Is this good to run minecraft?

Intel® Celeron® processor G1610T Features a 2MB cache and 2.3GHz processor speed. The Intel® Celeron® processor Delivers reliable performance for everyday computing. 4GB DDR3 SDRAM For multitasking power, expandable to 16GB. Multiformat DVD±RW/CD-RW drive with double-layer support Records up to 8.5GB of data or 4 hours of video using compatible DVD+R DL and DVD-R DL media; also supports DVD-RAM. 500GB Serial ATA hard drive (7200 rpm) Offers spacious storage and fast read/write times. Intel® HD Graphics 2500 Feature up to 1664 total available video memory as allocated by Windows 8 for lush visuals. 7-in-1 digital media reader Supports Secure Digital, Secure Digital High Capacity, SDXC, Memory Stick, Memory Stick Select, Memory Stick PRO and Memory Stick MagicGate formats. 6 high-speed USB 2.0 ports Deliver fast digital data transfer and easy peripheral connectivity. Built-in 10/100Base-T Ethernet LAN Offers quick and easy wired Web connection. Microsoft Windows 8 64-bit operating system

NO intel graphics are by far THE WORST

get a laptop with an AMD A8 or 10 series processor, that should run minecraft at at least 60fps

It's got awful Intel integrated graphics.

It'll play MC on low settings and you'll still get lag

No. The beyond awful integrated graphics (even Intel HD 4000 can't run it) and the processor also can't handle MC with decent visual settings and frame rate. Word of the wise: don't ever game on a laptop unless something nice like an Alienware. Get a decent desktop with a cheap GPU like an EVGA 8400 GS (can confirm 35fps along with an Intel Pentinum dual core E5200 @ 2.3GHz).

For Minecraft, I'd suggest i3 (i5 or better ideally), plus a dedicated graphics card from either Nvidia or AMD for ideal performance.

If you're playing with a fair amount of mods, you need more RAM. That's a simple fact, and it's something people overlook quite a lot. If you use mods, you need more.

Even though Minecraft isn't that demanding of a game, you would struggle with that system.

Sorry but that is a horrible system you have there with no graphics card. The Intel Celerons are an incredibly weak CPU series- even the newer ones. Time to upgrade.