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Old 2021-03-06, 03:46   #1
grafix
 
Mar 2021

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Default Prime gaps completely searched region

I would like to ask who know which region is completely scaned by first occurence particular prime gaps? See e.g https://faculty.lynchburg.edu/~nicely/gaps/gaps.html
and https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html
is information 2^64 = 18446744073709551616.
Last date is 2018 is any progress since 2018?
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Old 2021-03-06, 10:27   #2
mart_r
 
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Dec 2008
you know...around...

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There hasn't been significant progress since then, mostly because the program for the exhaustive search is rather inefficient for numbers larger than 264.

ATH has searched a little further: https://www.mersenneforum.org/showpo...0&postcount=69. But that's about it for the time being.
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Old 2021-03-07, 20:04   #3
Bobby Jacobs
 
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I look forward to finding the next maximal prime gap over 264.
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Old 2021-03-07, 22:36   #4
grafix
 
Mar 2021

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Default Is possible to cooperate?

I would like to ask if is available on this forum to try scan region out of last prime 18454478540221538011 on next successive gaps occurences?
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Old 2021-03-07, 22:49   #5
grafix
 
Mar 2021

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Default Is possible to cooperate?

If scaned region in 2018 was a little bit more that 18454478540221538011 let me know on which prime stop.
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Old 2021-03-09, 16:16   #6
grafix
 
Mar 2021

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Default First occurences of particular gaps

Because region to 2^64 + 10^16 is scaned by KIM now,
I start today full scanning on gaps bigger as 500 in region above x=2^64 + 10^16 starting prime is 18456744073709551651
Procedure will scan region 10^10 next primes after start prime.
Primary informations will be in the form successive records of gap and all gaps>500:

{n-th prime after start prime, gap, after this prime occured case of gap, number of gap=6 (most frequently in this region)

sample of data output:

{1,35,18456744073709551616,0}

{2,42,18456744073709551651,0}

{4,42,18456744073709551697,0}

{9,68,18456744073709551811,0}

{10,90,18456744073709551879,0}

{18,92,18456744073709552147,1}

{19,114,18456744073709552239,1}

{35,224,18456744073709552987,2}

{164,234,18456744073709558819,4}

{734,268,18456744073709584129,29}

{3038,294,18456744073709687453,149}

{4365,380,18456744073709745917,234}

{12345,408,18456744073710102229,694}

{32132,466,18456744073710981253,1792}

{248204,544,18456744073720578793,13984}

{370315,544,18456744073725976831,20890}

{836968,556,18456744073746658717,47384}

{870826,644,18456744073748158109,49309}

{1110589,644,18456744073758770489,62871}

{1112244,644,18456744073758844303,62971}

{1194365,644,18456744073762495351,67565}

{1387282,644,18456744073771083859,78420}

{1609936,644,18456744073780970719,91031}

Because my procedure count also full frequency of gaps in searching region is slow.
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Old 2021-03-10, 11:58   #7
robert44444uk
 
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Jun 2003
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Quote:
Originally Posted by grafix View Post
Because region to 2^64 + 10^16 is scaned by KIM now,
I start today full scanning on gaps bigger as 500 in region above x=2^64 + 10^16 starting prime is 18456744073709551651
Procedure will scan region 10^10 next primes after start prime.
Primary informations will be in the form successive records of gap and all gaps>500:

{n-th prime after start prime, gap, after this prime occured case of gap, number of gap=6 (most frequently in this region)

sample of data output:


Because my procedure count also full frequency of gaps in searching region is slow.
You might want to work out what your speed of checking is. How many billions of prime gaps per second is a reasonable measure.

At 1e9 prime gaps per second, you would move from 2^64 (=1.84467e19) to 2e19 in about 49 years.

You might also want to consider how many gigs of memory your gaps >500 will take up. The write speed will be a factor that slows you down.

Last fiddled with by robert44444uk on 2021-03-10 at 12:03
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Old 2021-03-10, 12:08   #8
grafix
 
Mar 2021

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Default First occurences of particular gaps time estimation

Because under Wolf conjecture first occurence of gap = 1432 have to be in range from 8.46*10^16 up to 6.52*10^19. We have searched region from 1.84567*10^19 up to 6.52*10^19 (in most pessimistic case). Sill needed about 4.67433*10^19. My computer on primitive Mathematica procedure search 10^13 region per each 48 hours that mean to full scan this method we need 35727 years or 35727 computers in one year. But mayby C++ procedures are 1000 times quicker as Mathematica and 35 computers per 1 year will be enough. But most probable occurence gap 1432 is about 7*10^18 we are much more behind this point and probability increase.

Last fiddled with by grafix on 2021-03-10 at 12:33
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Old 2021-03-10, 12:19   #9
grafix
 
Mar 2021

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Quote:
Originally Posted by robert44444uk View Post
You might want to work out what your speed of checking is. How many billions of prime gaps per second is a reasonable measure.

At 1e9 prime gaps per second, you would move from 2^64 (=1.84467e19) to 2e19 in about 49 years.

You might also want to consider how many gigs of memory your gaps >500 will take up. The write speed will be a factor that slows you down.
I change gap limit from 500 to 1000. These gaps are very rare and do not increase searching time very much because average 1 occurence per hour.

Last fiddled with by grafix on 2021-03-10 at 12:25
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Old 2021-03-13, 15:47   #10
grafix
 
Mar 2021

108 Posts
Default pari gap searching procedure on gaps 1000

This is pari code which is 2.5 times quicker as similar Mathematica code.
Mayby some members are interested in searching next CFC and CNC successive gaps.
skip value can be changed on e.g. 1420 than speed increase yet 1.5 times but new values will be very rare (1 per month I hope).
Good will be coordination. My computer searching up to 2^24+10^16+2*10^13.


{default(breakloop,1);
aa = List(); p1 = nextprime(2^24+10^16+2*10^13);
for(n=1,oo,p2 = precprime(p1 + 1000-1);
if(p1 == p2, p2 = nextprime(p1 + 1000-1); print([p2 - p1, p1]);
listput(aa,[p2 - p1, p1]); p1 = p2, p1 = p2));
Vec(aa)
}

Last fiddled with by grafix on 2021-03-13 at 15:50
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Old 2021-03-14, 23:19   #11
grafix
 
Mar 2021

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Default gap>1000

First gap bigger as 1000 for x>2^64+10^16 is gap 1078 after prime 18456745190157408331
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