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2022-06-14, 18:39   #1651
EdH

"Ed Hall"
Dec 2009

470010 Posts

Quote:
 Originally Posted by garambois Excellent ! This is very interesting ! I understand that this is only a very small sample ! I will write the same program in early summer and compare our results. I can't wait to see the full file and examine this data. I'm already asking myself a few questions just by seeing this little sample : 1) For each prime number, do we always have one of the two bases that is necessarily base 2 ? (I think this is just due to the way the program is written and the fact that the sample is small ?) 2) Do you also test primes larger than 10 digits ? 3) Do you test all the bases listed on the project page ? Have we then overestimated the computation time that this test would take ? 4) Is this program written in C, python or another language ?
What I listed was a few lines from an output of one of my tests. Oddly, a complete base 2 run only yielded one more prime that spanned multiple bases, so I'm not sure how I made a grab of the perfect part of an overall list to show what looked like better results. Part of the trouble was that my overall listing also included numbers where the prime digits were within a larger prime. I have since been able to omit such cases. But, I still don't see how my sample was so close to the whole set.

1) The list was limited to the primes found within the base 2 sequences. This will be expanded later, but I will need to find a way to avoid total duplication of finds.

2) This test is running everything greater than 9 digits.

3) Currently, I'm using all bases through 200, except for the recently added. I haven't run a full update in a while, due to the db limitations.

4) It's a mixture, but mostly bash scripts, with one C++ program that harvests the primes.

ATM, I am becoming totally confused! I'm going to take a break until I sort out what I'm doing.

 2022-06-14, 20:03 #1652 garambois     "Garambois Jean-Luc" Oct 2011 France 16368 Posts OK, thanks Edwin for those answers. In any case, all the sample data seems to match except for one. I can't find the prime number 2159188693 at index 18 of sequence 2^327. Let us know if you do more tests in the next time and if you find other "big" prime numbers that are present in several bases. I will look into this. We never know, we have to check, even if I think that all this is only a coincidence and that we will not have much larger primes being in two different bases. It would surprise me a lot if there were such prime numbers of 12 digits or more ! As far as I'm concerned, I have one fear : I write my programs in python and I'm afraid it's infinitely slower than what you write in C. We'll see in July, because I unfortunately don't have enough time at the moment !
2022-06-15, 00:39   #1653
EdH

"Ed Hall"
Dec 2009

22×52×47 Posts

Quote:
 Originally Posted by garambois . . . I can't find the prime number 2159188693 at index 18 of sequence 2^327. . . . As far as I'm concerned, I have one fear : I write my programs in python and I'm afraid it's infinitely slower than what you write in C. We'll see in July, because I unfortunately don't have enough time at the moment !
The problem with cleaning things up manually for posting - that should be 2^372:18. I have made that part of the scripts now, and below is another set, with your requested formatting. I didn't verify anything, but something seems very wrong with this listing! I'm going to let it sit for now and try for a clearer "big picture," maybe tomorrow.

As for the programming, the C++ program is a very small part and most of the time is spent in the scripts. I hope to do a lot of work refining how the data are collected. I'll also need to do another full update of all my local sequences. I did add all the new bases below 200, so when I resume work, they will be represented.

Latest run:
Code:
1051654267,19,22,2102
1051654267,2,468,58
1097038783,2,501,61
1097038783,67,83,11
1129552253,19,18,510
1129552253,2,341,25
1639132051,22,41,508
1639132051,2,422,11
2159188693,2,372,18
2159188693,50,98,7
3206363219,2,448,19
3206363219,2,516,53
3206363219,59,36,1559
3258313481,2,305,11
3258313481,24,17,1520

2022-06-15, 07:55   #1654
garambois

"Garambois Jean-Luc"
Oct 2011
France

2×463 Posts

Quote:
 Originally Posted by EdH The problem with cleaning things up manually for posting - that should be 2^372:18. I have made that part of the scripts now, and below is another set, with your requested formatting. I didn't verify anything, but something seems very wrong with this listing! I'm going to let it sit for now and try for a clearer "big picture," maybe tomorrow. As for the programming, the C++ program is a very small part and most of the time is spent in the scripts. I hope to do a lot of work refining how the data are collected. I'll also need to do another full update of all my local sequences. I did add all the new bases below 200, so when I resume work, they will be represented. Latest run: Code: 1051654267,19,22,2102 1051654267,2,468,58 1097038783,2,501,61 1097038783,67,83,11 1129552253,19,18,510 1129552253,2,341,25 1639132051,22,41,508 1639132051,2,422,11 2159188693,2,372,18 2159188693,50,98,7 3206363219,2,448,19 3206363219,2,516,53 3206363219,59,36,1559 3258313481,2,305,11 3258313481,24,17,1520
Thank you very much Edwin for all this work.
The format is perfect like this.

I can still spot an error : the prime number 3206363219 doesn't seem to appear anywhere in the sequence 2^448.
I immediately checked this prime, because it appears in three lines of the list and 516 is not a multiple of 448 and anyway, the indexes are > 1.
So it was very intriguing and very unlikely that this prime would appear in 3 lines.

Edwin, you are already doing a lot for this whole project !
Only take on this extra work if you find interest in it !
But I must admit that you have discovered a very interesting path to explore in my humble opinion.
It's risky to go into this alone, there are many sources of error.
It is very stimulating to work on such an idea with several people and especially, so, we have means to verify.
Thanks Edwin !

2022-06-15, 12:50   #1655
EdH

"Ed Hall"
Dec 2009

22·52·47 Posts

Quote:
 Originally Posted by garambois . . . I can still spot an error : the prime number 3206363219 doesn't seem to appear anywhere in the sequence 2^448. I immediately checked this prime, because it appears in three lines of the list and 516 is not a multiple of 448 and anyway, the indexes are > 1. So it was very intriguing and very unlikely that this prime would appear in 3 lines. . . .
I must have grabbed this from an earlier run. This was part of my original problem:
Code:
base2/2^448.elf:19 .   15006007375820463402452561600162328700320636321975920107434993415977015910414828098588984394591 = 17 * 2389 * 2016739 * 141986827 * 190519331 * 6772722565336945433810924560372709070485550949679612135489377339249
I think I have that fixed. I plan to run base 2 again in a little while. I'll see if 2^448 is absent in those results

 2022-06-15, 13:12 #1656 garambois     "Garambois Jean-Luc" Oct 2011 France 2·463 Posts OK, I understand the problem much better with this example, thanks.
 2022-06-15, 15:52 #1657 chris2be8     Sep 2009 26·37 Posts My first cut would be: Put all primes into a flat file, called primes.txt below. sort primes.duplicates That should get a list of all primes that appear more than once in the list. Then see how many there are and decide how to process them.
 2022-06-15, 17:02 #1658 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 111348 Posts Thanks Chris! I will add this into my study.
 2022-06-15, 18:50 #1659 garambois     "Garambois Jean-Luc" Oct 2011 France 11100111102 Posts Yes, many thanks Chris. I think you are right and the program will be more effective this way. Perhaps even incomparably more effective !
 2022-06-15, 19:29 #1660 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 22×52×47 Posts @Chris: uniq is definitely helping! Another wrinkle has made itself known, that I will have to look into: If you check prime 989948318349327032515056706609970813346117930160196095662320313189860502565627388119428970284861410132787555691, you will find six occurrences across as many sequences: Code: 3^10:3460 5^26:3674 24^57:5346 47^97:3551 70^3:3478 85^2:3467 But, it's because they all merge with 1134. Additionally, all other primes in those terms from then on will be multiple hits as well: Code: 2^4 7 31 107 1747 32869 151597 28936680745039
 2022-06-15, 20:25 #1661 garambois     "Garambois Jean-Luc" Oct 2011 France 39E16 Posts Wow, wow, wow ! It's going to be a lot more complicated than I thought if we have to remove the multiple cases due to mergers. I hadn't thought of that. For the moment, as far as I am concerned, I do not see how to deal with this problem !

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