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Old 2018-07-20, 09:14   #23
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Quote:
Originally Posted by ATH View Post
It does not *need* 120GB, because I did a few curves a while back and I only have 32 GB RAM. It took ~95 hours with all 8 cores on Haswell-E assigned to it, but I am not sure how much effect many cores have on ECM tests.
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I am using a single core, and stage 2 takes about 40 hours and uses 95% of the memory. No doubt it could use less memory at the expense of taking extra time. Stage 1 takes about five days.
I misspoke when I said one week. I actually timed it instead of estimating, and using one core of an r4.4xlarge instance (with the other 7 cores doing ECM on small Mersenne exponents), it takes about 78 hours to do stage 1 and 40 hours to do stage 2, so just under 5 days to do a single curve for F29 (exponent = 536,870,912).

So 118 hours on a single core (Haswell 2.3 GHz) using 120 GB of memory actually compares pretty favorably to your 95 hours on eight cores using 32 GB. Either using many cores doesn't provide much benefit, or using less memory imposes a considerable cost, or both.

By the way Amazon has just announced the r5 instance type will be coming soon, which should also help. For comparison, the transition from c4 to c5 instance types produced about a 20 to 25% speedup for LL testing.
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Old 2018-07-20, 18:56   #24
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Found one 10p+12243 for which 32 Mersenne prime exponents p also is prime, and the last 11 Mersenne prime exponents also have 1843p+221460 as prime.

Code:
32:
10p+12243:  2 13 17 19 31 61 107 127 607 1279 2203 2281 4253 4423 9689 9941 21701 23209 44497 86243 110503 132049 216091 1257787 1398269 6972593 13466917 20996011 30402457 37156667 43112609 77232917

11:
1843p+221460:  77232917 74207281 57885161 43112609 42643801 37156667 32582657 30402457 25964951 24036583 20996011
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Old 2018-07-22, 02:41   #25
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Quote:
Originally Posted by ATH View Post
It does not *need* 120GB, because I did a few curves a while back and I only have 32 GB RAM. It took ~95 hours with all 8 cores on Haswell-E assigned to it, but I am not sure how much effect many cores have on ECM tests.
Quote:
Originally Posted by GP2 View Post
So 118 hours on a single core (Haswell 2.3 GHz) using 120 GB of memory actually compares pretty favorably to your 95 hours on eight cores using 32 GB. Either using many cores doesn't provide much benefit, or using less memory imposes a considerable cost, or both.
Hmmm... if F29 has really been tested up to k = 1017 along with all the other big Fermat exponents, then 1017 Γ— 229+2 = a bit more than 1026.3. So there's not much point in testing F29 with bounds of B1=50,000 and B2=100 Γ— B1 because that only takes you to the t25 level, which has already largely been covered.

So we'd really need to do B1 = 250,000 instead, to get to the t30 level. But then each curve takes a lot longer and there's a lot more of them. Might need to rethink the wisdom of working on F29, and maybe think about finding a first factor for F20 or F24 instead.

For the curves you did with a 95 hour timing, was that using B1 = 50k or B1 = 250k ?
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Old 2018-07-22, 10:23   #26
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Quote:
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For the curves you did with a 95 hour timing, was that using B1 = 50k or B1 = 250k ?
B1=50K but I'm not 100% sure I used all 8 cores. I can test again sometimes.
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Old 2018-07-22, 14:25   #27
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Quote:
Originally Posted by a1call View Post
https://en.m.wikipedia.org/wiki/Fermat_number

How is that not meaningless, given that there are infinite number of Fermat numbers?
Thank you in advance.
There are only a finite number of even primes, even though there are an infinite number of even numbers.

Do not make the mistake of assuming that because a set of numbers is infinite a particular subset must itself be infinite.
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Old 2018-07-22, 18:37   #28
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Looks to me like another nonsense sworn to by folks just because it is referenced in Wikipedia.
I don't think there is any other case of claim of a probability of success, greater than 0 and less than 1 in infinite trials. I don't think such a notion makes any mathematical sense.
Any probability greater than 0 (no matter how small) will have a probability of 1 in infinite trials.
Unless the probability of existence of a new Fermat primes is (absolutely) equal to 0, then there is definitely another Fermat prime out there in the infinitum.

Last fiddled with by a1call on 2018-07-22 at 18:56
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Old 2018-07-22, 19:52   #29
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I raised a similar question in part number 6 here:
http://www.mersenneforum.org/showthr...t=22586&page=2
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Old 2018-07-22, 20:00   #30
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Quote:
Originally Posted by a1call View Post
Any probability greater than 0 (no matter how small) will have a probability of 1 in infinite trials.
Unless the probability of existence of a new Fermat primes is (absolutely) equal to 0, then there is definitely another Fermat prime out there in the infinitum.
You fail at infinite sums. There are plenty of infinite series that converge to values smaller than 1, even though no individual term is zero. Consider 1 over (100^n) starting at n=1; each term is nonzero, but the sum of the terms is barely over 0.01. Now, consider what the sum is if we start at n=6, or n=29.
These sums do not even use calculus; search "geometric series" for summation formulae.
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Old 2018-07-22, 20:05   #31
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Quote:
Originally Posted by a1call View Post
Looks to me like another nonsense sworn to by folks just because it is referenced in Wikipedia.
You may be correct. I very much doubt it.

There are respected mathematicians who have extremely good reasons for believing that the number of Fermat primes is finite. Those reasons are entirely independent of whether or not they are referenced in Wikipedia. I suggest that you investigate the mathematics in detail and see whether you still hold to your opinion afterwards.

Another example: there are an infinite number of terms in the sum 1+1/2+1/4+1/8+ ... 1/(2^n} + ... so the sum must be infinite by your argument, right? In fact the sum never gets larger than 2 no matter how many terms you take.

While you're investigating, check out "Zeno's paradoxes".
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Old 2018-07-22, 20:19   #32
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Don't know how did this post get duplicated.
Apologies.

Last fiddled with by a1call on 2018-07-22 at 20:22
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Old 2018-07-22, 20:21   #33
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I am well aware of converging sums of some infinite series.
But that is not the discussion here. What's discussed here is probability of existence of a Fermat prime in infinitum given that the probability of existence of a Fermat prime in a given range decreases very quickly as the range goes higher, but it is always greater than 0 for any given range. I think it is common mathematical sense that as long the probability is greater than 0 in any given range then the probability is 1 in infinitum.
But I'm done repeating myself and partaking in circular discussions..
Just my 2 cents. Feel free to believe as you wish.

Last fiddled with by a1call on 2018-07-22 at 20:24
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