Prime Gap News

[henryzz]

Have just submitted 177 new gaps of which 23 are new gap lengths(assuming I counted correctly). This might take a while for the queue to clear.

How deep does Danaj's surround_primes function sieve for gaps of length 150000? Also is there a way of determining what % of time is spent sieving vs prp testing by this function? I am wondering where the cross-over point is for switching to testing using pfgw.

[SethTro]

Originally Posted by henryzz

Have just submitted 177 new gaps of which 23 are new gap lengths(assuming I counted correctly). This might take a while for the queue to clear.

How deep does Danaj's surround_primes function sieve for gaps of length 150000? Also is there a way of determining what % of time is spent sieving vs prp testing by this function? I am wondering where the cross-over point is for switching to testing using pfgw.

I believe surround_primes uses

def sieve_depth_pg(log2n):
  log2log2n = int(math.ceil(math.log2(log2n)))
  return log2n * (log2n >> 5) * int(log2log2n * 1.5) >> 1

I've personally found the cross-over point for pfgw to be around ~8000 bits but I haven't profiled the overhead from Danaj's script.

I believe % time in sieve is very small (0.1% - 1%).

[robert44444uk]

For very large gaps I used the sieve_primes routine and then pfgw. Here is a ready to use perl program - clearly change your variables. It produces a pfgw-ready file.

#!/usr/bin/env perl

# takes a specific A - the best of a range of A already tested for candidates of type A*p#/46410 and sieves deep. 1tn takes about 14 hours. 50m takes 70 minutes.

use warnings;
use strict;
use Math::BigFloat lib=>"GMP";
use Math::Prime::Util qw/:all/;
use Math::GMPz;
use feature ':5.10';
use File::Slurp;
use ntheory ":all";
$| = 1;

my $mult = 1787;
my $prim = 80021;
my $range = 1_021_020;
my $sievelim = 1_000_000_000_000; 
my $div = 46410;

my $fact = Math::GMPz->new("".primorial($prim));
my $filetitle = "ABC"." ".$mult."*".$prim."#"."/".$div."+".q[$a];

my $n = $mult*$fact/$div; 
my @f = Math::Prime::Util::GMP::sieve_primes($n-($range/2), $n+($range/2), $sievelim); 

foreach my $item (@f) {
    $item = $item-$n;
}

#say scalar(@f);
#print "@f\n";

my $filename = '1787to1tn.txt';
open(my $fh, '>', $filename) or die "Could not open file '$filename' $!";
print $fh "$filetitle\n";
print $fh join "\n", @f;
close $fh;
print "done\n";

[SethTro]

Originally Posted by robert44444uk

For very large gaps I used the sieve_primes routine and then pfgw. Here is a ready to use perl program - clearly change your variables. It produces a pfgw-ready file.

I can't run perl right now on my computer, would you mind sharing what the result looks like for a 17 * 40009#/30030 +- 4000 also a rough runtime (Xminutes). That would be much appreciated.

[robert44444uk]

Originally Posted by SethTro

I can't run perl right now on my computer, would you mind sharing what the result looks like for a 17 * 40009#/30030 +- 4000 also a rough runtime (Xminutes). That would be much appreciated.

I ran the program - it took about 2 seconds to produce the results below. It needs code in there to sort the file by absolute value of remaining candidates.

My strategy looked at a range of 1 million and sieved lightly over many $mult (typically 1 to 20000) to get the candidates that left the smallest remaining values for pfgw. I had a separate program for that.

ABC 17*40009#/30030+$a
-4000
-3900
-3840
-3750
-3744
-3640
-3564
-3528
-3328
-3300
-3168
-3150
-3072
-2880
-2808
-2800
-2772
-2640
-2560
-2500
-2464
-2430
-2268
-2184
-2178
-2160
-2112
-2100
-2080
-2058
-2028
-2002
-1980
-1944
-1890
-1872
-1848
-1800
-1792
-1782
-1690
-1540
-1452
-1408
-1404
-1344
-1320
-1260
-1210
-1200
-1188
-1152
-1144
-1134
-1120
-1092
-1014
-1008
-990
-960
-924
-910
-900
-864
-858
-840
-832
-810
-780
-768
-700
-640
-624
-600
-594
-550
-528
-490
-480
-468
-462
-448
-432
-420
-378
-330
-312
-288
-252
-250
-234
-180
-168
-160
-144
-132
-130
-120
-112
-108
-78
-64
-48
-40
-28
-22
-18
18
20
30
36
48
56
60
66
90
108
126
128
156
162
168
192
216
242
288
308
360
396
420
450
480
486
500
540
546
560
648
650
660
702
750
840
882
896
960
990
1008
1080
1100
1152
1176
1200
1248
1250
1320
1352
1386
1430
1452
1500
1512
1560
1728
1782
1820
1890
1980
2058
2100
2156
2160
2178
2268
2288
2310
2352
2430
2450
2520
2592
2640
2688
2730
2880
2912
2916
2940
2970
3150
3168
3200
3276
3300
3402
3510
3528
3696
3780
3822
3840
3872
3888

[SethTro]

Originally Posted by robert44444uk

I ran the program - it took about 2 seconds to produce the results below. It needs code in there to sort the file by absolute value of remaining candidates.

My strategy looked at a range of 1 million and sieved lightly over many $mult (typically 1 to 20000) to get the candidates that left the smallest remaining values for pfgw. I had a separate program for that.

You are going to love my prime-gap code; It does similar things but is very fast and has good debug info to help choose constants.

[SethTro]

Most of my work is on a single K=P#/d (see how these form lines on this graph)

I was curious which primorial had the most records so I wrote this ugly command.

$ sqlite3 gaps.db 'SELECT startprime FROM gaps' | sed -n 's!^[^/]*[^0-9/]\([0-9]\+#\).*!\1!p' | sort | uniq -c | sort -nr | awk '$1 > 200 { ("sqlite3 gaps.db \"SELECT discoverer, count(*) FROM gaps WHERE startprime like \\\"%" $2 "%\\\" GROUP BY 1 ORDER BY 2 DESC LIMIT 1\"") | getline freq; print($0 "\t" freq); }'
   1361 4441#    S.Troisi|1310
    962 9439#    Jacobsen|868
    925 6761#    Jacobsen|913
    786 49999#   Rosnthal|786
    739 4139#    Jacobsen|717
    617 2221#    S.Troisi|537
    579 9973#    Rosnthal|525
    535 10343#   Jacobsen|528
    400 6199#    DStevens|370
    376 6661#    S.Troisi|322
    372 5003#    Jacobsen|344
    351 9629#    RobSmith|269
    350 10709#   RobSmith|334
    276 4409#    Rosnthal|229
    262 23197#   RobSmith|258
    240 5333#    S.Troisi|219
    228 18481#   PierCami|226
    223 20963#   RobSmith|221
    217 8887#    S.Troisi|199
    216 3331#    Jacobsen|186
    211 23189#   RobSmith|209
    206 5557#    S.Troisi|174

[SethTro]

I created a colab script to plot the improvements to the records over the last year and turn it into a animation similar to mersenne.ca

[robert44444uk]

Originally Posted by SethTro

I created a colab script to plot the improvements to the records over the last year and turn it into a animation similar to mersenne.ca

Love it

[SethTro]

Let's do some end of year celebration of progress. 🥳🎁📅🎉🎊

I'll update these in late December
* by year merit status
* prime gap animation

I calculated
* Number of updates this year >12,000!
* Largest merit this year (Seth's 38.0479)
* largest gap found this year (Martin's 1898630)
* Smallest update to a record (#173, Gapcoint +0.00025 merit)
* Smallest gap updated this year (Rob Smith's 1906 merit 26.7)

I still need to find
* largest update to a record (Probably 122542 14.5 -> 28.1 merit)
* largest gap with an update
* Total merit improved this year

Any other fun statistics people would like me to calculate?

Humblebrag: I submitted 1340 records for 4441# and 930 for 2221# with an average merit of 20.8 and 24.37 respectively.

$ sqlite3 gaps.db 'SELECT startprime FROM gaps' | sed -n 's!^[^/]*[^0-9/]\([0-9]\+#\).*!\1!p' | sort | uniq -c | sort -nr | awk '$1 > 200 { ("sqlite3 gaps.db \"SELECT discoverer, count(*),round(max(merit),2),round(avg(merit),2) FROM gaps WHERE startprime like \\\"%" $2 "%\\\" GROUP BY 1 ORDER BY 2 DESC LIMIT 1\"") | getline freq; print($0 "\t" freq); }'

count primorial  Who|HowManyTheydid|MaxMerit|AvgMerit
   1391 4441#    S.Troisi|1340|28.98|20.82
   1002 2221#    S.Troisi|930|33.03|24.37
    962 9439#    Jacobsen|868|24.27|16.32
    923 6761#    Jacobsen|911|25.2|17.67
    786 49999#    Rosnthal|786|25.86|12.62
    736 4139#    Jacobsen|714|27.0|20.05
    579 9973#    Rosnthal|525|25.17|16.41
    535 10343#    Jacobsen|528|25.55|16.37
    400 6199#    DStevens|370|27.27|18.99
    376 6661#    S.Troisi|322|27.31|18.02
    371 5003#    Jacobsen|343|26.42|19.71
    351 9629#    RobSmith|269|26.52|16.87
    276 4409#    Rosnthal|229|27.07|19.95
    228 18481#    PierCami|226|19.12|12.15

[SethTro]

I updated two tables on the lists site

"Top 20 gaps by merit" is now "Top 20 largest gaps ordered by merit"
https://primegap-list-project.github...gaps-by-merit/

"Top 20 overall merits" is now "Top 20 overall merits [plus 50th,100th,200th,...,500th]"
https://primegap-list-project.github...verall-merits/

I also added a weighted average line to the merit plot on cloudygo and min_x, max_x input.
https://primegaps.cloudygo.com/graphs?max=70000
You can see where the focused efforts from gapcoin & S.Troisi have increased average merit in the neighborhood of 5000-6000 and 45000-52000