ok im not sure if this is what ur asking but ya lol (this is what i think you guys are asking for)
Im rank 70


Scanning Power: 414
Planets Discovered: 90
Planets In Galaxy: 4,272,362
Scan Chance Rating: Very Poor
(scan NOT avalible)

Scanning Power: 438
Planets Discovered: 90
Planets In Galaxy: 4,272,362
Scan Chance Rating: Very Poor
(SCAN AVALIBLE)

So somewhere between there scan becomes avalible, Hope thats what you wanted lol cause it cost me quite some creds to install and uninstall a bunch of mods just to get the perfect combination lol

I know these numbers are a bit higher then what you wanted but


Scanning Power: 839
Planets Discovered: 136
Planets In Galaxy: 4,272,362
Scan Chance Rating: Very Poor
(scan NOT available)

Scanning Power: 840
Planets Discovered: 136
Planets In Galaxy: 4,272,362
Scan Chance Rating: Very Poor
(scan available)

The thing is, between 1 and 500 is where we are missing the most data, which is crucial to this, considering from the data that Chloron gracefully gave us, we are almost certain that scan after a certain part is essentially linear, but under that number it is not, and we need more plot point to figure out the equation of the curve.

Scanning Power: 51
Planets Discovered: 40
chances, very poor (greyed out)

Scanning Power: 226
Planets Discovered: 40
chances, poor

Scanning Power: 260
Planets Discovered: 40
chances, poor

these are just from using arties to boost my research since i have no scan modules installed. (tachyon cylinder, sub-space seeker, continuum beacon)

*sigh* guys, they are not looking for approximations, because that would seriously mess up the equation, if it is not completely unworkable. They are looking for an EXACT number of scan that you can use to get a planet. Here's an example.
You have 23 planets scanned. You have 229 scan. You rearrange your modules to get one more scan, bringing it up to 230. You can then scan planet 24. Then the absolute minimum scan that you could use to get 24 planets is 230.
Do you get it? That's about as well as I can explain it.
THE ABOVE NUMBERS ARE NOT VALID, I JUST PLUCKED THEM OUT OF THE AIR. DO NOT USE THEM!!!!

EDIT: I thought of something else. Please do not use percentage buffs (Continuum Beacon and Stryll Seeker). They could also mess up the equation slightly.