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Forum: Prime Gap Searches 2020-11-22, 20:06
Replies: 32
Views: 7,531
Posted By mart_r
Quite a difference, yes. The difference between...

Quite a difference, yes. The difference between my unconventional CSG and the formula with the initial prime p1 is even bigger than the one between my formula and the conventional which uses p2, and...
Forum: Prime Gap Searches 2020-11-21, 16:42
Replies: 32
Views: 7,531
Posted By mart_r
TWIMC

max. p searched:
q <= 1000: 1.748e+13
1000 < q <= 2690: 8.734e+12
2690 < q <= 1e+5: 1.435e+11
1e+5 < q <= 2e+5: 4.730e+10
2e+5 < q <= 5e+5: 3.205e+10
5e+5 < q <= 1e+6: 2.050e+10
1e+6 <...
Forum: Lounge 2020-11-21, 16:14
Replies: 1,068
Views: 67,648
Posted By mart_r
Mr Trump's behavior is absolutely unpresidented. ...

Mr Trump's behavior is absolutely unpresidented.

:leaving:
Forum: Miscellaneous Math 2020-11-19, 18:09
Replies: 10
Views: 395
Posted By mart_r
I have to say I'm quite astounded about how big...

I have to say I'm quite astounded about how big of a deal this discovery seems to be.
If I had done some of those calculations and found out how primes (in base 10) with the same end digits seemed...
Forum: Prime Gap Searches 2020-11-14, 12:14
Replies: 223
Views: 26,793
Posted By mart_r
Forum: Prime Gap Searches 2020-11-09, 20:41
Replies: 223
Views: 26,793
Posted By mart_r
:groan: I knew something was odd about this...

:groan:
I knew something was odd about this phrasing...

There's a larger variety in the size of the gaps.

Is that somewhat understandable an explanation?
Forum: Prime Gap Searches 2020-11-09, 14:20
Replies: 223
Views: 26,793
Posted By mart_r
Naturally, twin primes are rarer, so the gaps...

Naturally, twin primes are rarer, so the gaps between them are more numerous.

I was a bit lazy to finish my range, but new results should arrive this week.

Looking at arXiv: 1807.08777 (J. P....
Forum: Lounge 2020-11-01, 10:37
Replies: 447
Views: 19,400
Posted By mart_r
Hmm... I wanted to post a new number, but still...

Hmm... I wanted to post a new number, but still can't figure out Viliam Furik's number.
And I don't know much about graph theory either.
Forum: Prime Gap Searches 2020-10-29, 20:58
Replies: 113
Views: 13,406
Posted By mart_r
It was the scene where Goofy and Max were...

It was the scene where Goofy and Max were approaching the most important junction of their trip, and Goofy asked whether they go left or right, and Max took a long time until, at the last second, he...
Forum: Number Theory Discussion Group 2020-10-27, 18:17
Replies: 27
Views: 1,160
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: 1,160
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: 113
Views: 13,406
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: 1,160
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: 113
Views: 13,406
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: 1,160
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: 1,160
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: 305
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: 32
Views: 7,531
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: 113
Views: 13,406
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: 113
Views: 13,406
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: 113
Views: 13,406
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: 113
Views: 13,406
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: 197
Sticky: Prime Gap News
Views: 28,169
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: 197
Sticky: Prime Gap News
Views: 28,169
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: 113
Views: 13,406
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...
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