The GTX 340 is perhaps one of the strangest and rarest graphics cards you can find online today. As covered by the Budget-Builds Official YouTube Channel, the GTX 340 is, in fact, an unofficial GeForce 300 series card that Nvidia never actually produced. Instead, enterprising modders created the cards from standard GT units by adding souped-up dual-slot coolers, modifying the BIOS, applying a hefty overclock, and then changing the identifier string to make the card appear as a "GTX" model in the system.
First, a quick backstory into Nvidia's 300 series; the 300 series started as a rebrand of the 200 series and was based on the Tesla 2.0 architecture, which proved to be very efficient but very weak in terms of raw horsepower. Due to Tesla's low performance, the 300 series cards were primarily geared for 2D video playback and basic display adapters, but they could run some 3D applications. Oddly enough, the 200 series were nothing more than rebrands of the 200 series. (The only exception being the GT 320 and GT 330, which had very slight improvements over the 200 series counterparts.)
So what about the GTX 340? Apparently, someone years and years ago got into the business of upgrading GT 340s, which were then re-sold to system builders. The mods included a dual-slot cooler, a modified BIOS with the GTX nomenclature, and a hefty core overclock. In fact, the card shows up as a GTX 340 in GPU-z.
This strategy does make sense — the GT 340 is already very power efficient, consuming just 51W, so getting a good overclock out of the GT 340 wasn't hard at all with a cooler that's twice the size of the original.
Unfortunately, we don't know why this person (or people) decided to give the GT 340 the GTX 340 badge. Still, it was probably to help differentiate these heavily modified cards from the traditional GT 340.
The GTX 340 features a Tesla 2.0 GPU with 96 Shader Units, 32 TMUs, 1GB of GDDR5, and a 51W TDP. The GTX card has a core clock speed of 650 MHz and 1700 MHz memory clock, a decent increase from the GT's original 500 MHz core clock and 850 MHz memory clock.
Of course, with how old this card is, performance is very underwhelming; the card can barely manage 30FPS in CSGO at 480P (yeah, it's that bad), and the performance delta between the GT 340 and the "GTX 340" is barely 2%, at most.
That's the story of the GTX 340; it's perhaps one of the most boring GPUs ever to be released, but it's cool that someone made a brand new SKU out of "thin air," and it seemed to have worked for them. At least from a business perspective. But good luck trying to buy one — they are super scarce on eBay and can only be bought overseas.