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 Showing results 1 to 25 of 782 Search took 0.13 seconds. Search: Posts Made By: mart_r
 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...
 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...
 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 Sticky: Prime gap records 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 Sticky: Prime gap records 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...
 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 Sticky: Prime gap records 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 Sticky: Prime gap records 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:
 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...
 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 [$]s_r:=\sum_{q=7,\,q\,prime}^x...  2022-07-12, 21:37 Replies: 7 Views: 938 Posted By mart_r I keep up until I hit a raw nerve Follow-up question: Is there a similar measure for the numbers of the form 2kp+1 yielding a lot of composites, in which case the generalized repunits (b^p-1)/(b-1) would produce an above-average...  Forum: Prime Gap Searches 2022-07-11, 16:14 Replies: 143 Views: 38,525 Posted By mart_r How can I read a room when all the lights are out? And no, I don't have infrared vision. Now, assume that the density of gaps between primes [$]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 Sticky: Prime gap records Views: 36,085 Posted By mart_r Taking the last remaining range 2e6 <= x <=... Taking the last remaining range 2e6 <= x <= 3e6.
 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...
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