I have seen some photos of aluminum based Prusa i3 printers, and I like to know the numbers and the specs of the profiles? Also I want to know Is the first pic strong enough for reliable printer or I must use the second(respect to profiles I mean).
They are 2020 (20mm x 20mm) T-slot extrusions. They should not be confused with V-slot extrusions, which are similar to T-slot, but have a 45-degree slot profile to accommodate V-slot wheels.
If you are contemplating a new build, I would recommend using V-slot. Note that T-slot and V-slot come in a number of sizes (in multiples of 20mm). A 2040 profile is 20mm x 40mm, and will have two slots on the wider sides. Other sizes are available, such as 2060, 2080, 4040, and even C-shaped profiles.
You may want to use 2040 profiles for greater rigidity, especially if you are contemplating a large build volume.
Note that there are imperial as well as metric T-slot profiles. RepRap uses metric profiles.
The specs for 2020 aluminum profile is here. https://8020.net/20-2020-black-fb.html This site even has the cad profile files for download.
I have noticed that some people have suggested using V-Slot from open builds... however, V-Slot has a V for the V groove wheels which this design is not using so in my opinion there is absolutely no reason to pay a lot more for V-Slot when your not even using V groove wheels.
I have also noticed that some people have suggested using 2040 T-Slot and the link above has a search and you can find the profile for 2040 T-Slot. I agree that T-Slot could be better; however, I would build first with 2020 T-Slot to see for yourself and then report your findings after upgrading to 2040 T-Slot. My guess is that you will find that 2020 T-Slot is enough if you use the recommend corner brackets... if your planning on using 3D printed corner brackets... then it might be necessary to use 2040 T-Slot.
It can really depend on where you are in the world. A few years ago, I was unable to obtain standard V-slot (& T-nut) 2020 extrusion, at a reasonable price, and so I ended up using an extrusion from a local supplier instead, and managed to obtain 6 m of extrusion for only $15!
My aluminium extrusion has this profile, which has V-Slot style grooves.
Also, it uses simple, and cheap, M5 nuts, rather than T-nuts, which are much more expensive (comparatively)
Please see Will standard M5 T-slot nuts fit these different 2020 aluminium extrusions?, for more information.
You can also use 1515, depending on the size of the printer... if you have a larger printer design then you can always double up and use two adjacent lengths of 1515 to effectively have 3015 (or 2040 - if using two pieces of 2020). Basically use whatever is available and cheap, it isn't necessary to pay a lot of money, just to have the perfect extrusion profile. Remember that you are designing/building the printer yourself, so you will have some leeway. Other sizes that may be available to use are 2525, 2040, 3030, 3060, etc..
However, if you are using 3D printed parts for the frame (such as the end or corner pieces), then you may be restricted in what type of extrusion that you can use, by the printed parts themselves and what type of extrusion they will fit. However, if you are only using aluminium parts for the frame (including aluminium corner brackets/braces) then you should be OK.