# How do I write 870037764750?

If 2 is b, 12 is cb'b, and 286992882 is f'cb,c'b'b,,b then how would I write 870037764750?

• for math class? chegg.com/homework-help/questions-and-answers/… – omikes Nov 27 '17 at 21:15
• @oMiKeY, if so, I want to downvote it. Very bad form posting homework questions on Puzzling.SE – NH. Nov 27 '17 at 23:02
• Hahaha! Oh man, that's a really funny coincidence to me. No I have never seen this question before, and I simply constructed the number on the question to be an interesting one to construct. I guess whoever wrote that maths question had a similar idea. – Jake Conkerton-Darby Nov 28 '17 at 0:48

You would write 870037764750 as

f'd,e'b'b,,d'c,c'b,b

The rule behind this is

based on the prime factorization. The letters represent the prime numbers (b=2, c=3, d=5, ...), while ' stands for ^( and , stands for ).
b $= 2$
cb'b, $= 3 \times 2^{2} = 12$
f'cb,c'b'b,,b $= 11^{3 \times 2} \times 3^{2^{2}} \times 2 = 286992882$
f'd,e'b'b,,d'c,c'b,b $= 11^{5} \times 7^{2^{2}} \times 5^{3} \times 3^{2} \times 2 = 870037764750$

• Good work, that is exactly right. I came up with this as an entirely alien form of writing numbers (compared to our common positional number systems), and then thought people here might be interested in puzzling out the answer. – Jake Conkerton-Darby Nov 27 '17 at 10:43
• Your new system has the disadvantage of what happens after z? Other then that, its pretty fun. – Cheiron Nov 27 '17 at 11:49
• @Cheiron, try adding two of those numbers in that notation ;) – Hans Janssen Nov 27 '17 at 13:05
• @Geliormth On the other hand, multiplication and exponentiation are a cinch! ;) – João Mendes Nov 27 '17 at 13:16
• @Geliormth 12+286992882 is only three characters in this notation! I have no idea which character the first one would be, but only needing 3 characters is clearly superior! – w l Nov 27 '17 at 13:18