Intel clarification i3 vs i5 vs i7

Am I correct in saying that
i3 = dual core
i5 = quad core
i7 = quad core plus hyperthreadinbg

Is is that simple or no?

[for my purposes, only looking to clarify desktop parts, not mobile/laptop etc.]

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i3 might be a case of dual core & hyperthreading

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I3 is dual+hyperthreading.

Then there are the laptop chips.

For the purpose of my question. Lets consider desktop only chips, not laptop m etc.

i3 - Dual-Core w/ HT, no TurboBoost
i5- Quad-Core w/o HT, TurboBoost
i7 - Quad-Core (or higher) w/ HT, TurboBoost

There are other features that get enabled/disabled depending on which product you look at, but that's more convoluted and generally unnecessary for comparison.

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And there are also E3 and E5 series of Xeon´s.

E3- series: 4 cores with and without HT.
And with and without igpu.

E5- series: 4 cores (or more) w/ HT, no igpu.

Pentium G 4560 to 4620 2 Cores 4 Threads
I3......2 cores 4 threads plus 50 extra bucks or so
Adding hyper-threading to the Pentium G has thrown their traditional lineup into chaos

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i7s have multiple segments. The lowest is 4c/8T, the highest currently is 10c/20T.

Yeah... For users that would be willing to settle for an i3 or that's all they need, why get the i3 when a Pentium G will suffice? I am sure there are i3 SKU's that may have a slightly higher clock than the Pentium's, but for users at the low end, they won't notice or care.

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For desktop mainstream, you are correct. The "small socket" line (Lga 1151, 1150, 1155..) have so far always had the structure of

I3 = dual core + Hyperthreading
I5 = Quad core no Hyperthreading
I7 = Quad core + hyperthreading

It has been long speculated that the next Intel refresh (Coffee Lake) will bring a 6 core to the mainstream, small socket with a new Lga socket and new chipsets. So, at this moment, the structure listed above has held true for desktop small socket, but that might change with the next generation.

With the G4560 and some others the pentium line are also dual cores with hyperthreading

Mate he said desktop only

Based on Intel's upcoming X299 architecture, its numbering scheme seems to make the i3 obselete now... Only time will tell if it's permanent

X299 is the top tier HEDT chipset. Just like X99 and X79. It never included any parts besides i7s. Intel just created the idiotic Kaby Lake X parts which are 7600 and 7700s on the big chipset for some reason..... However this doesn't mean i3s are gone. i3s still do and will continue to exist on the mainstream LGA 115X platforms like Z270 ect...

i3s are obsolete though even though continues to made them. They got obliterated by the Pentium and Ryzen

If you are looking for specific features on Intel products, check out http://ark.intel.com. You can filter by most features and compare the parts.