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-   -   Report top-5000 primes for all k<=1001 (https://www.mersenneforum.org/showthread.php?t=9891)

 TimSorbet 2008-08-18 22:33

[quote=gd_barnes;139481]Oh, wow! Congrats on a nice pair! If I had to guess, I doubt there are 2 primes so close together for ANY n>200K for all values of k<=1001.

If you have a little time and are a little bored, see what the closest 2 n-values together are for primes on the top-5000 site where k<=1001 and n>200K.[/quote]
507*2^217588-1 and 495*2^217588-1 are both prime, as are 891-2^261255 and 313*2^261255-1. These are the closest in n-value through n=600K (what's on the Prime Search page anyway). The next smallest n gap in the n=500K range is 25*2^587585-1 and 301*2^587635-1.

 gd_barnes 2008-08-19 09:46

[quote=Mini-Geek;139488]507*2^217588-1 and 495*2^217588-1 are both prime, as are 891-2^261255 and 313*2^261255-1. These are the closest in n-value through n=600K (what's on the Prime Search page anyway). The next smallest n gap in the n=500K range is 25*2^587585-1 and 301*2^587635-1.[/quote]

Interesting. So yours are the closest together for n>265K. That's remarkable for n>530K!

Of course Primesearch does not have a lot of primes for k<300 and is missing some for k>300 that are reserved by others there but found by us. You'd have to use a recent k<300 page (I keep one updated at all times) or try searching the top-5000 site to know for sure, which would be very time consuming.

Gary

 gd_barnes 2008-08-19 09:57

955*2^521891-1 is prime

 TimSorbet 2008-08-19 11:12

[quote=gd_barnes;139505]Interesting. So yours are the closest together for n>265K. That's remarkable for n>530K!

Of course Primesearch does not have a lot of primes for k<300 and is missing some for k>300 that are reserved by others there but found by us. You'd have to use a recent k<300 page (I keep one updated at all times) or try searching the top-5000 site to know for sure, which would be very time consuming.

Gary[/quote]
My first idea was to look at the top-5000 site, but it has so many primes of so many forms that just limiting it to riesel base 2 k < 1002 would be difficult, not to mention it wouldn't have the full list of < #5000, which would be needed to look down to n > 200K.
Here's the top of the CSV file I worked up to see the gaps:
[code] 261255 0
217588 0
464001 1
458098 1
234304 1
343303 2
314000 2
307794 2
286103 2
246354 2
215859 2
357331 3
287537 3
215614 3
374455 4
278054 4
259537 4
251754 4
222606 4[/code]So, mine's not the smallest n gap n>265K, I was just pointing out the two that had identical n's. Mine's the smallest [B]n-gap[/B] for n>464001, but for the smallest [B]size[/B] (# of digits and what they are) difference, you'd have to check the k values and multiply the number out and everything.
But yeah, regardless of past primes, that's quite an amazingly small gap, and I'm glad I got it. :smile:

 gd_barnes 2008-08-19 20:22

[quote=Mini-Geek;139507]
But yeah, regardless of past primes, that's quite an amazingly small gap, and I'm glad I got it. :smile:[/quote]

For one of our most faithful searchers, I'm glad you got it too. I know you had some dormant reservations for quite a while. As is the nature of randomness, everything evens out in the long run. In this case, had you not chosen to take the higher n-range with all n-values at the higher fftlen, you likely wouldn't have gotten the nice pair or 3 within just an n=600 range.

Gary

 TimSorbet 2008-08-19 22:05

[quote=gd_barnes;139522]For one of our most faithful searchers, I'm glad you got it too. I know you had some dormant reservations for quite a while. As is the nature of randomness, everything evens out in the long run. In this case, had you not chosen to take the higher n-range with all n-values at the higher fftlen, you likely wouldn't have gotten the nice pair or 3 within just an n=600 range.

Gary[/quote]
Yep, the randomness of primes is annoying at times and so so much fun at other times (depending on how it's treating you, of course :smile:). The gap between the 3 is actually just n=120. It's part of a n=600 range I reserved, as you know and pointed out, but the distance between the first of these primes and the most recent is only 120.
Well, it makes up for that mistake Anon made a while back that gipped me out of 3 primes (he didn't notice my reservation and sent a range which I partially reserved to an LLRnet server, which promptly returned 3 primes in an n=64 part of the n=100 range I should've had). Those primes were:
[code]615*2^419082-1 AES
451*2^419059-1 AES
831*2^419018-1 AES[/code]Oh well, I got a nice triplet of primes now, and they're a lot bigger! :smile:

 gd_barnes 2008-08-20 09:50

465*2^522168-1 is confirmed prime

817*2^522253-1 is prime

 gd_barnes 2008-08-22 15:16

user=Beyond_Free-DC
[20/08/2008 02:19:01 PM]
521*2^522422-1 is prime! Time : 5697.0 sec.

 gd_barnes 2008-08-26 08:37

After a bit of a dry period on drive 1:

595*2^524229-1 is prime

 gd_barnes 2008-08-26 20:11

711*2^524387-1 is prime

 gd_barnes 2008-08-28 07:22

Here's one from the lowest k in the 1st drive:

401*2^524862-1 is prime

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