Patients with type 1 diabetes (T1D) do not produce their own insulin. They must continuously monitor their glucose and make decisions about insulin dosing to avoid the consequences of adverse glucose excursions. Continuous glucose monitoring (CGM) systems and insulin pumps are state-of-the-art systems that can help people with T1D manage their glucose. Accurate glucose prediction algorithms are becoming critical components of CGM systems that can help people with T1D proactively avoid the occurrence of impending hyperglycemia and hypoglycemia events. We present Glucop30, a robust data-driven glucose prediction model that is trained on a big dataset (27,466 days) to forecast glucose concentration along a short-term prediction horizon of 30 minutes. Our proposed prediction method is composed of (i) a recurrent neural network with long-short-term-memory (LSTM) units that predicts the general trend of future glucose levels, followed by (ii) a patient-specific smoothing error correction step that accounts for inter- and intra-patient glucose variability. We retrospectively test our proposed method on a clinical dataset obtained from 10 T1D insulin pump users who were continuously monitored during a 4-week trial under free-living conditions (255 days), and assess the impact of the size of the training set on the accuracy of the proposed model. In addition, we report on the accuracy of our method when both CGM and insulin data are used for prediction; however we discovered that adding insulin as an additional input feature improves prediction accuracy by only 1%. Glucop30 achieves leading performance as measured by the RMSE of 7.55 (SD = 2.20 mg/dL) and MAE of 4.89 (SD = 1.43 mg/dL) for an effective prediction horizon of 27.50 (SD = 2.64) minutes. Moreover, Glucop30 accurately anticipates the occurrence of 97.79 (SD = 5.35)% of hyperglycemia events (glucose > 180 mg/dL), and 90.87 (SD = 6.79)% of hypoglycemia events (glucose < 70 mg/dL) with remarkably few false alerts (1 and 2 false alarms per week for hypoglycemia and hyperglycemia events, respectively).