Menu
Assuming we are not concerned about running time of the program (which is practically infinite for human mortals) and using limited amount of memory (2^64 bytes), we want to print out in base 10, the exact value of 10^(googolplex), one digit at a time on screen (mostly zeros).
Describe an algorithm (which can be coded on current day computers), or write a program to do this. Since we cannot practically check the output, so we will rely on collective opinion on the correctness of the program.
NOTE : I do not know the solution, or whether a solution exists or not. The problem is my own invention. To those readers who are quick to mark this offtopic... kindly reconsider. This is difficult and bit theoretical but definitely CS.
687
A googolplex is the number 10googol, or equivalently, 1010100 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 . Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by googol zeroes.
A googol, officially known as ten-duotrigintillion or ten thousand sexdecillion, is a 1 with one hundred zeros after it. Written out, a googol looks like this: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
Graham's number is bigger than the googolplex. It's so big, the Universe does not contain enough stuff on which to write its digits: it's literally too big to write. But this number is finite, it's also an whole number, and despite it being so mind-bogglingly huge we know it is divisible by 3 and ends in a 7.
This is impossible. There are more states (10^(10^100)) in the program than there are electrons in the universe (~10^80). Therefore, in our universe, there can be no such realization of a machine capable of executing the task.
162
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
