Prime number thought experiment

[MooMoo2]

Suppose a magical wizard makes all man-made objects vanish and restores Earth to its pre-human, 200,000 BC state. What’s left is 7.4 billion naked humans, standing on grassy plains, in forests, in swamps, on tundra, and in deserts in the exact spots where their cities and villages were just a second ago.

The humans themselves are unchanged. They're the same physical condition and age, and each person knows everything they know right now.

The wizard also leaves three things behind for every person:
1.) A reasonably healthy 1,000 calorie meal
2.) One litre of potable water
3.) A piece of paper with a note in their language that says, “I’ve cast a spell on all of humanity as an experiment. Here’s how it works: everything will remain as is until someone manages to discover a prime number larger than 2^74,207,281-1. To prevent random guesses, anyone who submits false claims will be tortured and then killed. Once that prime number is found, the spell will be reversed and all man-made objects you had in 2017 will reappear.

Read this carefully and enjoy your food and water, because those items will all disappear after an hour.”

So the question is, how would this play out, and what’s your estimate for how long it would take for humanity to find a 22,338,618+ digit prime and reverse the spell? There would be mass casualties during the first few days and weeks, but could humanity find that prime within a few decades? What about a few centuries?

Bonus question: How would this change if the wizard demanded a round-trip manned moon landing instead of a 22,338,618+ digit prime? Would the time be a lot shorter?

[Dubslow]

Round trip moon landing may well be easier. It requires significantly less computing resources than finding primes. To zeroth order, computing power seems to be the scarcest resource in this scenario. Significant coordination among those suitably knowledgeable, as well as persuasion of the other 90-99% of the world who know nothing about the computational search for primes, will be required to get even manufacturing of new silicon going. The persuasion and coordination of those not in the know would probably be hardest.

And that entire previous paragraph assumes no communication problems, which is of course non trivial. Years at a minimum, if not an entire lifetime or more. That doesn't even count the cost of actually searching for the putative prime (which would almost certainly be Mersenne).

[axn]

Option 1) Humanity collectively gives the middle finger to the wizard and rebuilds civilization from scratch.
Option 2) The people who are in immediate danger of dying makes random guesses and succeeds.
Option 3) A few (million) people decides to take one for the team and systematically guess the next mersenne exponent. [There are about 7 million exponents between 74e6 and 200e6, which can be cut to about half thru very basic TF].

If the requirement is to go to moon, then option 1 is the best. Seriously, I don't understand the difference between having a civilization that can go to the moon vs having 2017 things. 2017 things can't even go to the moon! If you have a civilization that can go to moon, then going to 2017 standard is actually a regression!

Also, what is the relevance of the food and water thing? What difference does that make to the whole thing?

[Dubslow]

We got to the moon 50 years ago (admittedly for a decade straight of 4% GDP), so I wouldn't *quite* call "now" a regression from "getting to the moon". In fact it would be substantially cheaper to do it today (if you're an ultra-rich billionaire starting from scratch, that is).

[rudy235]

I just wonder how will they take them to make a perfect can of Coca Cola or a running 1960 Jaguar E Type.

Add twenty to twenty five years to that and you'll have your prime number... and your trip to the moon.

[retina]

Originally Posted by MooMoo2

So the question is, how would this play out, and what’s your estimate for how long it would take for humanity to find a 22,338,618+ digit prime and reverse the spell? There would be mass casualties during the first few days and weeks, but could humanity find that prime within a few decades? What about a few centuries?

Without the tools to make the tools to make the tools, there is no way anyone, or any group, could build a working high speed large RAM computer -- even if everyone was a genius with perfect knowledge of every process involved with making, powering, programming and running a computer -- within "a few centuries". So many other factors would come into play: for example, oh, I don't know, maybe ... surviving. The average modern day human of this era would have very little idea how to survive in the prehistoric world they suddenly found themselves occupying. Food, water, disease, predators, temperatures, shelter, sanity, sanitation, war, etc., would all become major issues that must be dealt with immediately. Forget about prime numbers or rockets, that ain't gonna get any attention for a very long time. And by the time everyone is into the fourth or fifth post-2017 generation memories of "the good ol' 2017s" would be long gone. So my answer would be: No, not within a few decades or a few centuries.

I like axn's options 2 and 3. But they don't really "solve" the question as posed because the number is not really found, but it would be guessed.

[kladner]

It does seem that the vast majority of humans dying would be the first order of business. After that, how many would even know what a prime number is? It could easily take a millennium for the remaining humans to get to the "small farming communities" stage.

[Dubslow]

Originally Posted by kladner

It does seem that the vast majority of humans dying would be the first order of business. After that, how many would even know what a prime number is? It could easily take a millennium for the remaining humans to get to the "small farming communities" stage.

I think you and retina underestimate what the most knowledgeable humans are capable of doing even if you ignore the average person (and I think you guys underestimate the average person too).

I think we could get *some* form of manufacturing going within at most a lifetime. It wouldn't be *that* hard to re-learn how to smelt iron ore into iron into steel, after which you can build steam engines, basically taking you to no-earlier-than the 1800s, technologically speaking. And enough people would remember about computers (and all the other science in between) to be able to at least create new books about them, even if silicon forges take another few decades to get going again. Recreating humanity's progress would be a lot easier, relatively speaking, than re-discovering it from scratch. (P vs NP and all that. Just because I can appreciate the genius of Mozart doesn't mean I could accomplish something similar myself.)

And I highly doubt the majority of people would die. Many would be highly stressed and unable to immediately contribute any sort of scientific knowledge, but most would be able to fend for themselves... I think. Maybe I'm overestimating the average person. Hard to say.

I think axn's point that the number of (Mersenne Prime candidates we expect to require "testing" before we find another) is more than an order of magnitude smaller than the number of people is an excellent point, though of course coordinating such a search, nevermind finding enough suicidal people, would probably rule it out on practical grounds if not ethical grounds as well.

[science_man_88]

Originally Posted by Dubslow

I think you and retina underestimate what the most knowledgeable humans are capable of doing even if you ignore the average person (and I think you guys underestimate the average person too).

I think we could get *some* form of manufacturing going within at most a lifetime. It wouldn't be *that* hard to re-learn how to smelt iron ore into iron into steel, after which you can build steam engines, basically taking you to no-earlier-than the 1800s, technologically speaking. And enough people would remember about computers (and all the other science in between) to be able to at least create new books about them, even if silicon forges take another few decades to get going again. Recreating humanity's progress would be a lot easier, relatively speaking, than re-discovering it from scratch. (P vs NP and all that. Just because I can appreciate the genius of Mozart doesn't mean I could accomplish something similar myself.)

And I highly doubt the majority of people would die. Many would be highly stressed and unable to immediately contribute any sort of scientific knowledge, but most would be able to fend for themselves... I think. Maybe I'm overestimating the average person. Hard to say.

I think axn's point that the number of (Mersenne Prime candidates we expect to require "testing" before we find another) is more than an order of magnitude smaller than the number of people is an excellent point, though of course coordinating such a search, nevermind finding enough suicidal people, would probably rule it out on practical grounds if not ethical grounds as well.

we could use the human mind to figure it out if we had enough people close together. each person could mentally hold a bit.

[S485122]

Originally Posted by MooMoo2

Suppose a magical wizard makes all man-made objects vanish
...
What’s left is 7.4 billion naked humans, standing on grassy plains, in forests, in swamps, on tundra, and in deserts in the exact spots where their cities and villages were just a second ago.
...
The wizard also leaves three things behind for every person:
1.) A reasonably healthy 1,000 calorie meal
2.) One litre of potable water
3.) A piece of paper with a note in their language that says, “I’ve cast a spell on all of humanity as an experiment. Here’s how it works: everything will remain as is until someone manages to discover a prime number larger than 2^74,207,281-1. To prevent random guesses, anyone who submits false claims will be tortured and then killed. Once that prime number is found, the spell will be reversed and all man-made objects you had in 2017 will reappear.
Read this carefully and enjoy your food and water, because those items will all disappear after an hour.”
...
Bonus question: How would this change if the wizard demanded a round-trip manned moon landing instead of a 22,338,618+ digit prime? Would the time be a lot shorter?

Originally Posted by Dubslow

...
And I highly doubt the majority of people would die....

Since nowadays the majority of humans live in big cities, that big cities are not viable without technology, I think at least half of the population would die very rapidly : just imagine the time it requires to disperse enough... Then most of the current crops and current flocks are not viable without technology. In cold places people would freeze to death before even starving to death.

Jacob

[Dubslow]

Originally Posted by S485122

Since nowadays the majority of humans live in big cities, that big cities are not viable without technology, I think at least half of the population would die very rapidly : just imagine the time it requires to disperse enough... Then most of the current crops and current flocks are not viable without technology. In cold places people would freeze to death before even starving to death.

Jacob

Mmm, excellent point. Much farmland (e.g. in the US) would need to be reclaimed by the wild before it could begin to support a non-technological human population again. Yes now I'm certain lots of people would die (though not from their own stupidity I don't think).