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> ...this record, which stood for 75 years, MAY stand > forever as the largest prime found by hand calculations. I shudder to imagine the holocaust which wou
by Estragon 15y ago
> ...this record, which stood for 75 years, MAY stand
> forever as the largest prime found by hand calculations.
I shudder to imagine the holocaust which would have to happen before this record could be broken. Though I suppose we may find an alien species who might have found a larger prime "by hand."
- rwmj 15y agoIt could happen (without catastrophe/aliens) if: (a) someone discovered a pattern like the Mersenne numbers which unreliably produces primes that are much larger than Mersenne numbers, and (b) someone discovers, by hand, a proof that one of these new numbers is prime. Such a discovery would be wonderful: new mathematics that could give us insight into what primes really are. https://en.wikipedia.org/wiki/Double_Mersenne_number https://en.wikipedia.org/wiki/Double_Mersenne_number might be one place to start.
- pestaa 15y agoI'd like to understand why primes are believed to be really something, can you please elaborate?
- Estragon 15y agoFor instance, they are points in the geometric object known as the scheme over the integers.[1] The Riemann Zeta function of the Riemann Hypothesis generalizes to other schemes, and reflects their geometric properties (being vague because it's over a decade since I studied this stuff.) It is just barely in the realms of possibility that a new computationally simple way of finding large primes would also reflect something about the geometric structure of schemes over Z. (But it seems pretty damn unlikely to me.) [1] http://en.wikipedia.org/wiki/Scheme_(mathematics)#Modern_definitions_of_the_objects_of_algebraic_geometry http://en.wikipedia.org/wiki/Scheme_(mathematics)#Modern_def...
- eru 15y agoSorry, could you please clarify your question?
- pestaa 15y agoI didn't know why primes are considered special, apart from the basic requirement they fulfill. GP sounded like they might serve a bigger unknown purpose.
- eru 15y agoA study of number theory will enlighten you. By the way, 2 is most special prime. Lots of nice theorems about prime numbers have special cases for 2.