There are three types of PSPs:
1- 1000 Series (Also known as Phat/Fat)
2- 2000 Series (Also known as Slim or Lite & Slim)
3- 3000 Series (Also known as Brite)
Now, what do I mean by "Hackable"?
That means you can install a Custom Firmware (CFW) on it. The most popular (& sometimes only) way to do it is by using a Pandora Battery & Magic Memory Stick (MMS).
Why Hack a PSP?
Not my concern, but there are limitless reasons.
Why can't I hack 'this' PSP?
'This' PSP probably has a TA-088v3 (Found in some 2000 series units) or TA-090v2 (Found in all 3000 series units) Motherboard, both of which are unhackable, as in, you can't install CFW on them.
Let’s start now.
All 1000 Series PSPs are hackable to date.
To some, there are other methods than just using a Pandora & an MMS.
On the other hand, 2000 Series are a little complicated. There are old units, new units, & Really new units. The old ones, containing a motherboard before the TA-088v3, are all hackable. While the new ones that have the TA-088v3 Motherboards are unhackable. Finally, the Really new ones have a TA-090v1 Motherboard, which is hackable. There are 7 different ways to tell whether ‘that’ 2000 series PSP is hackable or not, but we'll get to that later on.
Finally, the 3000 series PSPs. All of those have the TA-090v2 Motherboard, all of which are unhackable to date.
Though, there is hope for the PSP 3000 series. According to the site, an error that might lead to a complete hack has been found. This error has been used to install "Hello World" on the PSP so far. Let's hope someone utilizes it completely to install Custom Firmware.
Of course, new updates might come to change everything one day, & that's why there's a date at the start of the topic (To indicate when this topic was last updated).
So, now it's easy to tell whether a 1000 series and a 3000 series are hackable or not. The only complication is when trying to figure out a 2000 Series PSP. Whether you want to know before you buy it, or before you bother learning how to hack it, you choose the way that suits you best.
I want to note that most of the information I know I learned through research. Only a small percentage of it is from actual testing or experimentation. So far, I can't tell whether a PSP has a TA-090v1 Motherboard or a TA-088v3 Motherboard. But, I could tell whether it's an old unit (Before TA-088v3) or a new one in general (TA-088v3 & after).
1- What is the Firmware the PSP came with?
If it's 4.01, your PSP has a slight (Very, very Small Chance) that it's hackable, but it's most likely unhackable. If over 4.01, it's unhackable (Unless if it's a TA-090v1, but I don't know what firmware it comes with yet). If less than 4.01, then it's hackable.
What does the Firmware have to do with it if it's the motherboard we're looking for? I'd say that Sony started manufacturing PSPs with the TA-088v3 Motherboards while the firmware 4.01 was their current firmware.
2- What is the PSP's Serial Number?
The Serial Number is found on a label where the battery is supposed to go (As shown in the picture)

If that serial starts with HU2, then the PSP most likely has a TA-088v3 Motherboard, if it doesn't, that doesn't really mean it's hackable, it's just more likely if it starts with HU2.
Most of the HU2 PSPs are Piano Black PSPs. Check Method 4 for the best Piano Black Hackability help.
Also, a lot of people with unhackable PSPs have serials starting with "HC". Though I believe I saw an HC PSP that was hacked, so I'll have to verify.
(Note that this PSP starts with HU0, & it's hackable).
3- What's the unit's Identification letter (A letter on a label on the box that indicates what version it has)?
Here's a picture of a label found on the PSP box that has the letter on it:

I'm sorry the picture is unclear, but that's the best my phone could get.
Note that this label is only present on an original style box (The small, normal box. Not like those large "Limited Edition" Boxes).
Anyways, See the G there?
PSP-2000 CW
100v
G
That G is that letter. Here's a list that I found:
(No Letter) = 3.60
A = 3.71
B = Unknown
C = 3.72
D = Unknown
E = 3.80
F = 3.90
G = 3.95 (TA-088v1) / 4.01 (TA-088v2) / 4.01 (TA-088v3)
If the letter is absent or from A to F, then it's hackable. If it's a G, it's 60 to 67% Hackable. If something else, It's unhackable (Unless if it's a TA-090v1 Motherboard).
Note that the G PSP in the picture is my personal PSP. It came with a 3.95 Official Firmware (OFW) & I hacked it (Has Custom Firmware 5.00 M33-4 5.02 GEN-A (Full)).
4- What's the Box's Serial Number?
If your box doesn't have a label with a letter in it, like the G in the third method, then it should have a label with another serial that's not related to the PSP unit.
Here's a picture given to me by one of our members:

If that serial is like the one on this image, starting with AB02, then that PSP is most likely unhackable (The chance of it being hackable is so small, it doesn't count). On the other hand, if it starts with AB01, then it's hackable. My brother has a box with such a label, I'll get him to take a picture & send it to me later on to prove or contradict this. His PSP was hacked by me, & it has CFW 5.00 M33-4.
5- What's the PSP's Date Code?
So far, I could verify that if the PSP has an 8C Date Code, then it's unhackable.
I still need to investigate this a little longer.
An image will be coming soon. Though I'd like to note that American PSPs (2001) usually don't have that code on them (just like the Piano Black with HU0 Serial number pictured above).
6- Using Dark_AleX's TA-088v3 Identifier:
For the time being, I'll just post a link to the location I found it at. When I test it, I'll put a step by step tutorial for it. (Link: http://forums.exophase.com/showthread.p ... #post47672 ) I personally am disappointed by it, as I thought it would actually spell out the type of motherboard in the PSP, but all it does is shut down or not to indicate if it's hackable or not...
I'm also not sure how this would react to the TA-090v1 Motherboards...
7- If it's a Limited Edition PSP, here's the list of the ones I know of so far:
Daxter Limited Edition Pack, comes with 3.80 OFW & a TA-085v2 Motherboard, and is hackable.
God of War Limited Edition Pack, comes with 3.95 OFW & a TA-088v2 Motherboard, and is hackable, & cool too
Madden 09 Limited Edition Pack, comes with either 3.95 OFW & a TA-088v2 Motherboard ~~OR~~ 4.01 OFW & a TA-088v3 Motherboard. If it's 3.95, it's hackable, but if it's 4.01, then it's not, simple as that.
I found this on Dark_AleX's Forum:

Note that saying that the TA-090v1 is hackable could indicate that letters after G on the box (say around I or J I'm guessing) are hackable, but I don't know exactly.
Right now, I personally believe it, because I found a Post by "Alek" that states so in Spanish.
If any of you guys or girls have anything you want to add (or prove wrong) please do. The more the information to figure this out, the better. & it helps if it's accurate.
There is one method I'd like to say has nothing to do with whether the PSP is hackable or not:
The PSP series full series number (2000/2001/20002/etc) just as seen in both pictures (2001 black PSP Slim, & 2000 White PSP Slim) Those have nothing to do with whether the PSP is hackable or not.
There was a rumor that version 5.02 OFW is unhackable. This is not true. If you say that it is, then you most likely have done something wrong, or your PSP isn't hackable to begin with.
I have personally updated to 5.02 OFW on my PSP (White, TA-088v2 Motherboard, came with 3.95 OFW, & Serial Number starting with "HJ2") I used my Pandora (Phat Battery, Softmodded) & an MMS with 3.80 CFW. I install CFW 3.80, then updated to 5.00 M33-4 CFW.
Final Note:
As I mentioned before, this post is mainly based on online research, & hardly any of it is from personal testing or experimenting. Though I do try to verify what I can, when I can.






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