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 Showing results 1 to 25 of 1000 Search took 0.23 seconds. Search: Posts Made By: robert44444uk
 Forum: Prime Gap Searches 2021-12-07, 15:57 Replies: 55 Sticky: Prime gap records Views: 22,789 Posted By robert44444uk Nice gap! I also gave Seth some 1m+ gaps a while... Nice gap! I also gave Seth some 1m+ gaps a while back.
 Forum: Prime Gap Searches 2021-12-06, 10:16 Replies: 6 Views: 335 Posted By robert44444uk I'm taking all gaps up to 50 in case anyone is... I'm taking all gaps up to 50 in case anyone is interested in extending other ranges. 60 looks a soft target, as are all 0mod30 cases What I find gratifying about this search is that the higher you...
 Forum: Prime Gap Searches 2021-12-04, 08:10 Replies: 6 Views: 335 Posted By robert44444uk The first instance of 13 and 14 consecutive 50+... The first instance of 13 and 14 consecutive 50+ gaps is at 3057601284499 where subsequent gaps are 60, 54, 58, 50, 100, 90, 62, 156, 124, 60, 60, 68, 76 and 86
 Forum: Prime Gap Searches 2021-12-03, 12:06 Replies: 6 Views: 335 Posted By robert44444uk The first instance of 7 consecutive 100+ gaps is ... The first instance of 7 consecutive 100+ gaps is 5183073661943 with gaps 116,130,114,158,286,102,102 The first instance of 3 consecutive 200+ gaps is provided by 20222645954633 with gaps of...
 Forum: Prime Gap Searches 2021-12-02, 18:17 Replies: 6 Views: 335 Posted By robert44444uk Long ranges of gaps larger than a given value Take a range of integers p1 to p(n+1) within which there are primes p1,p2,p3...p(n+1), with gaps between these primes of g1,g2,g3...gn Take an integer to represent the smallest gap in the set...
 Forum: Math 2021-11-21, 11:00 Replies: 27 Views: 1,329 Posted By robert44444uk Yes, the last of these is the lowest ratio, N-1... Yes, the last of these is the lowest ratio, N-1 prime, seen once small N are taken out of the consideration.
 Forum: Math 2021-11-20, 13:55 Replies: 27 Views: 1,329 Posted By robert44444uk Using 2^30 as the major set of prime factors in N... Using 2^30 as the major set of prime factors in N suggests N= e^75.33 corresponding to 5e32. At this type of value of N, the ratio again drops below 1, last seen with N=20 The data below was...
 Forum: Math 2021-11-18, 17:21 Replies: 27 Views: 1,329 Posted By robert44444uk Coming back to Goldbach. It is proved that... Coming back to Goldbach. It is proved that there is a prime between N/2 and N (Bertrand- Chebyshev), with N even Using this prime residue technique, is it correct to paraphrase Goldbach to say...
 Forum: Math 2021-11-18, 12:32 Replies: 27 Views: 1,329 Posted By robert44444uk c2-c1 negative - these are common at low N. There... c2-c1 negative - these are common at low N. There are 3158 examples in N< 135536 but none after this, checked up to N=304000. Between N=13336 and N=304000 the least difference is c2-c1=6 demonstrated...
 Forum: Math 2021-11-18, 11:47 Replies: 27 Views: 1,329 Posted By robert44444uk The attached photo suggest that if N is 0modp for... The attached photo suggest that if N is 0modp for very small primes, then c1 is comparatively small. prime 3 dominates. (prime 2 dominates N odd). At the top of the list would be any N that are mod...
 Forum: Math 2021-11-18, 09:33 Replies: 27 Views: 1,329 Posted By robert44444uk Overnight I ran N-1 from 1 to 2477789 and looked... Overnight I ran N-1 from 1 to 2477789 and looked at all of those with ratio >2.4. There were 4416 of these. 4408 of these N-1 were 9 mod 10, 3 were either 5 mod 10 or 7 mod 10, and 1 each for 1 mod...
 Forum: Math 2021-11-17, 17:47 Replies: 27 Views: 1,329 Posted By robert44444uk The graph below suggest that prime N-1 enjoy an... The graph below suggest that prime N-1 enjoy an advantage, measured by larger ratio, compared to N-1 composite The highest ratio was achieved by 125 i.e. 5.5.5, but 95 (5.19) and 119 (7.23) also...
 Forum: Math 2021-11-17, 10:31 Replies: 27 Views: 1,329 Posted By robert44444uk I looked in depth at much higher powers of 2, and... I looked in depth at much higher powers of 2, and the intercept with the ratio = 1 appears at much lower levels than my previous estimates. Below is data and a graph at 2^22. Interestingly, the best...
 Forum: Math 2021-11-15, 18:14 Replies: 27 Views: 1,329 Posted By robert44444uk Some more data - I ran out the calculations for... Some more data - I ran out the calculations for p(2)+1 = N = 2^n*(p3), where p3 is also a prime, and n= 1 to 5. The graph below shows the results for x=p(2) with n=5, and that shows a natural log...
 Forum: Prime Gap Searches 2021-11-15, 15:27 Replies: 55 Sticky: Prime gap records Views: 22,789 Posted By robert44444uk Not everyone is comfortable with .sql files, .txt... Not everyone is comfortable with .sql files, .txt is well understood, and a .zip or .7z or well known compression compression can keep the file size down It would be good to have all of the...
 Forum: Math 2021-11-15, 12:25 Replies: 27 Views: 1,329 Posted By robert44444uk I'm now looking at the regular series to find... I'm now looking at the regular series to find properties exhibited by the worst performing primes. From the limited work done to date, those performing badly are such that are such that p(2)+1 =...
 Forum: Math 2021-11-15, 10:23 Replies: 27 Views: 1,329 Posted By robert44444uk Here are two graphs showing possible log curve... Here are two graphs showing possible log curve fits, for 23#, only looking at the values that are along the lower portion of the comprehensive n.23#-1 graph shown in the previous post. The...
 Forum: Math 2021-11-15, 09:30 Replies: 27 Views: 1,329 Posted By robert44444uk Thank you Dr Sardonicus for hugely helpful... Thank you Dr Sardonicus for hugely helpful contributions. Here are graphs of n.p#-1, where p is 13,17,19 and 23, n is an integer such that n.p#-1 is prime. There is discernible internal structure...
 Forum: Prime Gap Searches 2021-11-15, 09:06 Replies: 269 Sticky: Prime Gap News Views: 68,403 Posted By robert44444uk Congrats on the gap - a goodly sized merit as... Congrats on the gap - a goodly sized merit as well. I had already reported the "gap too large" message and informed Seth. This led to his recent poll where he asked 4 questions, one of which...
 Forum: Prime Gap Searches 2021-11-13, 13:19 Replies: 55 Sticky: Prime gap records Views: 22,789 Posted By robert44444uk My tuppence worth, 1. Yes, other than a few... My tuppence worth, 1. Yes, other than a few big results, these records can also be broken easily I would say that it would be good if those that are merit 20 or above are checked 2. Yes, if from...
 Forum: Math 2021-11-13, 09:50 Replies: 27 Views: 1,329 Posted By robert44444uk Overnight I looked at 13#, 17#, 19#, 23# and 29#... Overnight I looked at 13#, 17#, 19#, 23# and 29# and have not found a better result than the 6.29#. ATH's results are super-interesting! A run of 713469626 consecutive primes where residues of...
 Forum: Math 2021-11-12, 18:19 Replies: 27 Views: 1,329 Posted By robert44444uk A first approximation of the prime after 19 that... A first approximation of the prime after 19 that provides next first density ratio of less than 1, based on a logarithmic equation relating to the results for primes of the form n.19#,...
 Forum: Math 2021-11-11, 18:05 Replies: 27 Views: 1,329 Posted By robert44444uk A few more observations on this: ... A few more observations on this: Actually as these numbers get larger, I do think that there is a possibility that some primes will provide values for the density ratio less than 1, as the...
 Forum: Prime Gap Searches 2021-11-10, 09:03 Replies: 269 Sticky: Prime Gap News Views: 68,403 Posted By robert44444uk Well - my candidate did not last long after our... Well - my candidate did not last long after our exchange of messages. Still good enough for 18th largest gap tough. Here are the gaps I found during the breakaway from my regular searching. None of...
 Forum: Math 2021-11-08, 18:07 Replies: 27 Views: 1,329 Posted By robert44444uk Prime residues of near-prime modulo a prime I'm not sure if the title of this thread captures what I am trying to convey. Take two distinct primes p(1) and p(2), with p(2)>p(1) then if (p(2)+1) mod p(1) is prime, say p(3), with p(3) <...
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