I appreciate all of your responses and the surprising amount of work that some of you put in to your guesses/estimations/scientific equations. After talking with a couple of you I realize that I could have come up with several different numbers even from the same source, but I'm sticking with the original number I was given.
I first had my friend Kyoung ask a potato farmer in her ward how many potatoes he thought were in one of his typical cellars. He said there were 87,000 hundred weight sacks in a typical cellar and that a hundred weight sack held 180 average-sized potatoes, which would bring the number to 15,660,000. However, I didn't have the size of the cellar and I figured people would ask. The next day I contacted Teton West, who manufactures potato cellars in the area. They told me the dimensions of a typical cellar (301' long, 62' wide, 31' high) and told me that if they filled that cellar 20' high it would hold 130,000 hundred weight sacks of potatoes. 130,000 x 180 (medium sized potatoes) = 23,400,000 - the winning number.
The funny thing is I spoke with my sister Carrie last night who said that Nalani called Teton West and they told her that a cellar of that size would hold 14,000,000 potatoes. So, who knows?
My sister Carrie guessed the closest. When I asked her about her guess she said "Sally seems pretty smart, so I just guessed a little higher than her she did". So, Sally you shouldn't have written out your reasoning, which seemed to be your demise. In order to avoid the appearance of nepotism I'm going to disqualify Carrie (even though I'll probably bring her a print at Thanksgiving if she wants one).
So in appreciation, I'm going to send 12x16" Inkjet prints to the following individuals who guessed between 14,000,000 and 30,000,000 potatoes:
Nalani
Barry
David L'hoste (I was pleasantly surprised to see you post to my blog by the way, are you still in N.O.?)
Eden
Idaho Spud Boy (GP is that you?)
James
I'm giving the 16x20 silver print (assuming I get in the darkroom soon) to Sally, who guessed closest to the original number of 23,400,000 (once we disqualify my sister).
It will probably take a little while to get things printed, but you all should expect a print soon. Please email me your mailing address to - riversilt at gmail dot com (obviously you would format the email address like an email address, I'm just trying to avoid getting spam).
To those of you who weren't that close better luck next time. This was so much fun that there will probably be a next time. And don't feel bad if you weren't even close. My guess before I did any research was 900,000.