4 ms·
As someone who knows nothing about advanced mathematics, could someone explain why this matters? (i.e. beyond that this is rare and theoretically interesting)
by ambivalents 9y ago
As someone who knows nothing about advanced mathematics, could someone explain why this matters? (i.e. beyond that this is rare and theoretically interesting)
- cortesoft 9y agoThe link has another link to a page describing why this matters: http://primes.utm.edu/notes/faq/why.html http://primes.utm.edu/notes/faq/why.html
- biot 9y ago> Mersennes are beautiful and have some surprising applications. Unfortunately that page doesn’t elaborate on what these surprising applications are, which is itself surprising on a page that purports to answer “why”.
- schoen 9y agoIt automatically results in the discovery of a new perfect number. :-) https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem (combining two of history's greatest mathematicians with names that have confused generations of students by being pronounced very differently)
- Cyph0n 9y agoEuler and Gauss are (for now, at least) in my opinion the greatest mathematicians of the past two millenia (1000-1999, 2000-). Al-Khawarizmi takes the cake for the millennium before that. Then it's Euclid all the way back ;)
- jacobolus 9y agoWe know almost nothing about Euclid: we can figure out when he was active to within a century or two, and according to Pappus writing 500 years later some of his students/followers lived in Alexandria where Apollonius studied with them. That’s pretty much it for biographical details. The earliest remaining editions of the Elements have no author mentioned, and our source that Euclid compiled it is a brief remark from Proclus 700 years later. Most of what is in the Elements was results from earlier, and it’s all but impossible to break down which bits were first done when or by whom. Most of what we can see today of the Elements or Euclid’s other books is later copies, much of it probably added/changed/reordered/... later. If you want a 2000-year-old idol, go for Archimedes. In the last 1000 years, the most influential mathematician is surely Newton, with an honorable mention for Leibniz. For the computer age (from 1950 through the upcoming few centuries), I’d put my vote on Grassmann (1809–1877), though his work was long ahead of its time and still substantially underappreciated. Euler and Gauss were of course both brilliant and prolific and well worth studying, along with Descartes, Lagrange, Riemann, Poincaré, ....
- thomasahle 9y agoOne application is that it's fairly cheap to take `n mod p` when `p` is on the form $2^q-1$. In particular x ≡ x mod 2^q + ⌊x/2^q⌋ (mod p). If you are making a hash function, and need to take mod a prime, this is useful. Another application of slightly larger Mersennes is https://en.wikipedia.org/wiki/Mersenne_Twister https://en.wikipedia.org/wiki/Mersenne_Twister
- kristianp 9y agoI imagine these record-breaking primes are too large to be useful in a hash function though.
- thomasahle 9y agoCertainly. These are just for fun, or maybe in the future giving some motivation for some number theory conjectures. Who knows.
- loeg 9y agoThose reasons boil down to people liking novelty. Finding new primes is just one particularly nerdy form of that.
- madez 9y agoThese numbers are for as far as we know irrelevant for mathematics.
- loeg 9y agoIt doesn't, really. It's just a novel prime that happens to be a Mersenne number (2^n - 1).