20180720, 09:14  #23  
Sep 2003
2^{2}×3×5×43 Posts 
Quote:
Quote:
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. 

20180720, 18:56  #24 
Einyen
Dec 2003
Denmark
2^{7}·23 Posts 
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 
20180722, 02:41  #25  
Sep 2003
2^{2}·3·5·43 Posts 
Quote:
Quote:
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 ? 

20180722, 10:23  #26 
Einyen
Dec 2003
Denmark
2^{7}·23 Posts 

20180722, 14:25  #27  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10265_{10} Posts 
Quote:
Do not make the mistake of assuming that because a set of numbers is infinite a particular subset must itself be infinite. 

20180722, 18:37  #28 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·13·73 Posts 
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 20180722 at 18:56 
20180722, 19:52  #29 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11101101010_{2} Posts 
I raised a similar question in part number 6 here:
http://www.mersenneforum.org/showthr...t=22586&page=2 
20180722, 20:00  #30  
"Curtis"
Feb 2005
Riverside, CA
1000011100101_{2} Posts 
Quote:
These sums do not even use calculus; search "geometric series" for summation formulae. 

20180722, 20:05  #31  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
5×2,053 Posts 
Quote:
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". 

20180722, 20:19  #32 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·13·73 Posts 
Don't know how did this post get duplicated.
Apologies. Last fiddled with by a1call on 20180722 at 20:22 
20180722, 20:21  #33 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·13·73 Posts 
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 20180722 at 20:24 
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