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If an alien were abducted by humans, and it memorized a much larger prime number, what would we give in exchange for that piece of information?
by yen223 11y ago
If an alien were abducted by humans, and it memorized a much larger prime number, what would we give in exchange for that piece of information?
- kazazes 11y agoApparently a $3,000 GIMPS research discovery award. What's the practical utility of knowledge of a prime, especially considering that upon announcement it's immediately disseminated?
- zitterbewegung 11y agoThe point of searching for these primes is to motivate research in finding primes so there isn't much practical utility.
- contravariant 11y agoIt's a very large prime number which has a very convenient representation, which makes it useful. You could use it in a Mersenne Twister RNG, for instance.
- scorpion032 11y agoSome Hacker News points, for sure!
- jacquesm 11y agoThe amount of CPU cycles burned to get this result surely translates into some dollar value. Everybody contributes to the MP for free but that doesn't mean there isn't any value involved. It's a donation of sorts.
- owenversteeg 11y agoInterestingly, if the alien's memorized number was significantly larger (e.x. tens of billions of digits) we would not be able to verify it. It took three and a half days to verify the correctness of M74207281 on two 18-core Xeon servers, and with speed increases in computing slowing down it may be a very long time before we are able to verify a number that large. So, nothing. The alien could say "Oh yeah, we have 2^34240923842043983204982-1" and they could be absolutely correct but there's nothing we could do to know. Or, if their number was big but not that big, it might be able to be verified in, say, a year, in which case it might win the EFF's prize and could possibly get some other sort of prize money. So, $150k + some undefined amount.
- fdej 11y ago2^34240923842043983204982-1 is divisible by 3.
- cdelsolar 11y agoHow'd you do that?
- dsr_ 11y agoWrite out the number in decimal, add the digits together: if the result is larger than a single digit, repeat. When you have a single digit, if it is 3, 6 or 9, the number is divisible by 3. The proof is left as an exercise for the student.
- nickodell 11y agoHow did you write out the number? It's 10307545155701210591839 digits long.
- morsch 11y agoI'll get back to you once I find a piece a paper large enough to write down the 10 sextillion decimal digits.
- LeifCarrotson 11y agoThat's the divisibility check for 3, yes, but I am pretty sure fdej didn't write that number out in decimal. The proof doesn't work with exponents. You'd have to represent the number in base 10 for digit summing to work. To check, 2^6-1=63 is divisible by three (it might work), but 2^9-1 has a sum of 12 and a value of 511, which is not divisible by three (it's 170 * 3 = 510 + 1).
- cousin_it 11y agoThe sequence 2^n mod 3 goes 2, 1, 2, 1, 2... That's how you solve all problems of this form. For any a and b, a^n mod b eventually becomes periodic as n grows. It's easy to prove because there's only a finite number of possible remainders mod b. As an exercise, calculate 3^1000000 mod 7.
- bcoates 11y agohttp://www.amazon.com/The-Peripheral-William-Gibson/dp/0399158448 http://www.amazon.com/The-Peripheral-William-Gibson/dp/03991...
- JoeAltmaier 11y agocorrection: some rational alien society