20151117, 16:23  #1  
Aug 2006
5,987 Posts 
Betting on Mersennes  update #1
Five years ago I bet axn 25¢ that GIMPS wouldn't discover 8 Mersenne primes by Jan 1 2030. In that time we've discovered one new prime and moved the wavefront from 31M to 58M.
Following a simple exponential model, this suggests we'd hit the original expectation of 675M in mid2034 (with the implicit Moore doubling every ~27 months). But having only found one prime so far, the expectation is now 884M. Of course 2030 is still far off, and many technologies will be discovered between now and then. Quantum computation would be particularly disruptive: with Beauregard's circuit for Shor's algorithm, 'only' 1.8 billion qubits would be needed to factor all the Mersenne candidates up to the above bound, leaving (whp) just the primes for MM to verify. But I don't expect quantum computing to be practical by 2030  I'd be thrilled with ten thousand reliable, nondecohering qubits. Quote:
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20151118, 03:17  #2 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×3×5×337 Posts 
Ha! This does not consider new theoretical developments, like "LaurV found a new algorithm for squaring and found the next 10 mersenne primes over night". Or, why bother with squaring, say "LaurV found a heuristic to pick the exponents that lead to mersenne primes, directly"
(or "LaurV found that the number of mersenne primes is bounded and we already found all of them, and we are wasting the time here in vain" ) 
20151118, 03:56  #3 
Jun 2003
1010100011100_{2} Posts 
So far, CRG appears to be "winning". The DP performance from GPUs have stagnated or even regressed, especially from the NVidia camp. This doesn't appear to be a technological issue, so much as a market segmentation issue  NVidia appears to be protecting its scientific computing market by gutting the consumer GPUs.
Something like a Titan coupled with HBM should be a killer LL GPU, but it doesn't look like anything like that will happen soon. HBM is going to eventually come to NVidia camp as well, but the DP story might not change. Perhaps we should look at some NTTbased software for LL. Recently, there has been some significant development in the Generalized Fermat testing with this approach. All in all, I'm still waiting for that gamechanging technology to emerge 
20151118, 05:06  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,313 Posts 
If I were you, I would double down!

20151118, 17:08  #5 
Aug 2006
1763_{16} Posts 
This is a bet I would be very happy to lose! Practical quantum computers, gamechanging technology, muchimproved algorithms, etc.  I'd love to see it.

20151120, 23:42  #6  
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
Quote:
My point is that an industry doubling in "awesomeness" every 23 years, or even 510 years, is unheard of outside of electronics. Assuming I'm correct about the 23% improvement with most industries, and also assuming the electronics industry went through 25~ doublings since the transistor was invented, I wonder what we get if we solve the equation 1.03^x=2^25(33.5m~)? Assuming I didn't flub the math, if the computing industry behaved like other industries, than the improvement over the past 50 years would've been about 1216% We truly live in fantastic times. Edit:I'd forgotten about the genetics industry, although a lot of that simply involves automated processing, so it's at least loosely connected to the computing industry. Last fiddled with by jasong on 20151120 at 23:43 

20160330, 20:48  #7 
Aug 2006
5,987 Posts 
At the time of the original bet 47 Mersenne primes were known; the bet asks if 55 will be known by the start of 2030.
The retroactive discovery (two months before this thread) of 2^{74,207,281}1 does tip the scales, so I thought I'd recalculate. Only six more Mersenne primes are needed, though four months have passed and the wavefront has pushed forward. With it currently at 63,350,927, the expected search depth needed for the next 6 Mersenne primes is 654,409,841 which means that \[k=\frac{\sum_{p\le654409841}p^2\log p\log\log p}{\sum_{p\le63350927}p^2\log p\log\log p} \approx 1300\] times the current effort should be needed to finish. This corresponds to a Moore doubling every 16 months, if I've computed correctly: implicitly define x by \[\int_{2010}^{2030}x^tdt=k\int_{2010}^{2016.25}x^tdt\] then computer speed needs to double every \[\frac{12\log2}{\log x}\approx16\] months. 
20160330, 21:23  #8  
"Forget I exist"
Jul 2009
Dumbassville
10000011010000_{2} Posts 
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20160331, 13:37  #9  
Aug 2006
5,987 Posts 
Quote:


20160331, 13:41  #10 
"Forget I exist"
Jul 2009
Dumbassville
2^{4}×3×5^{2}×7 Posts 

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