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Search: Posts Made By: mart_r
Forum: Prime Gap Searches 2022-11-25, 21:50
Replies: 17
Views: 1,060
Posted By mart_r
The Cramér-Shanks-Granville analogue would also...

The Cramér-Shanks-Granville analogue would also be interesting to consider, in this table the records for k=1..7 (not pattern-specific):
k gap gap start gap end CSG
1 ...
Forum: Prime Gap Searches 2022-11-25, 20:57
Replies: 69
Views: 18,465
Posted By mart_r
Eins Zwei Drei Vier Fünf Sechs Sieben Acht

Not a record in terms of CSG, but a close contender - and the largest p for which a CSG (or "scarcity/paucity ratio") > 1 is known:
A region with exceptionally few k+1 consecutive primes for...
Forum: Science & Technology 2022-11-21, 18:58
Replies: 3,032
Views: 357,579
Posted By mart_r
:huh: In the GWR book of 1990, there was an entry...

:huh: In the GWR book of 1990, there was an entry about prefixes which mentioned "Dea" for 1030 and "tredo" (IIRC) for 10-30. I've never seen them in action and was wondering for years if there was...
Forum: Prime Gap Searches 2022-11-15, 18:53
Replies: 47
Views: 12,724
Posted By mart_r
I've had a closer look at A048670 lately. I...

I've had a closer look at A048670 lately. I noticed that in the b-file with the offset terms, half of them could be reduced mod p(n)#, where p(n) is the n'th prime. What's really peculiar though is...
Forum: sweety439 2022-11-11, 18:47
Replies: 1
Views: 308
Posted By mart_r
Where's my number? :not prime:

Where's my number?

:not prime:
Forum: Prime Gap Searches 2022-11-11, 18:26
Replies: 10
Views: 1,037
Posted By mart_r
That's left as an exercise for the reader :smile:...

That's left as an exercise for the reader :smile:
Should be pretty close to the gaps before the primes in A277552, I guess...
Hey! Look at the name of the author of this sequence ;))



No, I...
Forum: Other Mathematical Topics 2022-11-07, 21:51
Replies: 11
Views: 3,736
Posted By mart_r
Take it, it's free

While this thread is still on the front page, let me drop this number here:...
Forum: Prime Gap Searches 2022-11-07, 19:52
Replies: 10
Views: 1,037
Posted By mart_r
These are the successive minima below -5: ...

These are the successive minima below -5:
-5.4265: p=20831323
-5.6812: p=191913031
-6.2752: p=436273291
-6.6031: p=2300942869
-6.7932: p=3842611109
-7.1677: p=4302407713
-7.4571: p=10726905041...
Forum: Prime Gap Searches 2022-11-05, 09:40
Replies: 10
Views: 1,037
Posted By mart_r
I'm trying to understand how the sum of primes up...

I'm trying to understand how the sum of primes up to x would help to calculate the following prime, or the next maximal gap.
Let's say, the bound you described in your OP would be between 1 and -7...
Forum: storm5510 2022-11-04, 18:50
Replies: 25
Views: 1,766
Posted By mart_r
Never seen this approach described so nicely...

Never seen this approach described so nicely before - then again, I never looked that closely into Collatz. Interesting though, and I might add the pertinent sequence A076227 here for further reading.
Forum: Prime Gap Searches 2022-11-04, 15:29
Replies: 10
Views: 1,037
Posted By mart_r
From the cited paper: We have, for sufficiently...

From the cited paper:
We have, for sufficiently large x,

[$]\frac{x^2}{2 \log x}+\frac{x^2}{4 \log^2 x}+\frac{x^2}{4 \log^3 x}+\frac{1.2 x^2}{8 \log^4 x} < S(x) < \frac{x^2}{2 \log...
Forum: Prime Gap Searches 2022-11-03, 21:07
Replies: 10
Views: 1,037
Posted By mart_r
You can use that the sum of primes up to x is...

You can use that the sum of primes up to x is asymptotic to [$]\frac{x^2}{2 \log x}+\frac{x^2}{4 \log^2 x}+...[/$], see e.g. arXiv:1606.06874 (https://arxiv.org/pdf/1606.06874.pdf).
You can then use...
Forum: Prime Gap Searches 2022-10-31, 18:35
Replies: 279
Sticky: Prime Gap News
Views: 83,704
Posted By mart_r
Awesome! Great work :thumbs-up::bow:

Awesome! Great work :thumbs-up::bow:
Forum: Prime Gap Searches 2022-10-30, 17:09
Replies: 279
Sticky: Prime Gap News
Views: 83,704
Posted By mart_r
Yes, this page is not up-to-date. I thought you...

Yes, this page is not up-to-date. I thought you were maintaining it? You might like to sync it with the data from these tables (https://primegap-list-project.github.io/lists/).
Forum: Prime Gap Searches 2022-10-28, 11:04
Replies: 279
Sticky: Prime Gap News
Views: 83,704
Posted By mart_r
I'm still looking for non-conventional gaps as...

I'm still looking for non-conventional gaps as well as conventional ones occasionally, although I'll resume my 49877#-ish range only when it gets colder, currently in Germany there's no need for...
Forum: Lounge 2022-10-18, 19:01
Replies: 164
Views: 25,834
Posted By mart_r
Well... cat's cat.:smile: 27467

Well... cat's cat.:smile:
27467
Forum: Prime Gap Searches 2022-10-17, 11:50
Replies: 69
Views: 18,465
Posted By mart_r
The replies that I get mean more to me than any...

The replies that I get mean more to me than any amount of money (which is too tight to mention anyway :smile:).
Forum: Lounge 2022-10-17, 11:30
Replies: 4,520
Views: 465,851
Posted By mart_r
Well, it still sounds better than most of the...

Well, it still sounds better than most of the contemporary "pop music" :smile:
Forum: Other Mathematical Topics 2022-10-15, 16:59
Replies: 11
Views: 3,736
Posted By mart_r
Brain malfunction, sorry. Those integers should...

Brain malfunction, sorry. Those integers should be infinite in number. If we find an example where [$]\Delta = 7.57 d[/$] (in fact, [$]\Delta = 5 d[/$] would suffice), it would take about...
Forum: Lounge 2022-10-13, 17:41
Replies: 1,742
Views: 173,385
Posted By mart_r
#annoyingautomaticupdates: Well, the laptop that...

#annoyingautomaticupdates: Well, the laptop that I utilised to calculate prime gaps in arithmetic progression on, for about 18 months nonstop, runs on Win10. It simply wasn't connected to the...
Forum: Other Mathematical Topics 2022-10-12, 19:54
Replies: 11
Views: 3,736
Posted By mart_r
The internet is sooo overrated

Looking through various works concerning the sum of digits of different functions (a rather recent one being "The sum of digits of floor(nc)" by J. Morgenbesser: see here...
Forum: Other Mathematical Topics 2022-10-09, 17:21
Replies: 11
Views: 3,736
Posted By mart_r
Has even any work been done toward proving or...

Has even any work been done toward proving or disproving the infinitude of integers <> 0 mod b such that the digit sum in base b is larger than the digit sum of their cube?
I was working my way...
Forum: Other Mathematical Topics 2022-10-06, 17:47
Replies: 11
Views: 3,736
Posted By mart_r
Happy to be curious still

Just out of curiosity: would it impress anyone to have 100+ digit integers not ending in zero whose digital sum is larger than the digital sum of their cubes?
Forum: Prime Gap Searches 2022-10-03, 12:45
Replies: 69
Views: 18,465
Posted By mart_r
For that comment? Yeah, that was a tremendous...

For that comment? Yeah, that was a tremendous outburst of creativity possibly worthy of a Pulitzer :wink:
But you lifted my mood, so I give a small update.
Prime scarcities with CSG > 1 are hard to...
Forum: Soap Box 2022-09-25, 20:08
Replies: 564
Views: 36,054
Posted By mart_r
My thoughts exactly. I'll always remember...

My thoughts exactly.

I'll always remember driving home from work on Feb 24 with the song "Dancing with tears in my eyes" playing in my head. (It was actually about 5 PM.)
It's becoming...
Showing results 1 to 25 of 832

 
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