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Forum: Other Mathematical Topics 2022-08-11, 21:21
Replies: 5
Views: 171
Posted By mart_r
Ah yes, the automorphs :smile: I dug out some...

Ah yes, the automorphs :smile:
I dug out some calculations of mine from 2010 - man, it's already been twelve years! -, where I found that if b is the product of exactly k distinct primes or prime...
Forum: Other Mathematical Topics 2022-08-10, 22:00
Replies: 5
Views: 171
Posted By mart_r
Nope. :smile: I just phrased the question as...

Nope. :smile: I just phrased the question as simply as possible.



Interesting indeed! Thanks :thumbs-up:
I was in fact typing the question into mathstackexchange but didn't get this particular...
Forum: Other Mathematical Topics 2022-08-10, 20:32
Replies: 5
Views: 171
Posted By mart_r
Sum of digits of x and powers of x

Given a base b >= 2 and an odd integer exponent n >= 3, consider the difference (or ratio) between the sum of the last d digits (in base b) of x and the sum of the last d digits of x^n, where x mod b...
Forum: Prime Gap Searches 2022-08-01, 18:44
Replies: 56
Views: 11,142
Posted By mart_r
Error terms, prime number scarcities, and trains

Just an intermediate result that made me go "hmmmm...". Suppose we assume [$]CSG=1+O(1)[/$] for the gaps between non-consecutive primes, then, if I did the math right, this would imply that we also...
Forum: Prime Gap Searches 2022-07-30, 08:56
Replies: 143
Views: 38,525
Posted By mart_r
I count that as a "like". Thanks! :smile: ...

I count that as a "like". Thanks! :smile:



It's dark outside as well - but lo! it looks like the dawn breaks on the horizon! Or is it just a faint sheet lightning? :smile:

Metaphors aside, I...
Forum: Prime Gap Searches 2022-07-27, 19:13
Replies: 122
Views: 36,085
Posted By mart_r
As you can see in the big lists, I do have some...

As you can see in the big lists, I do have some gaps to show :smile:
And I'm aiming for the Top Ten in the list of discoverers.
The initial motivation to work in that range came from an idea how to...
Forum: Lounge 2022-07-25, 19:19
Replies: 55
Views: 10,786
Posted By mart_r
When listening to Al Stewart...

In the year of the cat, should we expect some commotion during the dog days?
:leaving:
Forum: Prime Gap Searches 2022-07-21, 14:17
Replies: 143
Views: 38,525
Posted By mart_r
dum de-dum de-dum ...

Another tidbit of information I'd like to share.

Craig's data shows that the bias [$]f(m) \approx 5 \cdot (m-5/3+O(1))[/$] for m > 2 (see previous post) - if we assume that the values aM in post #...
Forum: Lounge 2022-07-19, 17:05
Replies: 757
Views: 89,266
Posted By mart_r
"Blessed weather pattern looks exactly like a...

"Blessed weather pattern looks exactly like a Ninja Turtle"

https://futurism.com/the-byte/weather-pattern-ninja-turtle
Forum: Prime Gap Searches 2022-07-17, 18:04
Replies: 122
Views: 36,085
Posted By mart_r
It doesn''t look like we're getting any closer at...

It doesn''t look like we're getting any closer at the moment. The discussion in this thread (https://www.mersenneforum.org/showthread.php?t=26924) petered out in November, I also don't know what...
Forum: Other Mathematical Topics 2022-07-15, 19:35
Replies: 7
Views: 938
Posted By mart_r
Maybe so. But those would depend on two or three...

Maybe so. But those would depend on two or three different variables, I reckon that they would be much harder to calculate. I don't yet have the prerequisites to figure out efficient ways to do that,...
Forum: Prime Gap Searches 2022-07-15, 19:27
Replies: 122
Views: 36,085
Posted By mart_r
Glad to hear that you're still alive. :smile: ...

Glad to hear that you're still alive. :smile:
It's been getting hauntingly quiet in the prime gap search area lately.

Should you, or anyone for that matter, be in the mood for hunting down a 10M...
Forum: Prime Gap Searches 2022-07-14, 20:30
Replies: 122
Views: 36,085
Posted By mart_r
Congrats, it's a world record!

Michiel's gap is now verified. PFGW output files from my range are attached.
Early in the verification process I also did a sieving check up to 2e11, where the remaining candidates matched with...
Forum: Prime Gap Searches 2022-07-14, 20:22
Replies: 56
Views: 11,142
Posted By mart_r
Don't answer me, don't break the silence, don't let me win

Attached are the numbers of first occurrence gaps for k <= 109 and p <= 2e14.
Don't look for me, I'm already moving on.:digging:
Forum: Other Mathematical Topics 2022-07-14, 20:12
Replies: 7
Views: 938
Posted By mart_r
OK, thanks! It's interesting to note that the...

OK, thanks!
It's interesting to note that the prime terms in A120857 are similar to those I gave in post # 2. Maybe compute more terms of A120857 and see how many more coincide with my list?
Until...
Forum: Other Mathematical Topics 2022-07-13, 21:38
Replies: 7
Views: 938
Posted By mart_r
Many thanks for your reply! I had devised a...

Many thanks for your reply!

I had devised a scheme some years ago to compare how prolific the generalized repunits are w.r.t. the values of p, by taking a sum

[$]s_r:=\sum_{q=7,\,q\,prime}^x...
Forum: Other Mathematical Topics 2022-07-12, 21:37
Replies: 7
Views: 938
Posted By mart_r
I keep up until I hit a raw nerve

Follow-up question:

Is there a similar measure for the numbers of the form 2kp+1 yielding a lot of composites, in which case the generalized repunits (b^p-1)/(b-1) would produce an above-average...
Forum: Prime Gap Searches 2022-07-11, 16:14
Replies: 143
Views: 38,525
Posted By mart_r
How can I read a room when all the lights are out? And no, I don't have infrared vision.

Now, assume that the density of gaps between primes [$]p[/$] and [$]p+m\cdot \log p[/$] is [$]\sim e^{-m-f(m)/\log p}[/$].

What would it take to show that [$]f(m)[/$] is small enough as to not...
Forum: MattcAnderson 2022-07-09, 08:20
Replies: 4
Views: 200
Posted By mart_r
No, I didn't. It's in one of the cartoon shows...

No, I didn't. It's in one of the cartoon shows I'm watching.:smile:

Have a nice day as well!
Forum: chalsall 2022-07-02, 21:37
Replies: 20
Views: 710
Posted By mart_r
I have lucid dreams occasionally. (Not that...

I have lucid dreams occasionally.
(Not that anyone cares...)
Forum: MattcAnderson 2022-07-01, 17:45
Replies: 4
Views: 200
Posted By mart_r
Question # 1: Why do you ask? Question # 2: Why...

Question # 1: Why do you ask?
Question # 2: Why do I know?
Question # 3: What in the name of The mighty Saurus does "great north oops mets eggs" mean???
Forum: Prime Gap Searches 2022-06-28, 13:03
Replies: 122
Views: 36,085
Posted By mart_r
Taking the last remaining range 2e6 <= x <=...

Taking the last remaining range 2e6 <= x <= 3e6.
Forum: Other Mathematical Topics 2022-06-27, 15:09
Replies: 7
Views: 938
Posted By mart_r
Hardy-Littlewood constants for quadratic polynomials

The polynomial x2+x+a with integer x and odd integer a has a certain density of prime numbers which can be measured by an associated Hardy-Littlewood constant, HL(x2+x+a).
Example: HL(x2+x+1) =...
Forum: Soap Box 2022-06-19, 14:05
Replies: 37
Views: 1,430
Posted By mart_r
Huh. IIRC, M*A*S*H in the German version doesn't...

Huh. IIRC, M*A*S*H in the German version doesn't have any laugh tracks. My brother used to watch it a lot in the 90s.
Forum: Soap Box 2022-06-13, 19:35
Replies: 37
Views: 1,430
Posted By mart_r
I'm sorry, I got carried away:redface: Actually...

I'm sorry, I got carried away:redface:
Actually I've known for many years that placing the blame is to blame for many bad things in the world:devil:
(I should probably have formulated it actively...
Showing results 1 to 25 of 782

 
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