[igpay]

Some low primes above ten are slightly pointier than I'd expect them to be (not sure where that expectation is coming from...), but that trend doesn't continue for very long - stops way before triple digits. I think it's likely a characteristic I've assigned to those numbers after repeatedly encountering them in a context where I needed to know they were prime, rather than some innate sense I have for detecting which numbers are prime or not.

[jart]

Does thinking about numbers this way lead to human calculator abilities? For example, if someone asked you on the spot what 4343 * 1234 is, would you be able to immediately give the correct answer? I hope this doesn't come across as disrespectful. I'm only asking because I love magic tricks. For example, John Conway published his mental model once for computing the day of week for any date and it was simple enough that pretty much any school kid who learned it could use the doomsday algorithm to convince their peers they've got rainman level skills.

[igpay]

Nope, I definitely do not have human calculator abilities. I'd solve your example problem with long multiplication, and would likely be unable to do so without pen and paper. The only difference is that each single digit multiplication or addition would be done with shapes. The shapes and their interactions seem to be more of a memory recall aid for things I already know (small addition and multiplication tables), rather than tools for solving problems I haven't seen before.