The following is a background discussion of the use of "P" in HCP specs for entries responding to opening bids of 1N and 2N, as well as the use of "Min" for entries for rebids by the opener. Click here for the documentation page which displays this file or press the Back/left-arrow button.
A variety of opening 1N ranges can be used: 16-18, 15-17, 14-16, 12-14, 11-13, 10-12, and even lower. Next, opener's LHO has available a wide variety of systems for interfering after a 1N opening bid.
Let's say that BidBase has 50 entries for responding to an opening 1N bid of 15-17 HCPs when responder's RHO passes. (Only about half of these are active. The other half are alternative bids.)
The 50 NT response entries contain specs which are based on the NT range of HCPs. For example, if opener's 1N range is 15-17 HCPs, the customary HCP range for a quantitative raise to 3N is 10-14 HCPs, But if the 1N range is 12-14, then the raise to 3N requires 13-15 because in both cases, we need to have a combined total of 25-29 HCPs, minimum.
So if there are 6 ranges of HCPs commonly used for 1N, you would need 50 different entries for each range, or 300 total entries. And this is only for when RHO passes.
RHO has numerous systems available for interfering over an opening 1N -- DONT, Cappelletti, ASTRO, Brozel, Landy, and many others, including natural bids. Since an overcall, such as 2C, can have different meanings for each of these systems, we have to multiply the 300 entries so far by the number of different systems. For just 6 different defensive systems, that brings us up to 1800 entries.
If it were just a matter of making these 1800 entries and being done with it, that would probably be preferable to adding what admittedly can be a confusing feature. But the problem is that making the original entries is only the beginning.
Let's say that you usually play a 15-17 HCP NT, but you want to try a 12-14 HCP NT. To do that, the way things were prior to the "P" prefix, you would have to wade through those 1800 entries, activating the entries specific to 12-14 NTs and deactivating the rest.
The 1800 responses can be reduced by using the "P" prefix for the hand's HCPs. This allows you to specify that the HCPs of the current hand must equal the specified points or range of points when added to the minimum HCPs of opener's HCP range, so you no longer have to have a separate set of responses for each possible range of HCPs for 1N.
More importantly, you do not have to wade through 1800+ entries activating and deactivating entries for the desired HCP range. All you change is the opening 1N entry with the Bid Order Number of "131000".