As much as I want your life to fall apart as obsession and lack of resources eat at you from both sides, as the drive to succeed battles lack of computational power and time constraints, as you lie on your death bed still attempting to write down g_1, I really have to agree with jestingrabbit.
You are doomed.
Let's take the mass of the Earth: we get 6.0 x 10^24 kg from
here. The calculations here are reasonable; you shouldn't have any reason to doubt them.
So let's suppose that the entire Earth can be converted into electrons for the storage of numbers. Let's even assume that these electrons can hold decimal digits, which they obviously can't in real life.
We have the mass of the electron to be 9.109 382616 × 10–31 kg, according to
wikipedia. No calculations here, but hopefully you'll accept this number without too much hassle; if you want, you can set up one of many devices and measure the value yourself.
Anyway, suppose that the entire Earth is electrons. Then we get that there are 6.6*10^54 electrons, all capable of holding a single decimal digit. Let's round that up to 10^55 just for good measure.
So we can write a number of 10^55 digits, but not much more.
Note that 3 is slightly less than the square root of 10; therefore 10^55 should be somewhat more than 3^110, but not by all that much. Let's write down 3^200 just to be safe.
Note that 3^^4 > 3^200 > 10^55, and that 3^^6 > 10^(3^^4). Note that these bounds are horrible estimates; 3^^4 exceeds 3^200, and thus 10^55, by several billion orders of magnitude. Thus you can't write down 3^^6 even if you stick a decimal digit onto every hadronic particle on Earth (note that I'm not mentioning non-hadronic particles; you have no chance of writing on them, so I'm not concerned).
Now note that 3^^^3 > 3^^6, as 3^^^3 = 3^^(3^^3), and 3^^3 > 6 by a lot. Thus 3^^^3 absolutely cannot be written down. And since g_1 = 3^^^(3^^^3) > 3^^^3, well, let's just say that I wish you good luck and that I feel sorry for anyone who requires you to do absolutely anything else ever.
Note that the visible universe does not have particles on the order of several billions of magnitudes, as light does not travel that fast and the universe is not that old. So even if we perfected space travel, and could write decimal on, say, neutrinos, you're still doomed.
