Readmissions among Medicare beneficiaries are a major problem for the US healthcare system from a perspective of both healthcare operations and patient caregiving outcomes. Our study analyzes Medicare hospital readmissions using LSTM networks with feature engineering to assess feature contributions. We selected variables from admission-level data, inpatient medical history and patient demography. The LSTM model is designed to capture temporal dynamics from admission-level and patient-level data. On a case study on the MIMIC dataset, the LSTM model outperformed the logistic regression baseline, accurately leveraging temporal features to predict readmission. The major features were the Charlson Comorbidity Index, hospital length of stay, the hospital admissions over the past 6 months, while demographic variables were less impactful. This work suggests that LSTM networks offers a more promising approach to improve Medicare patient readmission prediction. It captures temporal interactions in patient databases, enhancing current prediction models for healthcare providers. Adoption of predictive models into clinical practice may be more effective in identifying Medicare patients to provide early and targeted interventions to improve patient outcomes.