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Forum: Number Theory Discussion Group 2020-10-27, 18:17
Replies: 27
Views: 773
Posted By mart_r
Correct - when the numbers have 1200 digits, on...

Correct - when the numbers have 1200 digits, on average about 1 in every 2762 numbers is a prime. This does not contradict the assumption that dense clusters of 447 primes of this size do exist....
Forum: Number Theory Discussion Group 2020-10-23, 18:38
Replies: 27
Views: 773
Posted By mart_r
Then, I'm afraid, the odds that anyone can help...

Then, I'm afraid, the odds that anyone can help you understand are about as good as the odds of finding an actual prime-447-tuplet.

Edit, FWIW:
If the first Hardy-Littlewood conjecture was wrong,...
Forum: Prime Gap Searches 2020-10-23, 18:24
Replies: 97
Views: 10,963
Posted By mart_r
I'm aware of Maier's paper, and I understand it...

I'm aware of Maier's paper, and I understand it for the most part (though I have to examine his 1981 paper again...). The main result is, with respect to the problem of gaps >= log2p, that there are...
Forum: Number Theory Discussion Group 2020-10-23, 16:12
Replies: 27
Views: 773
Posted By mart_r
Just because I can... Take, for instance, ...

Just because I can...

Take, for instance,
n = 1566280308578217520031412816790827048467516641360946961779273951
and set p = 163#, or in full,
p =...
Forum: Prime Gap Searches 2020-10-23, 14:23
Replies: 97
Views: 10,963
Posted By mart_r
Sticking with Borel-Cantelli, the same lemma that...

Sticking with Borel-Cantelli, the same lemma that proves (?) the existence of gaps > log2p in [$]\mathcal{R}[/$], could be used against conjecture 1.2 in 1908.08613 in the sense that the probability...
Forum: Number Theory Discussion Group 2020-10-23, 11:16
Replies: 27
Views: 773
Posted By mart_r
:lol: It's like you can read my mind, I have a...

:lol: It's like you can read my mind, I have a printout of that paper (actually one of the first math papers I have made a printout of) and wanted to look into it today to recap on logarithmic...
Forum: Number Theory Discussion Group 2020-10-22, 19:22
Replies: 27
Views: 773
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: ONeil 2020-10-22, 08:35
Replies: 9
Views: 209
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: 6,311
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: 97
Views: 10,963
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: 97
Views: 10,963
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: 97
Views: 10,963
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: 97
Views: 10,963
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: 187
Sticky: Prime Gap News
Views: 24,680
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: 187
Sticky: Prime Gap News
Views: 24,680
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: 97
Views: 10,963
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: 6,311
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: 17,626
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: 17,626
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: 23,029
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: 23,029
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: 17,626
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: 14,115
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: 187
Sticky: Prime Gap News
Views: 24,680
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: 187
Sticky: Prime Gap News
Views: 24,680
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.
Showing results 1 to 25 of 599

 
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