The solar disk is a bright gamma-ray source. Surprisingly, its flux is about one order of magnitude higher than predicted. As a first step toward understanding the physical origin of this discrepancy, we perform a new analysis in 1-100 GeV using 6 years of public Fermi-LAT data. Compared to the previous analysis by the Fermi Collaboration, who analyzed 1.5 years of data and detected the solar disk in 0.1-10 GeV, we find two new and significant results: 1. In the 1-10 GeV flux (detected at \(>5\sigma\)), we discover a significant time variation that anticorrelates with solar activity. 2. We detect gamma rays in 10- 30 GeV at \(>5\sigma\), and in 30- 100 GeV at \(> 2\sigma\). The time variation strongly indicates that solar-disk gamma rays are induced by cosmic rays and that solar atmospheric magnetic fields play an important role. Our results provide essential clues for understanding the underlying gamma-ray production processes, which may allow new probes of solar atmospheric magnetic fields, cosmic rays in the solar system, and possible new physics. Finally, we show that the Sun is a promising new target for ground-based TeV gamma-ray telescopes such as HAWC and LHAASO.