To run a Minecraft server, the hardware requirements can vary depending on the server’s player load and installed mods. **Basic requirements:** Your current dual-core PC should be adequate to run a small-sized Minecraft server (up to 10 players), assuming you have at least 2GB to 3GB of RAM dedicated for Minecraft, and your system isn't heavily loaded with other software. **Recommended specification:** For a server hosting around 20 players or more, the minimum would be a quad-core CPU, along with 4GB - 6GB of RAM dedicated to Minecraft. A SSD is also highly recommended as it dramatically improves the speed at which the server can access the game's data. It's essential to note that running a Minecraft server also requires a consistent and stable high-speed internet connection as upload speed can be a bottleneck, especially if you plan on having many players. **Software Requirements:** Minecraft servers can be run on various operating systems like Windows, Linux, and macOS. The system should have Java installed (Minecraft uses Java SE), many prefer the use of java 8. Remember, meeting hardware requirements is only half the battle, setting up and configuring the server properly is equally important. Be wary of potential security risks and manage your firewall settings carefully during setup. Monitor your game's performance and adjust accordingly after you have it up and running. Hardware needs can vary greatly depending on the way you or your players use the Minecraft server.

Running a Minecraft server can be a straightforward process but it will require certain minimum hardware. As of your PC with dual core processor, it can run a Minecraft server but the performance will depend on various factors like the specific processor you have and how many players you plan on hosting. Here's a basic guideline for Minecraft server hardware: 1. **CPU**: Minecraft servers can be CPU-intensive because of its real-time world physics and player actions. So a fast and modern CPU can greatly improve the performance of your server. As for your dual-core processor, it may run a small server (up to 20 players) fairly well, but for larger population servers, a quad-core processor or higher is recommended. 2. **RAM**: Minecraft is also well-known for requiring a substantial amount of memory (RAM), especially if you plan to use mods or servers plugins. For a server with 1-5 players, 1GB of dedicated RAM for Minecraft server is recommended. For every additional 10 players, you should add another 1GB of RAM. For instance, if you plan to host around 20 players, you'll need approximately 3 to 4GB of dedicated RAM for Minecraft server. 3. **Storage**: A Hard Drive or SSD where your server and associated files will be stored plays a significant role. If possible, an SSD is highly recommended over a traditional HDD as it can greatly reduce both server startup times and loading times for larger worlds. 4. **Internet connection**: If players are connecting from around the world, you will also need a good internet connection with a high upload speed. A rule of thumb is to have an upload speed of 3MBps for every 50 players. 5. **Operating System**: You can run a Minecraft server on Windows, Linux, or macOS. However, Linux is often better suited for server setups, as it uses less of your system resources on its own, compared to Windows. Please bear in mind these are rough estimates and actual requirements may vary. Your server's performance can also be improved by factors like optimized server software, plugins, and mods, but that's a topic beyond the scope of the hardware question. Lastly, don't forget to check the software prerequisites that you might need, such as the latest Java version. Make sure to monitor your server once it's set up to make sure it's running well; you may need to adjust your hardware as your server's population grows.