mersenneforum.org How long will it be until MM61 is within practical reach of PRP/primality testing?
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2020-01-29, 09:25   #12
xilman
Bamboozled!

May 2003
Down not across

3×17×193 Posts

Quote:
 Originally Posted by ewmayer 1/250,000th of a mole of liquid H, at a density of 1 g/cm^3, could fit in a sphere of radius r ~= 0.01cm = 10^-4m.
That is seriously condensed hydrogen. The density of regular liquid H2 is about a tenth of that, so the radius will be about twice as large. Your computation will take over a month.

Anyway, if you are hypothesizing computers on that scale you would probably be better off using not atomic but nuclear matter. Clock speeds would be thousands to millions of times faster.

2020-01-29, 19:41   #13
ewmayer
2ω=0

Sep 2002
República de California

101010101000102 Posts

Quote:
 Originally Posted by retina But how long is the FFT, and how many bits per point? What is the minimum FP precision needed? Those guys in 136 years will need to know!
"Will need to know" ... it's the job of those kinds of folks to figure it out. Also, you're thinking in IEEE-hardware terms, which is way, way too narrow. Consider:

o I used 1 bit per H atom in my estimate, but H is in fact likely bad because it wants to form molecules. So perhaps a noble-gas like He will prove more suitable. Also, cleverer people than us will likely figure out how to coherently store multiple bits per atom at some point. Sure, such heavier elements have larger atoms, but the atomic radius increases much more slowly than the atomic complexity, i.e. the potential bit-ness of the atoms;

o We've said nothing about taking advantage of quantum behavior, which is likely going to prove crucial to realizing such an atomic processor. Note that quantum entanglement doesn't allow us to make the processor arbitrarily fast - even "spooky action at distance" must obey the speed-of-light limit on net *information* transmittal, and a convolution is all about transmitting information about the state of each point - whether that be a point in spacetime or a data element in a discrete convolution - to all of the other points. But quantum effects might be used to manipulate such an atomic array in a coherent fashion so as to effect a desired computation. Bose-Einstein condensates have already proved very promising in this regard, no reason they couldn't move well beyond simple atomic clocks to more interesting behavior. And quite possibly by the point where humankind has developed the ability to coherentle manipulate the requisite number of quantum data elements, it'll be just as easy, or easier, to just completely factor MM61 than to perform a dinosaurian nonfactorial primality test, with its endlessly frustrating (in the case of compositeness, which is the overwhelmingly likely outcome for numbers the size of MM61) "I can tell you whether this number is prime or not, but I can tell you nothing about its prime factors except whether they be 1 or more than 1 in number" aspect.

We shall see - let's meet up here again in 136 years, ok?

Last fiddled with by ewmayer on 2020-01-29 at 19:47

2020-01-29, 19:55   #14
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

22×1,327 Posts

Quote:
 Originally Posted by ewmayer "Will need to know" ... it's the job of those kinds of folks to figure it out. Also, you're thinking in IEEE-hardware terms, which is way, way too narrow. Consider:
I'm not clear on what you are suggesting as an alternative. Shor? Grover?
Quote:
 Originally Posted by ewmayer We shall see - let's meet up here again in 136 years, ok?
I've marked the date in my calendar. Don't be late.

2020-01-29, 20:35   #15
xilman
Bamboozled!

May 2003
Down not across

231638 Posts

Quote:
 Originally Posted by ewmayer So perhaps a noble-gas like He will prove more suitable.
I refer the right honourable gentleman to the answer I gave a moment ago
Quote:
 Originally Posted by ewmayer Also, cleverer people than us will likely figure out how to coherently store multiple bits per atom at some point.
Similarly, I have already explained how it is possible, in principle, to store an arbitrarily large number of bits in a single hydrogen atom. For those here with a limited attention span, remember that the principal quantum number in a Rydberg atom is an unbounded integer.

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