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 Showing results 1 to 25 of 593 Search took 0.14 seconds. Search: Posts Made By: mart_r
 2020-10-22, 19:22 Replies: 8 Views: 124 Posted By mart_r That's merely the fallacy by looking at small... That's merely the fallacy by looking at small numbers only. You probably have seen the calculations that the first example is expected in the vicinity of 101198. With current methods, there's really...
 Forum: Miscellaneous Math 2020-10-22, 08:35 Replies: 9 Views: 166 Posted By mart_r If you are amazed by this, you'd be completely... If you are amazed by this, you'd be completely flabbergasted by learning what is actually possible these days. ? p=1741;m=2^p-1;q=2*p+1;while(m%q,q+=2*p);print(q) 1002817 *** last result...
 Forum: Prime Gap Searches 2020-10-21, 21:03 Replies: 29 Views: 6,114 Posted By mart_r Hm, I should wait 18 more days for the next update here... but I won't Attached are the first occurence gap results for q<=1000 between p=1×1012 and 15×1012. See post # 16 dated 2020-05-09 for results up to 1×1012. As for the quest for exceptional gaps, I found one...
 Forum: Prime Gap Searches 2020-10-20, 16:58 Replies: 91 Views: 10,473 Posted By mart_r So hspace is causing the trouble. I figured it... So hspace is causing the trouble. I figured it was something like that, but it's hard to discern when the whole formula isn't displayed. And # or \# doesn't go with TEX, although the mimeTeX editor...
 Forum: Prime Gap Searches 2020-10-20, 15:04 Replies: 91 Views: 10,473 Posted By mart_r You're lucky that I don't post here every time I... You're lucky that I don't post here every time I have a new idea :smile: But the formula above really needs some tweaking. The impact on the output is a constant factor as I expected, but it's...
 Forum: Prime Gap Searches 2020-10-19, 16:36 Replies: 91 Views: 10,473 Posted By mart_r (Testing with [$]) [$]\sum^a_{b =... (Testing with [$]) [$]\sum^a_{b = 1}{\frac{\log^2(b \cdot p\#)}{b \cdot p\#}} \gtrsim \frac{\log^2(p\#)}{p\#} \sum^a_{b = 1}{\frac{1}{b}} \sim \frac{p^2}{p\#} \log a \sim \frac{p^3(\xi -...
 Forum: Prime Gap Searches 2020-10-19, 15:57 Replies: 91 Views: 10,473 Posted By mart_r Okay, next level. After some more reading and computations my next question is: can it be shown that Granville's modified intervals are not too sparse in a sense that Cramér \cap Borel-Cantelli can still be applied? ...
 Forum: Prime Gap Searches 2020-10-17, 13:26 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r If my quick-and-dirty analysis was somewhere near... If my quick-and-dirty analysis was somewhere near correct, there wasn't a single case for a gap not yet in the list where two different discoverers other than Patrick were listed. So for example...
 Forum: Prime Gap Searches 2020-10-15, 20:56 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r Like in the example in your last post, they... Like in the example in your last post, they should both be credited. So, looks good to me (that's what the acronym stands for, right?) Also, "maa" = maart = March, "mei" = May.
 Forum: Prime Gap Searches 2020-10-14, 13:23 Replies: 91 Views: 10,473 Posted By mart_r Hmm. Page 15 in... Hmm. Page 15 in https://arxiv.org/pdf/2002.02115.pdf talks about the n-th ﬁrst-occurrence gap between primes in progression, but I don't think that's quite useful w.r.t. this question. I'm sure some...
 Forum: Prime Gap Searches 2020-10-08, 20:21 Replies: 29 Views: 6,114 Posted By mart_r yummy... Status of my search (max. p searched): q <= 1000: 1.365e+13 1000 < q <= 2690: 6.635e+12 2690 < q <= 1e+5: 8.135e+10 1e+5 < q <= 2e+5: 4.730e+10 2e+5 < q <= 5e+5: 1.6e+10 5e+5 < q <=...
 Forum: Lounge 2020-10-01, 20:04 Replies: 441 Views: 17,448 Posted By mart_r Perfectly correct!:tu: Still don't have a... Perfectly correct!:tu: Still don't have a clue regarding 20287, I'm afraid. Maybe tomorrow I wake up shouting "Heureka!"...
 Forum: Lounge 2020-10-01, 18:14 Replies: 441 Views: 17,448 Posted By mart_r Well, it's about whole numbers, not constants in... Well, it's about whole numbers, not constants in particular... :davar55: It's not about something currently known, not specifically related to prime proving, but at least in general related to...
 Forum: Prime Gap Searches 2020-09-26, 20:14 Replies: 218 Views: 22,594 Posted By mart_r I suppose you mean the range between 1e16 and... I suppose you mean the range between 1e16 and 1.05e16 - I've changed those in the list in my previous post accordingly.
 Forum: Prime Gap Searches 2020-09-26, 19:33 Replies: 218 Views: 22,594 Posted By mart_r Results 11e15 The next missing gaps are 4427, 4436, 4489, 4509, 4556. (You won't find 4266, 4439, and 4532 in the attached list, but these have first occurence k between 11.1e15 and 11.2e15. Below 5000 there are...
 Forum: Lounge 2020-09-26, 18:16 Replies: 441 Views: 17,448 Posted By mart_r A fun thread which deserves reviving, methinks. ... A fun thread which deserves reviving, methinks. Here's a number that I hope will increase during the next few years: 1432
 Forum: Prime Gap Searches 2020-09-25, 12:45 Replies: 140 Views: 13,872 Posted By mart_r Bobby, please stop doing that. Anyway, while... Bobby, please stop doing that. Anyway, while we're at it... @ ATH: I'd still be interested to know a bit more about your calculation above 264 here:...
 Forum: Prime Gap Searches 2020-09-21, 15:06 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r I thought that one might want to have a quick... I thought that one might want to have a quick check which gaps need verification. I was also worried about the several megabytes those lists would take up. Giving only the list of numbers with...
 Forum: Prime Gap Searches 2020-09-20, 20:13 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r It's only a crummy sieve via Pari, about 20... It's only a crummy sieve via Pari, about 20 minutes to less than 1G, without keeping factors.:down: But I definitely keep it in mind should I ever aim for a 10M gap.
 Forum: Prime Gap Searches 2020-09-20, 14:34 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r Sounds okay to me. Is there an extra query... Sounds okay to me. Is there an extra query available for all the yet not fully verified gaps?
 Forum: Prime Gap Searches 2020-09-19, 12:05 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r Thanks! I'll be looking for smaller gaps for... Thanks! I'll be looking for smaller gaps for the rest of the year.:smile:
 Forum: Prime Gap Searches 2020-09-18, 18:22 Replies: 91 Views: 10,473 Posted By mart_r I guess I'm trying to argue that there may be... I guess I'm trying to argue that there may be only finitely many gaps of length > (log x)². So I thought there may be an error in my outlined reasoning (worth elaborating...?) that one of the...
 Forum: Prime Gap Searches 2020-09-18, 13:40 Replies: 91 Views: 10,473 Posted By mart_r I suppose my rambling theories are, as the saying... I suppose my rambling theories are, as the saying goes, "not even wrong". Right?
 Forum: Prime Gap Searches 2020-09-18, 11:25 Replies: 184 Sticky: Prime Gap News Views: 23,945 Posted By mart_r So now, as promised, some new large gaps, ready... So now, as promised, some new large gaps, ready for a doublecheck: 1363608 90547#/9699690-366998 900144 90583#/9699690-523646 971716 90647#/223092870-359938 1293962 90679#/223092870-873966...
 Forum: Prime Gap Searches 2020-09-14, 12:57 Replies: 91 Views: 10,473 Posted By mart_r Thanks, Dana. That's quite an interesting read... Thanks, Dana. That's quite an interesting read indeed. The behaviour of aM is only a prelude to a known line of probabilistic reasoning, isn't it? (1-\frac{1}{\log x})^{M(\log...
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