How much can we trust in mathematical software when working with large numbers, and how much memory it needs to work with these numbers?

For example, I want to evaluate the expression:

$ 3^{3^{{3}^{3}}}$

so I used (it’s free, and I don’t own any software), which returned a decimal form of the number above, namely:

$ 1.258014290627491317860390698… × 10^{3638334640024}$

Which is huge. However, for the number below

$ 4^{4^{{4}^{4}}}$

Wolfram can’t return a decimal form, probably because it’s a much larger number and it needs a lot o memory.

Questions: a) How much can we trust that

$ 3^{3^{{3}^{3}}} \approx 1.258014290627491317860390698… × 10^{3638334640024} $

b) how much memory (aproximate) it needs to evaluate

$ 3^{3^{{3}^{3}}}$


$ 4^{4^{{4}^{4}}}$

I’m guessin a lot of terabytes and something that a home computer can’t handle. But for the first number, Wolfram can, and the second number, it can’t. How do we even find how much size we need to calculate these numbers?

It would be nice if someone improved the tags


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Trouble running these 3 apps at the same time

I am on Android 8.1.0. (Non-rooted. LG LM-X212TA.)

I would like to run all three of the following apps at the same time, but some seem to continue to crash when run at the same time. (I suspect conflicts related to [some of] their VPN capabilities, but I am not sure.):

NoRootFirewall (version 3.0.1 (build 41) )

Orbot (version 16.0.5-RC-2-tor- ) (version 2.0.7 (396) )

Looks like and Orbot have a conflict, or some other issue[s].

I turned off’s “VPN Mode” but that did not seem to help.

Any advice?


I have imported around 90 million unique URLs as new targets and they get deleted with these setting

I have crawled myself quite a few URLs and made them unique

I import them into a fresh project

After a while target URLs of the project get deleted

Here my settings

Are there a maximum amount of URLs file size that GSA ser supports?

Imported target urls file is 6.13 GB

The import process is being success because i see target urls file in projects folder

The GSA ser starts with around fetching 16k urls

And today when i wake up after like 10 hours i see target urls in project folder got reset and there are only several megabytes target urls

I am trying again

the fresh project starts as 

Loaded 16777 URLs from imported sites

And damn target urls already got reset

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By how much would these Savage Worlds systems affect the game in 5e?

In Savage Worlds, there are two systems I particularly like. One is the “Benny” system, the other is an initiative system determined by card draws.

So basically, the Benny system grants each PC 3 Bennys at the beginning of each session. Significant enemies can also be granted them as well. These can be used to “soak” damage taken, to re-roll damage dealt, or do “rule of cool” things like synchronising attacks, or performing stunts, or maybe things like allowing the magic user to imbue the Fighter’s weapon with magic damage.

The deck of cards initiative is fairly straightforward. At the beginning of each round, each player enemy (or group of enemies, for simplicity) is dealt a card. Ace goes first, then King, etc, down to 2 going last. Suits also determine initiative – hearts before diamonds, etc. However, this uses the Jokers in the deck as well. Jokers can go whenever they want, basically like a reaction (though not as a reaction, in 5e terms). It also grants a +2 to any rolls made this round. Then, at the end of the round, if a Joker was drawn, the deck is reshuffled.

If these systems were incorporated into 5e, how much would it affect the game, and more specifically, how much would it alter the CR calculation?

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