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 2017-12-11, 15:21 #19 Dr Sardonicus     Feb 2017 Nowhere 5·691 Posts 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.