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Forum: Prime Gap Searches 2022-01-17, 08:56
Replies: 32
Views: 2,427
Posted By robert44444uk
A couple more, getting closer, but not that close...

A couple more, getting closer, but not that close

124977806 92
125316443 90
Forum: Prime Gap Searches 2022-01-15, 11:35
Replies: 32
Views: 2,427
Posted By robert44444uk
A slight improvement in the prime count for n in...

A slight improvement in the prime count for n in n*p#+c+x, where p = 409, c = 492682..., x from 0 to 15900

123733011 91
120673847 88
121848887 88

In terms of sieves, I found it was useful to...
Forum: Prime Gap Searches 2022-01-14, 10:22
Replies: 32
Views: 2,427
Posted By robert44444uk
As an aid to the factorials and offsets approach,...

As an aid to the factorials and offsets approach, it is relatively simple to show that there is no range of 100 primes p1..p100 at relatively small p1 where p1 is larger than any gap smaller than p1....
Forum: Prime Gap Searches 2022-01-14, 09:44
Replies: 32
Views: 2,427
Posted By robert44444uk
After 20 hours of processing I'm afraid that I...

After 20 hours of processing I'm afraid that I can beat 87 primes in a range of 15900 - I'll continue the search though
In n*p#+c+x, where p = 409, c = 492682..., x from 0 to 15900, then 87 primes...
Forum: Prime Gap Searches 2022-01-12, 16:41
Replies: 32
Views: 2,427
Posted By robert44444uk
500 results - tested to approx. 1.1e12: ...

500 results - tested to approx. 1.1e12:

Largest gap: 16690 Average merit: 1.229114171 First prime: 622973626447
Smallest gap: 10306 Average merit: 0.795722241 First prime: 177726413581

200...
Forum: Prime Gap Searches 2022-01-12, 12:27
Replies: 32
Views: 2,427
Posted By robert44444uk
I was doing this very wrong, silly me. I...

I was doing this very wrong, silly me.

I think I was wrong to start at the deficient primorial 409#/30, I should have started with the primorial 409#, with a lower multiplier, in this case ...
Forum: Prime Gap Searches 2022-01-12, 09:04
Replies: 32
Views: 2,427
Posted By robert44444uk
I'm doing something wrong I think, although I am...

I'm doing something wrong I think, although I am not sure (maybe mart_r could check)

Average number of primes in a range of x=15900 integers from a = 3483347771*409#/30 is = 15900/ln(a) or approx...
Forum: Prime Gap Searches 2022-01-11, 16:38
Replies: 32
Views: 2,427
Posted By robert44444uk
so if I have done this right, the CRT offset is...

so if I have done this right, the CRT offset is...
Forum: Prime Gap Searches 2022-01-11, 10:04
Replies: 32
Views: 2,427
Posted By robert44444uk
I'm trying to understand the approach. I've...

I'm trying to understand the approach.

I've found a 1886-tuplet pattern width 15898 from the internet,https://math.mit.edu/~primegaps/tuples/admissible_1886_15898.txt so is the idea to get a...
Forum: Prime Gap Searches 2022-01-10, 17:43
Replies: 32
Views: 2,427
Posted By robert44444uk
This is much harder than I anticipated - it...

This is much harder than I anticipated - it really is an outstanding result. I have started to look at the next obvious candidate starting from 3483347771*409#/30 - 7016 (merit >39). I have only...
Forum: Prime Gap Searches 2022-01-10, 10:53
Replies: 32
Views: 2,427
Posted By robert44444uk
I already did a bit of work at k=1000 but I might...

I already did a bit of work at k=1000 but I might concentrate at k=200 and 500 and see where that goes
Forum: Prime Gap Searches 2022-01-10, 10:45
Replies: 32
Views: 2,427
Posted By robert44444uk
Here are some results for 20..25 Small...

Here are some results for 20..25

Small average merits and gaps:


n gap p(n) p(n+k) ave merit checked to

20 138 2037404713403 2037404713541 0.243448948 2.80E+12...
Forum: Prime Gap Searches 2022-01-10, 10:22
Replies: 32
Views: 2,427
Posted By robert44444uk
I confirm Marts values for 17,18,19 as the...

I confirm Marts values for 17,18,19 as the largest average merits between 18,19 and 20 primes respectively,

It is worth looking at the minimum value found to date for these, as no-one has found...
Forum: Prime Gap Searches 2022-01-10, 10:05
Replies: 32
Views: 2,427
Posted By robert44444uk
Hi all I did a bit of searching around the...

Hi all

I did a bit of searching around the average merit of 100 gaps in the range of 101 primes, and my best performance is (I've checked up to 9.675e11):

Gap=4354 Average merit=1.622541804,...
Forum: Prime Gap Searches 2021-12-24, 08:40
Replies: 18
Views: 1,578
Posted By robert44444uk
I'm no programmer, Sorry for this. What is wrong...

I'm no programmer, Sorry for this. What is wrong therefore is the statement "Initial prime is". As the same program is used for all examples, perhaps what we could say is that the stated prime is...
Forum: Prime Gap Searches 2021-12-23, 14:40
Replies: 32
Views: 2,427
Posted By robert44444uk
Nah, not really, Excellent work as always mart_r

Nah, not really, Excellent work as always mart_r
Forum: Prime Gap Searches 2021-12-22, 09:37
Replies: 5
Views: 371
Posted By robert44444uk
I have calculated the median gap merits in...

I have calculated the median gap merits in ordered arrays of gaps between primes 2 to p(x), where x represent primes up to 1e7.

The results are shown in the attached graph. Also to note, earlier...
Forum: Prime Gap Searches 2021-12-22, 09:31
Replies: 32
Views: 2,427
Posted By robert44444uk
Cocky!

Cocky!
Forum: Prime Gap Searches 2021-12-21, 17:32
Replies: 5
Views: 371
Posted By robert44444uk
As well as looking at the median merits for...

As well as looking at the median merits for arrays of primes from x=3 to x=1e7, where x represents the larger prime in the array 2..x, I have also calculated the median gap. The first few arrays show...
Forum: Prime Gap Searches 2021-12-21, 14:46
Replies: 18
Views: 1,578
Posted By robert44444uk
Please use the thread "Median Gaps" for further...

Please use the thread "Median Gaps" for further postings on this theme.
Forum: Prime Gap Searches 2021-12-21, 09:40
Replies: 18
Views: 1,578
Posted By robert44444uk
That does rather look like the case - I retract...

That does rather look like the case - I retract my earlier statement.
Forum: Prime Gap Searches 2021-12-21, 09:39
Replies: 18
Views: 1,578
Posted By robert44444uk
Here is an interesting pair of graphs - they...

Here is an interesting pair of graphs - they shows he median gap of a range of all gaps for primes 2 to x, with x up to 999983. The second graph ignores the results up to x=4409 so as to see the...
Forum: Prime Gap Searches 2021-12-20, 14:54
Replies: 18
Views: 1,578
Posted By robert44444uk
some findings about strings of minimum merits: ...

some findings about strings of minimum merits:

Merit >2


Min merit: 2 Run of merits: 2 Initial prime: 199 Following gaps: 12 12 Merits: 2.267014728 2.242211901 ...
Forum: Prime Gap Searches 2021-12-16, 09:02
Replies: 18
Views: 1,578
Posted By robert44444uk
I found the first instance of two consecutive 300...

I found the first instance of two consecutive 300 gaps.

2 ||| 1362810282139 1362810282439 1362810282781 || 300 342

In the search I discovered 6 such. The largest gap following the 300 pair...
Forum: Prime Gap Searches 2021-12-15, 11:00
Replies: 5
Views: 371
Posted By robert44444uk
Just looking at the middle curve C values in the...

Just looking at the middle curve C values in the graph C in the first post...when plotted against x = ln(p), rather than the x = series number gives a pretty decent match for the formula y =...
Showing results 1 to 25 of 1000

 
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