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Forum: Prime Gap Searches 2020-10-20, 16:58
Replies: 91
Views: 10,325
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: 10,325
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: 10,325
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: 10,325
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: 23,737
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: 23,737
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: 10,325
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: 28
Views: 6,037
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: 17,419
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: 17,419
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: 22,488
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: 22,488
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: 17,419
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: 13,807
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: 23,737
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: 23,737
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: 23,737
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: 23,737
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: 10,325
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: 10,325
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: 23,737
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: 10,325
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...
Forum: Prime Gap Searches 2020-09-13, 09:26
Replies: 218
Views: 22,488
Posted By mart_r
4239 has fallen. Twice. Reserving 1.1e16 to...

4239 has fallen. Twice.

Reserving 1.1e16 to 1.15e16.
Forum: Prime Gap Searches 2020-09-12, 08:56
Replies: 184
Sticky: Prime Gap News
Views: 23,737
Posted By mart_r
Can I submit megagaps with primes in the 39000+...

Can I submit megagaps with primes in the 39000+ digits range via the cloudygo window or is it advisable to rather post them here?
Forum: Prime Gap Searches 2020-09-08, 15:57
Replies: 28
Views: 6,037
Posted By mart_r
number crunching and munching...

The computation has now reached 1013 for all q<=1000.

Summary for the 13-digit range of p:
No new record CSG was found between p=1012 and 1013.
The largest CSG in that range was 0.9687994043 for...
Showing results 1 to 25 of 590

 
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