Hello there.
This is Numberphile. We mainly post videos about mathematics and just numbers in general.
This is Numberphile. We mainly post videos about mathematics and just numbers in general.
During production of our cannon ball number video, Matt supplied this extra information:
For the bigger numbers I checked until 10^11. Here is what I found (back in 2013)!
There are four triangle cannonball numbers below 10^9: 10, 120, 1540, 7140
There is one square cannonball number below 10^9: 4900
There is one pentagon cannonball number below 10^9: 946
There are two octagon cannonball numbers below 10^9: 1045, 5985
There is one decogon cannonball number below 10^9: 175
There is one 11-agon cannonball number below 10^9: 23725
There are two 14-agon cannonball numbers below 10^9: 441, 195661
There is one 17-agon cannonball number below 10^9: 975061
There is one 20-agon cannonball number below 10^9: 3578401
There is one 23-agon cannonball number below 10^9: 10680265
There is one 26-agon cannonball number below 10^9: 27453385
There is one 29-agon cannonball number below 10^9: 63016921
There is one 30-agon cannonball number below 10^9: 23001
There is one 32-agon cannonball number below 10^9: 132361021
There is one 35-agon cannonball number below 10^9: 258815701
There is one 38-agon cannonball number below 10^9: 477132085
There are two 41-agon cannonball numbers below 10^9: 55202400, 837244045
There is one 43-agon cannonball number below 10^9: 245905
There is one 50-agon cannonball number below 10^9: 314755
There is one 88-agon cannonball number below 10^9: 48280
There is one 145-agon cannonball number below 10^9: 101337426
There is one 276-agon cannonball number below 10^9: 801801
There is one 322-agon cannonball number below 10^9: 1169686
There is one 823-agon cannonball number below 10^11: 197427385
There is one 2378-agon cannonball number below 10^11: 432684460
There is one 2386-agon cannonball number below 10^11: 29437553530
There is one 31265-agon cannonball number below 10^11: 90525801730
And Matt sent this a day later (in April, 2019).
I just dusted off my old code and ran it unchanged on a much newer laptop and it was able (overnight) to check every value up to one trillion (10^12) for everything up to a megagon (one million sides).
It did not find anything bigger than a the 31265-agon but filled in a few gaps lower down (eg: there is a 44-agon cannonball number at 1,408,778,281). And to be fair, for the larger -agons checking to 10^12 is not enough as the numbers themselves are so big. I should re-code it slightly to raise the ceiling as the shapes get more sides.
