number acuity transferred to the ability to discriminate other types of quantity, specifically time and space that are thought to share common neural and cognitive substrates with numerosity discrimination. There was no transfer to other cognitive skills such as face perception and arithmetic. Conclusions: These results indicate that with a suitably chosen task and stimulation, cognitive training can cause large long-lasting enhancement of cognitive functions that are shared across associated tasks. [Copyright &y& Elsevier]