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Search: Posts Made By: mart_r
Forum: Soap Box 2022-09-25, 20:08
Replies: 405
Views: 22,005
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...
Forum: Soap Box 2022-09-25, 12:39
Replies: 405
Views: 22,005
Posted By mart_r
Putin's p martial mobilization is definitely not...

Putin's p martial mobilization is definitely not going according to plan.
That he appears to go easy on IT, financial and media experts speaks for itself - or rather, which domestic resources he...
Forum: jzakiya 2022-09-24, 19:19
Replies: 111
Views: 26,562
Posted By mart_r
Section 6, "The Infinity of Primes": "Thus, any...

Section 6, "The Infinity of Primes": "Thus, any prime p can be treated as r0 to a Pn modulus composed of all the primes < p, whose residues from p to p² are new primes. We can repeat this progression...
Forum: jzakiya 2022-09-24, 14:14
Replies: 111
Views: 26,562
Posted By mart_r
Were you addressing jzakiya? With the "not so...

Were you addressing jzakiya? With the "not so obvious" I was referring to the lack of proof for Polignac's conjecture. Or so I assume. :smile:
Forum: jzakiya 2022-09-24, 13:00
Replies: 111
Views: 26,562
Posted By mart_r
We would like to believe that Polignac's...

We would like to believe that Polignac's conjecture is correct. All the numbers explicitly calculated so far are in favor of the conjecture, and we have asymptotic formulas that predict the number of...
Forum: Prime Gap Searches 2022-09-24, 11:57
Replies: 64
Views: 13,279
Posted By mart_r
I stand corrected

yhugRD_XngM

While I'm at it, here are the values up to n=13, corrected to be within +/- about 2 sigma:
1 1
2 4
3 8
4 12.642007 ± 0.000009
5 17.75797 ± 0.00002
6 23.24943 ±...
Forum: jzakiya 2022-09-24, 11:28
Replies: 111
Views: 26,562
Posted By mart_r
I'm really happy to get a reply, so I've attached...

I'm really happy to get a reply, so I've attached the data for p>=43.
Strange... I thought I read the word "Pari" in one of your posts, so I thought you were already using this program.



The...
Forum: Prime Gap Searches 2022-09-21, 21:52
Replies: 64
Views: 13,279
Posted By mart_r
r_gm @ n=3 = 12.64200 ± 0.000015

All work and no pay makes me wish life wouldn't be so dull.

Here, I give you the first occurrence gaps for k=1000 up to p=2*10^14.

You'll find me in the kitchen.

PS: To this day I've never...
Forum: Lounge 2022-09-21, 21:39
Replies: 1,068
Views: 110,431
Posted By mart_r
Lately I've been watching...

Just because I can't get this song out of my head today. And yesterday. And the day before...
d-ILp4nQCK0
Forum: jzakiya 2022-09-21, 21:14
Replies: 111
Views: 26,562
Posted By mart_r
Been there, done that. See my post # 26...

Been there, done that. See my post # 26 (https://www.mersenneforum.org/showpost.php?p=555012&postcount=26) where I posted the program to do this in less than 0.01 seconds in Pari.

(22:52) gp >...
Forum: Prime Gap Searches 2022-09-19, 16:29
Replies: 64
Views: 13,279
Posted By mart_r
Where's the revolution? C'mon, people, you're letting me down!

The "puzzle" with the geometric mean of consecutive gaps can be generalized: for n consecutive gaps the average ratio of the largest gap divided by the smallest gap appears to be as follows (rounded...
Forum: Prime Gap Searches 2022-09-18, 12:59
Replies: 64
Views: 13,279
Posted By mart_r
What I have so far (without explicitly claiming...

What I have so far (without explicitly claiming to be correct):

Using a Poisson distributed random model, i.e. with random variables 0 < xn < 1 turned into a function equivalent to the merit mn =...
Forum: Lounge 2022-09-11, 21:55
Replies: 1,068
Views: 110,431
Posted By mart_r
Remembering the infant years of the new millennium

A gem from the early 2000's. Just because I like music videos where one can see the effort being put into them.

VF8LMQQ0rEw


Another random video from that era...

Hyk-Vdd_Qrk
Forum: Prime Gap Searches 2022-09-09, 16:12
Replies: 148
Views: 39,960
Posted By mart_r
I guess I wasn't working at full capacity the...

I guess I wasn't working at full capacity the other day... I think I meant to cite the approximation formula [$]f(g) \cdot e^{-g/log(p)} \cdot 2 \cdot c_2/log(p)[/$], which works well for all values...
Forum: Prime Gap Searches 2022-09-09, 16:03
Replies: 64
Views: 13,279
Posted By mart_r
No solution for T(38,16) for p < 10^16. Meh. ...

No solution for T(38,16) for p < 10^16.
Meh.
Oh well...
Anyone else holding their breath for the 3rd season of "The Owl House"?
Forum: Prime Gap Searches 2022-09-07, 14:41
Replies: 148
Views: 39,960
Posted By mart_r
Delighted to hear from you again, Robert! ...

Delighted to hear from you again, Robert!



Yeah, that might've been poorly worded, my mistake. I was hoping it would become clearer during all my explanations :)

For small gaps g and large...
Forum: Prime Gap Searches 2022-09-02, 18:53
Replies: 148
Views: 39,960
Posted By mart_r
Hmm. 2,170,000 gaps around 997# show a bias...

Hmm. 2,170,000 gaps around 997# show a bias similar to the usual one I found so far, including the effects of the Granville scarcity. The numbers around 2351*2351# I posted earlier are either off...
Forum: Prime Gap Searches 2022-09-02, 18:14
Replies: 64
Views: 13,279
Posted By mart_r
Dancing with tears in my eyes...

Is this not a well-known result? If so, I might try to tackle the proof myself...


They say that the gas pipeline Nord Stream 1 is kept shut indefinitely. So before power outrages become daily...
Forum: Lounge 2022-08-27, 13:35
Replies: 1,241
Views: 147,930
Posted By mart_r
This dumb joke I made up myself, but I'm pretty...

This dumb joke I made up myself, but I'm pretty sure someone else has thought of it before.

What's the name of the old Inca Pokémon temple in Peru? Machu Pikachu.
Forum: Prime Gap Searches 2022-08-24, 17:03
Replies: 64
Views: 13,279
Posted By mart_r
[$]\lim\limits_{\substack{x\to\infty}} r_{gm} =...

[$]\lim\limits_{\substack{x\to\infty}} r_{gm} = 4[/$], if I may so conjecture (based on a random model similar to Cramér's). Is there a proof available?


I'd like to take the search for T(38,16)...
Forum: Lounge 2022-08-23, 17:30
Replies: 1,241
Views: 147,930
Posted By mart_r
Saw this one recently: The EU now has 1 GB...

Saw this one recently:

The EU now has 1 GB of free space.
Forum: Information & Answers 2022-08-21, 18:42
Replies: 40
Views: 3,294
Posted By mart_r
Just practicing my programming skills

It would still take thousands of years to find a prime novemdecuplet with my program, but it might be useful for small searches and doublechecks.

- Working with "concat" was slowing the wheel...
Forum: Other Mathematical Topics 2022-08-20, 09:47
Replies: 6
Views: 457
Posted By mart_r
Slightly off-track

All this talk about automorphs made me kinda hungry and I tried to find primes in the sequences A214882 and A214883.

In A214882, a(n) is prime for n = {3, 5, 7, 9, 11, 12, 14, 23, 41, 69, 78, 223,...
Forum: Information & Answers 2022-08-18, 17:14
Replies: 40
Views: 3,294
Posted By mart_r
Thanks for the reply! You make me happy :smile: ...

Thanks for the reply! You make me happy :smile:

Different patterns can be looked at in parallel, but manually setting a starting point would also be nice. Should be no problem for me to implement....
Forum: Information & Answers 2022-08-17, 18:45
Replies: 40
Views: 3,294
Posted By mart_r
Houston, we've got a program. And a problem.

I've written a Pari program that captures the gist of the most important steps in a k-tuple finding algorithm. Problem is, it is quite slow. Finding 12- or 13-tuples can take several minutes, so it's...
Showing results 1 to 25 of 808

 
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