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Forum: Prime Gap Searches 2022-01-17, 21:19
Replies: 32
Views: 2,546
Posted By mart_r
Any chance you can still tweak the algorithm a...

Any chance you can still tweak the algorithm a bit in your favor?


Some possibly useful ideas, theory-wise:

Let [$]p_n[/$] be large (well, say, > 106), let [$]p_{n+k}[/$] be the k-th prime...
Forum: Prime Gap Searches 2022-01-14, 21:25
Replies: 32
Views: 2,546
Posted By mart_r
It took me a couple of days, so I do think you...

It took me a couple of days, so I do think you have a chance to beat me at my own game :smile:
I was also trying to squeeze even more primes into an interval of 8348, about two years ago, but a...
Forum: Prime Gap Searches 2022-01-11, 22:52
Replies: 32
Views: 2,546
Posted By mart_r
I get the same CRT offset with the pattern you...

I get the same CRT offset with the pattern you linked to, so that's correct.
For my result, I didn't bother too much about sieving and just tested n*p#+c+x for primes, incrementing n when not enough...
Forum: Prime Gap Searches 2022-01-10, 21:40
Replies: 32
Views: 2,546
Posted By mart_r
Thanks for your support! Your results for...

Thanks for your support!

Your results for maximum average merits are in accordance with my results in post # 12.

I didn't look for minimum average merits as they are theoretically covered by...
Forum: Prime Gap Searches 2022-01-09, 20:37
Replies: 32
Views: 2,546
Posted By mart_r
Building mountains out of molehills, I guess...

Building mountains out of molehills, I guess :smile:
I thought Robert was making fun of me ... one word responses can be confusing, maybe it was a misunderstanding on my part. Those language...
Forum: Prime Gap Searches 2022-01-09, 20:12
Replies: 17
Views: 1,062
Posted By mart_r
Sorry, hadn't taken Wilson's Theorem into...

Sorry, hadn't taken Wilson's Theorem into account.:blush:



That one also comes close, with 20 primes just inside the "century":
622803914376064301858782434517 + [0, 4, 6, 10, 12, 16, 24, 30,...
Forum: Prime Gap Searches 2022-01-09, 14:40
Replies: 17
Views: 1,062
Posted By mart_r
No cycles involved (well, not recently), I've...

No cycles involved (well, not recently), I've known that first century without primes by heart for more than 20 years now:smile:
Actually, if you weren't sure whether 100!+/-1 were prime or not,...
Forum: Prime Gap Searches 2022-01-05, 18:41
Replies: 17
Views: 1,062
Posted By mart_r
Excellent work! Thanks:thumbs-up: That brings...

Excellent work! Thanks:thumbs-up:
That brings the list I started back in around 2006 to completion :smile:
Forum: Prime Gap Searches 2022-01-04, 20:02
Replies: 17
Views: 1,062
Posted By mart_r
If that's what you like

Who doesn't?:razz:
(20:40) gp > primepi(1671900)-primepi(1671800)
%1 = 0
While we're at it, what about primes in millennia?
10+ years ago I crunched some numbers, but the calculation is on hiatus...
Forum: Prime Gap Searches 2022-01-03, 20:42
Replies: 32
Views: 2,546
Posted By mart_r
Staking claims

A measurably unusual scarcity of primes appears between 6,215,409,275,042 and 6,215,409,279,556 - there are only 83 primes in-between, just a little over half as many as expected on average, and the...
Forum: Prime Gap Searches 2021-12-31, 11:18
Replies: 32
Views: 2,546
Posted By mart_r
New Year's Eve consolidation

Some data for maximal gaps in the file in close proximity. In the next update, I'll include the data for p=2, I promise.

There are three primes (well, actually, 54 primes:) that await discovery,...
Forum: Other Mathematical Topics 2021-12-31, 10:45
Replies: 15
Views: 3,354
Posted By mart_r
tl;dr: some more results, potentially interesting further computations & a question

First, the question:
Calling y*p# the "slowest exponentially growing prime number sequence", would that be formally correct?


Further results:
Computation complete to 2111# on Sep 27, 2021....
Forum: Prime Gap Searches 2021-12-22, 17:22
Replies: 32
Views: 2,546
Posted By mart_r
What? What I wrote did look a little conceited to...

What? What I wrote did look a little conceited to me:smile:




That is, using a certain style of graph and a little imagination
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V
Forum: storm5510 2021-12-21, 18:09
Replies: 38
Views: 1,088
Posted By mart_r
I have some data stored on M-discs...

I have some data stored on M-discs (https://en.m.wikipedia.org/wiki/M-DISC) which are said to be more robust than run-of-the-mill DVDs or BluRays.
Regarding durability, probably more important than...
Forum: Prime Gap Searches 2021-12-20, 21:52
Replies: 18
Views: 1,699
Posted By mart_r
Well you already found 46318910903 (length 16),...

Well you already found 46318910903 (length 16), 103947089669 (17 and 18), and 184722051989 (19 and 20, the latter almost being of length 23), from your data in the OP at x=30. And those are probably...
Forum: Prime Gap Searches 2021-12-20, 21:33
Replies: 32
Views: 2,546
Posted By mart_r
Some data in the attachment, just to show off. ...

Some data in the attachment, just to show off.

The interested reader might also like to check, for instance, the differences p(n+42)-p(n) for p in the range [327076775000..327076783000]. Makes for...
Forum: Homework Help 2021-12-18, 18:08
Replies: 3
Views: 581
Posted By mart_r
I know, it works outside of the program. But...

I know, it works outside of the program.
But the trick with bracketing the "\Bbb P" part had the desired effect, now the outcome looks like it should. Thanks a lot!
Forum: Homework Help 2021-12-18, 16:51
Replies: 3
Views: 581
Posted By mart_r
TeX expression not right

I hope this roughly qualifies as homework help. I've been spending an hour to get this one line into the TeXworks program:
\Bbb P(\xi_n=1)={1\over\log n} \mbox{ and } \Bbb P(\xi_n=0)=1-{1\over\log...
Forum: Prime Gap Searches 2021-12-18, 13:52
Replies: 229
Views: 57,697
Posted By mart_r
Results k <= 13.7e15

Please find attached the results for k <= 13.7e15, in other terms, the first occurrence gaps between twin primes <= 82.2*10^15.
The first ten values gap/6 for which no first occurrence is known are...
Forum: Prime Gap Searches 2021-12-04, 10:47
Replies: 18
Views: 1,699
Posted By mart_r
A nice variation. The idea of e.g. consecutive...

A nice variation. The idea of e.g. consecutive gaps with certain merit value went through my head before, but I never got around to calculate specific numbers. I think that would fall out as a...
Forum: Prime Gap Searches 2021-11-29, 11:54
Replies: 32
Views: 2,546
Posted By mart_r
I have uploaded some data for posterity,...

I have uploaded some data for posterity, differences d between primes pn and pn+k for k <= 130 and d <= 740, see 2nd link for A086153.
Forum: Prime Gap Searches 2021-11-17, 13:51
Replies: 32
Views: 2,546
Posted By mart_r
It doesn't only seem like a big gap, it's listed...

It doesn't only seem like a big gap, it's listed in A339943 as a(56), since 56=(35729-35617)/2.
I have a lot of data ready for submission, it just takes me longer to actually submit it, my schedule...
Forum: Prime Gap Searches 2021-11-09, 18:10
Replies: 32
Views: 2,546
Posted By mart_r
Greetings Bobby, I'd like to run these...

Greetings Bobby,

I'd like to run these numbers through Pari again before posting more inconsistent/approximate numbers. The formula with the term "-k+1" (see 1) from previous post) is only...
Forum: Prime Gap Searches 2021-11-04, 21:55
Replies: 32
Views: 2,546
Posted By mart_r
Gaps between non-consecutive primes

In the last few days I dug my fangs into gaps between primes pn and pn+k (with k=1 these are the usual well-known prime gaps, for k=2 see A144103, for k=3 see A339943, for k=4 see A339944).

This...
Forum: Lounge 2021-10-29, 18:26
Replies: 415
Views: 65,298
Posted By mart_r
I'll always remember the call I got one Saturday...

I'll always remember the call I got one Saturday morning from a self-proclaimed MS employee with an Indian accent. I think these are well known by now, but that particular call was before I have...
Showing results 1 to 25 of 706

 
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