1st time cold crash - priming sugar question

Got 10 gallons chilling @ upper 30 degrees for 52 hours b4 I bottle. I know there will be plenty of yeast for carbonation, but I read some people say to add a little extra priming sugar. I obviously DO NOT want gushers. Any advice on amounts. I'm using regular cane sugar.

I've never used (nor heard people say to use) more priming sugar because of a cold crash.

There are a number of good calculators out there to get priming amounts, like this one.

Based on some average numbers that I put in (2.5 volumes of CO2 desired and a fermenting temp of 68 degrees) you would use 8.1oz of table sugar.

So what does it mean by beer temp of fermentation? Im cold crashing and lagering my alt bier for a month. Should I use the temp of 37F for the cold crash or the 57F that primary fermentation was at for figuring that out?

57F

What it's asking for is the highest temp achieved during or post fermentation. The reason is that CO2 is more soluble in colder liquids, so if you ferment at 65 degrees (for example) you will retain X% of CO2 in your beer.
If you ferment at 55 degrees, you are going to have Y% of CO2 in your beer (where Y>X).

When you cold crash, it doesn't change the amount of CO2 already in your beer, but if you went warmer post-fermentation you would lose more of what was already in there.

Does that make sense?

Wow thank you for that clear explanation. The highest I had it at was about 60, so It comes out to be 4.4Oz of corn sugar. Thanks again.

Should I still raise the beer temp when priming and bottling to around room temps? Or will that affect the calculations? Or can I just bottle and prime it still cold right after I transfer to my bottling bucket?

No need to raise the temps. Add your priming sugar, make sure it's mixed well by either adding the sugar first and racking on top or GENTLY stirring with a sanitized spoon.

Then just bottle immediately. As the bottles warm back up the yeast will get to work.

Part of the reason for the cold crash is to help things settle out, you don't want to put them back in suspension by raising the temps again.