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2019-12-21, 10:02   #23
robert44444uk

Jun 2003
Oxford, UK

2·7·137 Posts

Quote:
 Originally Posted by storm5510 I did the code test earlier. I stripped the code down to what was necessary, compiled it and ran the test. It did far better than I was expecting. Check out the screen capture. The floating-point numbers and the ends are start time and end time. Take away some digits at both ends and use what is near the decimal point. 25.44 seconds.
So danaj's suite of prime functions in perl Math::Prime::Util is 25 times faster - time to change to perl !!

If its any help I am not computer literate and did not start on perl before my 65th birthday

2019-12-21, 10:03   #24
robert44444uk

Jun 2003
Oxford, UK

35768 Posts

Quote:
 Originally Posted by sweety439 Well....
Well?

2019-12-21, 12:22   #25
storm5510
Random Account

Aug 2009
U.S.A.

22×11×41 Posts

Quote:
 Originally Posted by robert44444uk So danaj's suite of prime functions in perl Math::Prime::Util is 25 times faster - time to change to perl !! If its any help I am not computer literate and did not start on perl before my 65th birthday
Perl. Serously, I doubt I could learn enough of it to use it. Then again, perhaps I could. I found their site on the web. It has, what they call, ActiveStatePerl. Another is Strawberry. I am not sure which to look at.

Computer literate: After 32 years of it, I like to think I am. I have seen the evolution to where it is now. I never buy a new machine from a shelf. I build my own. None have ever gave me any problems.

 2019-12-22, 11:12 #26 robert44444uk     Jun 2003 Oxford, UK 2×7×137 Posts I use Strawberry Perl, which is the perl environment for Windows.
2019-12-22, 13:56   #27
storm5510
Random Account

Aug 2009
U.S.A.

22·11·41 Posts

Quote:
 Originally Posted by robert44444uk I use Strawberry Perl, which is the perl environment for Windows.
Thanks. I will give it a look.

Quote:
 Originally Posted by robert44444uk ...My best guess is that the smaller of the two primes that make up the first instance gap of length exactly 1,432 is less than 100,000,000,000,000,000,000.
I have been running some of these with what I wrote. I started at 5e19. All the gaps I am seeing are < 400.

2019-12-22, 15:39   #28
robert44444uk

Jun 2003
Oxford, UK

2·7·137 Posts

Quote:
 Originally Posted by storm5510 Thanks. I will give it a look. I have been running some of these with what I wrote. I started at 5e19. All the gaps I am seeing are < 400.
The first few gaps >400, 1st column is the nth gap after 5e19. Time elapsed for the first million gaps was 100 secs. There were no gaps >=600.The first gap at the 600 level is that following 50000000000211284873

Code:
8645 50000000000000387671 50000000000000388119 448
34553 50000000000001565667 50000000000001566087 420
49325 50000000000002234033 50000000000002234463 430
62247 50000000000002821217 50000000000002821617 400
77934 50000000000003533853 50000000000003534279 426
78922 50000000000003579203 50000000000003579723 520
89175 50000000000004045967 50000000000004046373 406
103428 50000000000004694897 50000000000004695321 424
107476 50000000000004883687 50000000000004884101 414
108772 50000000000004941917 50000000000004942409 492
113676 50000000000005167523 50000000000005167941 418
132173 50000000000006006213 50000000000006006681 468
154035 50000000000006985029 50000000000006985449 420
164841 50000000000007476039 50000000000007476449 410
174248 50000000000007904219 50000000000007904621 402
177893 50000000000008066247 50000000000008066661 414
182013 50000000000008251143 50000000000008251547 404
235214 50000000000010665303 50000000000010665707 404
242998 50000000000011017149 50000000000011017557 408
250508 50000000000011356541 50000000000011356949 408
304099 50000000000013792623 50000000000013793043 420
354501 50000000000016067159 50000000000016067579 420
365911 50000000000016590869 50000000000016591277 408
369508 50000000000016751999 50000000000016752431 432
389618 50000000000017667927 50000000000017668379 452
390675 50000000000017715717 50000000000017716137 420
392445 50000000000017794781 50000000000017795187 406
392640 50000000000017803641 50000000000017804069 428
395579 50000000000017938281 50000000000017938691 410
398647 50000000000018081141 50000000000018081561 420
410892 50000000000018637337 50000000000018637749 412
421815 50000000000019136829 50000000000019137261 432
424822 50000000000019274423 50000000000019274831 408
433663 50000000000019672697 50000000000019673181 484
458278 50000000000020787267 50000000000020787671 404
458609 50000000000020801897 50000000000020802317 420
478131 50000000000021687383 50000000000021687797 414
491265 50000000000022280321 50000000000022280787 466
496565 50000000000022518561 50000000000022519037 476
501250 50000000000022735853 50000000000022736253 400
508640 50000000000023075153 50000000000023075669 516
516120 50000000000023416289 50000000000023416691 402
519705 50000000000023580951 50000000000023581367 416
536596 50000000000024340619 50000000000024341129 510
537467 50000000000024378443 50000000000024378879 436
539029 50000000000024448317 50000000000024448779 462
589370 50000000000026733123 50000000000026733563 440
598449 50000000000027141153 50000000000027141591 438
624806 50000000000028331049 50000000000028331537 488
629368 50000000000028537841 50000000000028538267 426
632284 50000000000028673289 50000000000028673747 458
649090 50000000000029444103 50000000000029444507 404
665095 50000000000030174551 50000000000030174989 438
668424 50000000000030328401 50000000000030328803 402
681485 50000000000030913853 50000000000030914259 406
690803 50000000000031334291 50000000000031334699 408
703878 50000000000031928487 50000000000031928901 414
722278 50000000000032770277 50000000000032770689 412
733638 50000000000033284319 50000000000033284727 408
737072 50000000000033442241 50000000000033442731 490
743547 50000000000033735867 50000000000033736283 416
765778 50000000000034739901 50000000000034740479 578
766917 50000000000034791089 50000000000034791491 402
773953 50000000000035112827 50000000000035113253 426
774016 50000000000035116127 50000000000035116553 426
831195 50000000000037712319 50000000000037712733 414
837834 50000000000038012807 50000000000038013357 550
852115 50000000000038651469 50000000000038651891 422
888621 50000000000040311239 50000000000040311681 442
890510 50000000000040396841 50000000000040397261 420
903100 50000000000040962369 50000000000040962813 444
908429 50000000000041205581 50000000000041206013 432
912511 50000000000041391719 50000000000041392151 432
913646 50000000000041441577 50000000000041442051 474
956618 50000000000043377591 50000000000043378041 450
961002 50000000000043576733 50000000000043577163 430
961491 50000000000043598577 50000000000043598993 416
962494 50000000000043643427 50000000000043643871 444
999780 50000000000045334157 50000000000045334557 400
------
4657132 50000000000211284873 50000000000211285473 600
------
5621202 50000000000255031019 50000000000255031653 634
------
5946444 50000000000269759343 50000000000269760033 690

Last fiddled with by robert44444uk on 2019-12-22 at 15:53

2019-12-22, 15:56   #29
storm5510
Random Account

Aug 2009
U.S.A.

180410 Posts

Quote:
 Originally Posted by robert44444uk ...The first few gaps >400, 1st column is the nth gap after 5e19. There were no gaps >=600
I compared what you have here with what I have. I was able to match the first six of yours. I will never be able to run as fast as yours. At least, it is accurate.

I download and installed Strawberry and looked at some of the examples. I wish it had a really good front-end for code writing.

2019-12-23, 09:01   #30
robert44444uk

Jun 2003
Oxford, UK

2·7·137 Posts

Quote:
 Originally Posted by storm5510 I compared what you have here with what I have. I was able to match the first six of yours. I will never be able to run as fast as yours. At least, it is accurate. I download and installed Strawberry and looked at some of the examples. I wish it had a really good front-end for code writing.
The first thing to do is to learn how to download additional modules via the command prompt using the CPAN command. Typical modules that I use are:

Timer::Runtime
Math::GMPz
Math::BigFloat
Math::Prime::Util
File::Slurp

With these you can really motor with prime finding and gaps

I learnt some of the basics through https://perlmaven.com/. There are other sites such as https://www.learn-perl.org . Specific enquiries on "how to" can be found through Google searches or through https://www.perlmonks.org/, but with the last of these, if you ask a question, they get pretty angry if it is something you could have found through a search or by "learning by doing".

You can always adapt code you find in the Prime Search Group posts, which is what I do!

2019-12-24, 14:39   #31
storm5510
Random Account

Aug 2009
U.S.A.

22·11·41 Posts

Quote:
 Originally Posted by robert44444uk The first few gaps >400, 1st column is the nth gap after 5e19. Time elapsed for the first million gaps was 100 secs. There were no gaps >=600.The first gap at the 600 level is that following 50000000000211284873 Code: 8645 50000000000000387671 50000000000000388119 448 34553 50000000000001565667 50000000000001566087 420 49325 50000000000002234033 50000000000002234463 430 62247 50000000000002821217 50000000000002821617 400 77934 50000000000003533853 50000000000003534279 426 78922 50000000000003579203 50000000000003579723 520 89175 50000000000004045967 50000000000004046373 406 103428 50000000000004694897 50000000000004695321 424 107476 50000000000004883687 50000000000004884101 414 108772 50000000000004941917 50000000000004942409 492 113676 50000000000005167523 50000000000005167941 418 132173 50000000000006006213 50000000000006006681 468 154035 50000000000006985029 50000000000006985449 420 164841 50000000000007476039 50000000000007476449 410 174248 50000000000007904219 50000000000007904621 402 177893 50000000000008066247 50000000000008066661 414 182013 50000000000008251143 50000000000008251547 404 235214 50000000000010665303 50000000000010665707 404 242998 50000000000011017149 50000000000011017557 408 250508 50000000000011356541 50000000000011356949 408 304099 50000000000013792623 50000000000013793043 420 354501 50000000000016067159 50000000000016067579 420 365911 50000000000016590869 50000000000016591277 408 369508 50000000000016751999 50000000000016752431 432 389618 50000000000017667927 50000000000017668379 452 390675 50000000000017715717 50000000000017716137 420 392445 50000000000017794781 50000000000017795187 406 392640 50000000000017803641 50000000000017804069 428 395579 50000000000017938281 50000000000017938691 410 398647 50000000000018081141 50000000000018081561 420 410892 50000000000018637337 50000000000018637749 412 421815 50000000000019136829 50000000000019137261 432 424822 50000000000019274423 50000000000019274831 408 433663 50000000000019672697 50000000000019673181 484 458278 50000000000020787267 50000000000020787671 404 458609 50000000000020801897 50000000000020802317 420 478131 50000000000021687383 50000000000021687797 414 491265 50000000000022280321 50000000000022280787 466 496565 50000000000022518561 50000000000022519037 476 501250 50000000000022735853 50000000000022736253 400 508640 50000000000023075153 50000000000023075669 516 516120 50000000000023416289 50000000000023416691 402 519705 50000000000023580951 50000000000023581367 416 536596 50000000000024340619 50000000000024341129 510 537467 50000000000024378443 50000000000024378879 436 539029 50000000000024448317 50000000000024448779 462 589370 50000000000026733123 50000000000026733563 440 598449 50000000000027141153 50000000000027141591 438 624806 50000000000028331049 50000000000028331537 488 629368 50000000000028537841 50000000000028538267 426 632284 50000000000028673289 50000000000028673747 458 649090 50000000000029444103 50000000000029444507 404 665095 50000000000030174551 50000000000030174989 438 668424 50000000000030328401 50000000000030328803 402 681485 50000000000030913853 50000000000030914259 406 690803 50000000000031334291 50000000000031334699 408 703878 50000000000031928487 50000000000031928901 414 722278 50000000000032770277 50000000000032770689 412 733638 50000000000033284319 50000000000033284727 408 737072 50000000000033442241 50000000000033442731 490 743547 50000000000033735867 50000000000033736283 416 765778 50000000000034739901 50000000000034740479 578 766917 50000000000034791089 50000000000034791491 402 773953 50000000000035112827 50000000000035113253 426 774016 50000000000035116127 50000000000035116553 426 831195 50000000000037712319 50000000000037712733 414 837834 50000000000038012807 50000000000038013357 550 852115 50000000000038651469 50000000000038651891 422 888621 50000000000040311239 50000000000040311681 442 890510 50000000000040396841 50000000000040397261 420 903100 50000000000040962369 50000000000040962813 444 908429 50000000000041205581 50000000000041206013 432 912511 50000000000041391719 50000000000041392151 432 913646 50000000000041441577 50000000000041442051 474 956618 50000000000043377591 50000000000043378041 450 961002 50000000000043576733 50000000000043577163 430 961491 50000000000043598577 50000000000043598993 416 962494 50000000000043643427 50000000000043643871 444 999780 50000000000045334157 50000000000045334557 400 ------ 4657132 50000000000211284873 50000000000211285473 600 ------ 5621202 50000000000255031019 50000000000255031653 634 ------ 5946444 50000000000269759343 50000000000269760033 690
It looks like you started at 5e19. I never went that high. I suspect that if you were to put long-haul file I/O and configuration saving in your code, you would not get this sort of speed. One is always at the mercy of the OS. I wrote mine to save everything it finds.

I gave it a try. I was again able to match the first dozen of your results. Yours sort of threw me. You have your larger digit on the right where mine is on the left.

Code:
50000000000000388119, 50000000000000387671, 448
50000000000001566087, 50000000000001565667, 420
50000000000002234463, 50000000000002234033, 430
50000000000002821617, 50000000000002821217, 400
50000000000003534279, 50000000000003533853, 426
50000000000003579723, 50000000000003579203, 520
50000000000004046373, 50000000000004045967, 406
50000000000004695321, 50000000000004694897, 424
50000000000004884101, 50000000000004883687, 414
50000000000004942409, 50000000000004941917, 492
50000000000005167941, 50000000000005167523, 418
50000000000006006681, 50000000000006006213, 468
Regarding Perl. This will be a work-in-progress for quite some time to come.

Last fiddled with by storm5510 on 2019-12-24 at 14:40

 2019-12-24, 17:08 #32 storm5510 Random Account     Aug 2009 U.S.A. 22·11·41 Posts An addendum. I really jacked the numbers up. I think the correct expression would be 1e46. It is a "1" with 46 zero's behind it. Gaps over 1,000 are scarce even at this level. The largest I have seen in the data file is 1,292. The really vast majority are from 500 to 800.
2019-12-24, 23:04   #33
storm5510
Random Account

Aug 2009
U.S.A.

22·11·41 Posts

Quote:
 Originally Posted by robert44444uk ...The smallest gap where we do not know the first instance is 1,432. The smallest prime we know that this gap exists is 84,218,359,021,503,505,748,941 but there are likely to be many smaller instances with this gap size. My best guess is that the smaller of the two primes that make up the first instance gap of length exactly 1,432 is less than 100,000,000,000,000,000,000...
I have found "an" instance of 1,432. I had to start at 1e51 to do it. Are there instances of this gap in lower primes? I would say yes. Finding it could be time consuming...

Code:
1000000000000000000000000000000000000000000001871691
1000000000000000000000000000000000000000000001873123
1432
At 1e49, I started seeing some gaps over 1,000, but not many. I simply kept adding zero's.

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