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Overflow calculating the last 10, 000 digits of (((96717311574016^16777216^4)^8^4)^7)^2

Mark Raygorodsky
Posted 1 month ago
POSTED BY: Mark Raygorodsky
23 Replies
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POSTED BY: Mark Raygorodsky

is there a way to find out what the first 50, 000 digits of GRAHAM'S NUMBER are?

POSTED BY: Mark Raygorodsky

Some relevant tools for Implementation of level-index arithmetic for very large numbers were proto-typed by Swastik Banerjee (formerly at Wolfram Research).
POSTED BY: Paul Abbott
Hans Milton
Hans Milton
Posted 1 month ago

Deleted. My post was a mistake. By routine habit I considered exponentiation. While Swastik's idea involves tetration.
POSTED BY: Hans Milton

I am going to set the mantissa of this code to a MILLION digits. It’s basically 5, followed by a decimal point, followed by a million digits after that. Every method I tried to compute the first million digits of my number results in an overflow error. I don’t get the same error when computing the last million digits. To me the first and last million digits is the same size of the number and they both shouldn’t overflow. That “100” you wrote in your code should be at least 50, 000. I copied and pasted your code into my notebook and set the number to 10, 000. And I get an error “precision depth exceeded.”
POSTED BY: Mark Raygorodsky
POSTED BY: Mark Raygorodsky

For the last digits I use the mod function, but still haven't figured out how to calculate the FIRST digits! a log of a number shows how long the number is. Does it also calculate the first digits?!
POSTED BY: Mark Raygorodsky

I haven't found a way to get the first digits of my number and it's so EXTREMELY HARD that I must as well forget about them and focus on the last digits. I typed my expression in and it gave me something mod^2 power, 1977326743 followed by a million zeros and these ARE NOT THE LAST MILLION DECIMAL DIGITS I AM EXPECTING!
POSTED BY: Mark Raygorodsky
Bill Nelson
Bill Nelson
Posted 1 month ago
POSTED BY: Bill Nelson
POSTED BY: Mark Raygorodsky
Bill Nelson
Bill Nelson
Posted 1 month ago
POSTED BY: Bill Nelson
POSTED BY: Mark Raygorodsky
Bill Nelson
Bill Nelson
Posted 1 month ago
POSTED BY: Bill Nelson
POSTED BY: Mark Raygorodsky
Bill Nelson
Bill Nelson
Posted 1 month ago
POSTED BY: Bill Nelson

the notebook five minutes.nb is in my notes but i cant open it; clicking it just duplicates it in my notes
POSTED BY: Mark Raygorodsky

I now have it on my computer but I am still clueless how to use the language.

POSTED BY: Mark Raygorodsky
Bill Nelson
Bill Nelson
Posted 1 month ago
POSTED BY: Bill Nelson
POSTED BY: Mark Raygorodsky

thanks so much bill! so now my question is how to I calculate the last MILLION digits of my expression (((96717311574016^16777216^4)^8^4)^7)^2 * 7^11? I am basically asking to calculate mod 10^1, 000, 000 of 96717311574016^(16777216^4 * 8^4 * 7 * 2) * 7^11. but first I need to know how to use Mathematica on my computer.
POSTED BY: Mark Raygorodsky
Bill Nelson
Bill Nelson
Posted 1 month ago

Changing from 10 thousand digits to 1 million digits required changing 10^(10^4) to 10^(10^6) in two places. The output is then large enough that MMA doesn't immediately show you all of the result on the screen so adding //InputForm may overcome that. That may pop up a little window asking you if you really want an output that large. If so then you confirm you want that.

Try

Mod[PowerMod[96717311574016,16777216^4*8^4*7*2,10^(10^6)]*7^11,10^(10^6)]//InputForm

and see if that works for you.
POSTED BY: Bill Nelson
Hans Milton
Hans Milton
Posted 1 month ago

but first I need to know how to use Mathematica on my computer

You could download and install a free 15-day trial version: Mathematica trial
POSTED BY: Hans Milton
Bill Nelson
Bill Nelson
Posted 1 month ago

I think that 

(((96717311574016^16777216^4)^8^4)^7)^2==96717311574016^(16777216^4*8^4*7*2)

You must check that and convince yourself whether that is correct or not. As you have seen, Mathematica cannot simply directly calculate both those values and compare them for equality.

If that is correct then

Mod[PowerMod[96717311574016,16777216^4*8^4*7*2,10^(10^4)]*7^11,10^(10^4)]

returns the last 10 thousand digits of the result in a few seconds.

Study all the details of the documentation for PowerMod carefully and then find at least three completely different ways that you can try to check whether I have made any mistake or if the result might be incorrect.
POSTED BY: Bill Nelson
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