Prime number thought experiment

[science_man_88]

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

depends on if they walk or run and how much of a radius they can search to find food is related to that.

[Mini-Geek]

I think billions would die off in the first weeks and months, as people live either in inhospitable places, or otherwise-decent places that just can't support the large populations without shipping food in. (even assuming people aren't terribly ignorant about how to survive off the land...which they probably are)

Guessing would be the quickest way to resolve the situation. If people could make educated guesses, it may only take a few hundred thousand people. If not, it could easily be 50 million guesses to get it right. Given the lack of good communication and general mathematical ignorance of the population, people will likely not make great guesses, on the whole. But if people who are going to die anyway guess for the good of everyone else, our society could easily be restored within a short time (the mass dieoffs could work in our collective favor, if people put aside their aversion to torture).

A trip to the moon could not be faked/guessed at in the same way the prime number could, so it would definitely take some time. But I think that if we go the slow route of rebuilding society, the moon trip would be easier than the prime number. After all, in real life, we made a moon trip decades before discovering a prime of that size (with large amounts of money/effort driving both the Apollo missions and the progress of computing power), and I have a feeling that the knowledge we've gained there is significantly more transferable than the knowledge about our nano-scale computing power.

[GP2]

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).

[...]

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.

You badly underestimate the role of modern technology in keeping our current very large population alive.

Our distant ancestors had some rather sophisticated technology. But their population was maybe one-thousandth of what it is today. Even with all their knowledge and all their tools, that's all the land could support.

And remember, the terms of this thought experiment are that all man-made object disappear, every single one, even the most primitive. That is pre- Stone Age. Even with perfect knowledge of how to proceed, there simply wouldn't be enough time to bootstrap everything. You'd have to start making stone tools from scratch, and meanwhile everyone is starving.

The only possible choice is axn's option 3. Perhaps some place like North Korea would implement forced random guessing and save the world.

Otherwise we're back in the world of half a million years ago with a tiny remnant population, dividing into many different tribes whose languages will soon diverge. Knowledge will be reduced to a useless, badly garbled oral tradition by a multi-generational game of "telephone".

Assuming our very distant descendants a few hundred thousand years in the future somehow manage to create a modern industrial civilization, which will be problematic because all the easily accessible ores and petroleum and coal have already been used up by us, then the sudden appearance of billions of strange artifacts will take them completely by surprise.

[M344587487]

Originally Posted by axn

...
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].
...

This is the best course of action, the problem is being able to coordinate the effort without communication technology. Establishing adequate comms cannot be done immediately, so everyone is forced to focus on their immediate concerns, primarily food, water, shelter. As a result, the global population falls to 2 billion or less very quickly, maybe much less. Assuming everyone on the way out fails to luck out with their uncoordinated dying guess, it will take years at least to set up a partial global network with everyone communicating to their nearest neighbouring communities, longer depending on how thorough societal breakdown has become.

Regardless of whether it's been years or decades from the day of the wizard, eventually society is rebuilt. There are minor wars between neighbours for resources, but on the whole everyone is united against the wizard. We're now in a position where we can systematically guess our way back into getting modern day tech back. At which point population levels would be at a much more sustainable level, and society would have changed to not be as heavily reliant on tech. Society would self regulate to ensure population levels remain manageable with minimal tech requirements, and that tech is used as a tool not a way of life. After a few hundred years some people would even thank the wizard. After a few thousand years we are well into exploring the galaxy. Some people happen upon a senile old man in a rough shack on some backwater moon, babbling about how long it took to hand-write all those notes.

[R. Gerbicz]

Originally Posted by axn

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].

You would kill too many people. Better:
sieve (say) the next one billion integer after M74207281 and submit the survivors one by one.
With this you could reach roughly the same effective sieve depth as for Mersenne numbers,
but you will have not decreasing chance what would you get when you submit Mp for larger and larger p values.

Or maybe even better: sieve on (say) x^1024+1 numbers, these has got prime divisors of p=2 or p=2048*k+1, and you can sieve it more efficiently.

[axn]

Originally Posted by M344587487

This is the best course of action, the problem is being able to coordinate the effort without communication technology.

https://en.wikipedia.org/wiki/List_o..._by_population
https://en.wikipedia.org/wiki/List_o...lation_density

Just sayin'.

But you're right. Initial reaction will be panic and the mad dash to just survive. Hmmm... maybe there is use for that 1000 calorie food/water after all.
Without even basic things like paper/pencil, large scale communication/coordination would be tedious if not impossible. But best bet is a single city stepping up (but of course, without coordination, there will be multiple cities doing it independently). Physical proximity makes things easier. With the assistance of a few universities of mathematicians and students, this could be pulled off.

[bsquared]

All of the guessing strategies mentioned so far assume that when the wizard said "discover" he didn't mean "prove". Guessing random prime exponents will eventually "find" a prime number, but that fact will be unknown to the guesser. If the wizard demands proof then we are back to mass starvation, rebuilding society, etc.

[Dr Sardonicus]

Let's see. 7.4 billion naked humans. No modern agriculture. No ships, planes, or trucks to distribute food. No roads. No plumbing. No sanitary sewers. No metal tools.

My guess is, nearly the entire human population would die of thirst or waterborne disease within days, or starve to death within weeks. I suppose the corpses would serve as a food supply for a short time, but it would quickly become unusable. As one of the characters in Cyril Kornbluth's The Marching Morons pointed out, "Five billion corpses means five hundred million tons of rotting flesh." Surviving remnant populations would scour the surrounding areas for food and lay them waste.

In short, the prospect of being tortured and killed might not be much of a deterrent to making random guesses. But I have to make an assumption not stated in the OP's scenario: The "magical wizard" is actually able to determine whether a proffered candidate is actually prime, and, if it is, reverse the spell -- whether the claimant has a proof of primality or not. If a proof is required, I'd say humanity is toast.

Under this assumption, the solution is simple: Compute the primes p after 74207281 in succession, and, for each p, have a volunteer claim that 2^p - 1 is prime. The computations would have to be done with the most rudimentary of aids, and new primes p found continuously, but it seems a possible task. Even if ten million p's are required before 2^p - 1 is a prime, humanity is saved.

The willingness of people to endure torment -- especially for the sake of their families -- is something to wonder at.

One case that illustrates the point comes from the Salem witchcraft trials.

Under the legal system in force at the time, unlike today, an accused person could not be tried on a criminal charge until they entered a plea -- either Innocent (Not Guilty) or Guilty -- to the charge laid against them. Failure to enter a plea was -- and still is -- called "standing mute." Nowadays, when the accused stands mute in the good ol' USA, the Court simply enters a default plea of "Not Guilty" and the case proceeds. But back then, it was deemed essential that the accused formally recognize the state's authority to try them by entering a plea.

Defendants who stood mute, and thus refused to recognize the Court's authority, were quite literally pressed to answer the charge. They were subjected to the Peine fort et dure ("strong and hard punishment"). They would be laid out horizontally on the ground, sometimes with a board placed over their body, and stones gradually piled on, while court officials implored the accused to enter a plea. The weight was gradually increased until one of two things happened. The accused would either succumb to the pain and enter a plea, or would be crushed to death.

During the Salem witchcraft trials, this is what happened to Giles Corey, an 80-year-old man accused of witchcraft. He stood mute and, while enduring the agony of being pressed to death, said only "More weight." He was crushed to death without entering a plea.

The reason he was willing to endure so much agony was, at the end of it, he died without being convicted of witchcraft, as he surely would have been had he been tried. And if he had been convicted, then because witchcraft was a serious felony, part of the penalty was "forfeiture," or "corruption of blood," meaning his will would have been invalidated, his substantial assets confiscated by the state, and family would have been left destitute. But because he was never tried for witchcraft, he was never convicted of a felony, so his will remained valid and his family was provided for.

[The Carnivore]

The guessing strategy might not work. Without any way to coordinate the guesses, the people in North America may be guessing the same exact, wrong, exponents as the people in Europe and Asia. And out of those suicidal folks, most would take the easy way out (like throwing themselves off a cliff) instead of being subject to the wizard's torture before dying.

I doubt more than a billion would be alive after two months. At this time of the year, there might even be more deaths from hypothermia than from starvation.

With that said, I'm guessing 300 years for both the prime and the Moon landing. By that time, memory of 2017 will have faded considerably, and there'll be some debate about whether a return to 2017 conditions is even desirable after all.

[xilman]

Originally Posted by The Carnivore

With that said, I'm guessing 300 years for both the prime and the Moon landing. By that time, memory of 2017 will have faded considerably, and there'll be some debate about whether a return to 2017 conditions is even desirable after all.

How do you propose keeping any useful information about moderately high technology (how to build a blast furnace, for example, available for even fifty years?

More immediately, how do you build a plough or a stirrup without even stone tools, glue and string?

[R. Gerbicz]

Originally Posted by The Carnivore

The guessing strategy might not work. Without any way to coordinate the guesses, the people in North America may be guessing the same exact, wrong, exponents as the people in Europe and Asia. And out of those suicidal folks, most would take the easy way out (like throwing themselves off a cliff) instead of being subject to the wizard's torture before dying.

I doubt more than a billion would be alive after two months.

Yes, without any Math knowledge it is impossible to solve the following modified puzzle:

1. you can guess only Mersenne numbers
2. the wizard's task to check the primality of the submitted numbers
3. you can agree on any strategy, but after that (on the 1st day and later) no coordination is allowed
4. everybody is enough intelligent, so they can observe when the man-made objects are reappearing, so they can notice when somebody submitted a Mersenne prime

ps. the goal is to minimize the number of deaths.