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Old 2019-10-11, 20:07   #133
mart_r
 
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Default Data for k=6e15 to 6.5e15

Here's the first occurence data in the range k=6e15 to 6.5e15 and for gaps >= 4000*6:

Code:
4000 6094571062162170
4001 6075920626075277
4002 6014183106259230
4003 6203486197159115
4004 6137452198599068
4005 6185136680377518
4006 6360517752405187
4008 6003948316407272
4009 6329221631091503
4010 6241621066414382
4011 6437932440799447
4012 6064189427508508
4013 6091258905373537
4014 6290713103642573
4015 6011624442750153
4016 6098683312987962
4017 6071685243027793
4018 6265250066459102
4019 6283414188263733
4020 6141871001541490
4021 6432249414755927
4023 6079131996919242
4024 6235220231561513
4025 6019533778987152
4026 6194087059750802
4027 6226570078801793
4028 6053806834581767
4030 6009639339321032
4031 6133398547907137
4032 6052308387984005
4034 6339008746970338
4035 6046297602061560
4036 6165971245882707
4037 6040097294341698
4039 6483441933970673
4040 6030358581920563
4042 6122715569797250
4043 6084819609427240
4045 6064741064731220
4046 6105280065069657
4047 6370174910931673
4048 6047203955033852
4050 6035566050333095
4051 6341241132855102
4052 6304575087486345
4053 6164868853236555
4054 6075053192180928
4055 6092662638064497
4056 6015277975679772
4057 6001400253636420
4058 6040061104229857
4060 6056119854536987
4062 6263538579503278
4063 6325165860124757
4064 6100071331717473
4065 6062778881427940
4066 6241480910046077
4068 6020280443408017
4069 6012115289658033
4070 6296160629463257
4071 6139360540024717
4073 6005091591205472
4074 6114415979573773
4075 6285311374248945
4076 6273699085480472
4077 6324631782081440
4078 6357289430499355
4080 6058920186189490
4081 6052150891125197
4082 6232687723771443
4084 6091687796251498
4085 6230196866005635
4086 6078217615093407
4088 6496775139639537
4090 6119641029856492
4092 6202134162351435
4093 6419296472489465
4095 6163720106533033
4096 6203286774555112
4097 6103435310161558
4099 6325478506209408
4100 6116340465121010
4101 6355525139396417
4102 6174426844259965
4103 6157644909452880
4104 6298423150626903
4105 6162951787510277
4107 6247911818702663
4108 6161298941820012
4109 6491143111771663
4110 6001197641210922
4115 6178419659403778
4118 6096457491930097
4120 6184783264368112
4122 6360908928015520
4123 6100104578451060
4124 6311921669621948
4125 6068766964843665
4127 6425468039803410
4128 6037155878905807
4130 6034609587028502
4132 6349703990951890
4133 6227785213403945
4134 6046360591439598
4135 6135763865589705
4137 6167496502269783
4138 6184512798067860
4139 6312979228278488
4140 6042989127566540
4142 6154125015116090
4143 6010071056539260
4144 6006071589055498
4148 6045475721125802
4150 6143274987321798
4151 6211308403602407
4152 6211187980017218
4153 6115300701726272
4155 6024618880584370
4156 6165521195264137
4158 6089346501853585
4160 6009304072960370
4161 6198884291928232
4162 6177933687337613
4163 6127328267668965
4168 6267472535063905
4169 6083076911732653
4170 6420547446129392
4172 6261910700353485
4173 6262682960653837
4174 6340146887231083
4175 6292281218620518
4177 6157376896724338
4178 6160049855283320
4179 6373535030180763
4180 6133153668695540
4182 6478615816691820
4183 6212849761519677
4184 6011557251426258
4186 6464275260196747
4190 6173448467901958
4191 6053088670191087
4193 6018034505747897
4195 6019058576097432
4197 6295991689062505
4198 6115519475532800
4200 6197019800677087
4202 6297350794498500
4203 6087072764015532
4204 6456922859790263
4205 6130207210578745
4207 6009282685284770
4209 6002620211819773
4210 6298459464206870
4212 6304558953941703
4213 6331264705699825
4214 6070154999354528
4218 6148455048801385
4220 6182248338193338
4222 6064737061669008
4223 6068403816384367
4225 6041758660303985
4227 6285351143257763
4228 6028967627388702
4230 6095374747085445
4232 6308774830833160
4234 6472692620842438
4235 6032979702833583
4237 6223205133275135
4238 6355374326245737
4240 6111908871339233
4241 6040034267138427
4242 6085196195064775
4243 6305783891702710
4245 6044376436470603
4246 6468946760770807
4247 6337105660583213
4248 6409944492128042
4249 6123697391111678
4250 6149335180098092
4252 6151630983571378
4255 6101454388044922
4258 6055790842660410
4260 6236686071294943
4263 6424780177608930
4264 6072146817273063
4265 6272591475644555
4267 6037043089823795
4268 6096265411960257
4270 6377607685513617
4279 6118746171209448
4282 6346321057983923
4284 6404713277248748
4285 6124431663478998
4286 6106864751888057
4290 6264005685032037
4294 6187094564948983
4297 6489194348922498
4300 6000819923220717
4304 6080283436260038
4307 6360859588244695
4310 6336339484988490
4312 6068645852207570
4315 6052524000168543
4318 6148050526109665
4319 6026168702035498
4325 6230389263509745
4329 6323968769952428
4332 6430852847858808
4340 6338869827197252
4342 6144349027455298
4345 6124153943777070
4347 6135802376537215
4348 6276138229374072
4350 6054630814349292
4359 6311689567068163
4361 6315196750271272
4362 6084686902740198
4365 6128337936448283
4370 6342758660193728
4373 6202809716263480
4375 6137085163794373
4380 6250550842918960
4383 6001908527568025
4387 6077019630255373
4389 6499375127978028
4393 6289545895261027
4397 6277187164591478
4398 6489557912371410
4399 6469431967067538
4400 6146318193742877
4403 6232758496784040
4408 6213855204309090
4411 6012601808077337
4412 6035100023021865
4413 6086319365061985
4415 6463032243475532
4416 6279331129379157
4417 6084726611182070
4422 6058991382502105
4429 6055631253850623
4431 6218464321412922
4433 6452357611752337
4438 6257940818504007
4440 6404995105946990
4444 6026965908810528
4450 6093156525023668
4454 6499923087085358
4475 6115604180101397
4480 6201028692692617
4493 6058262748772790
4495 6283997654300398
4500 6432348112790863
4510 6149461651877038
4514 6306079042402963
4516 6193851656374552
4522 6240850066573573
4531 6049027718630057
4535 6392339912840788
4543 6389733723572952
4579 6462678073366078
4580 6207962315678163
4598 6073062207003957
4604 6062440255100688
4605 6371483174248552
4618 6208363632486995
4643 6353259076181440
4648 6237870159894132
4651 6063632091303742
4655 6216475783941955
4667 6409865780683138
4671 6087386050564807
4683 6156812464374737
4684 6062732223084008
4693 6212889974756245
4702 6049374079170973
4730 6081683340020388
4760 6429759578479347
4775 6405308047710198
4811 6426409727841007
4817 6041839013682615
4846 6100407976215147
4890 6158875096649807
4924 6161033965365603
4927 6277201048947448
4971 6201911946722937
5252 6223092271519683
5320 6327092175736258
5507 6436329324869348
Attached is a txt version including the count of single primes in the gap, and also a list of all gaps >= 4000.
Attached Files
File Type: txt 1st occ - sorted - incl #single_primes.txt (7.6 KB, 16 views)
File Type: txt all 4000+ gaps.txt (11.5 KB, 17 views)
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Old 2019-10-11, 20:21   #134
mart_r
 
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In case you haven't updated the list with my previous results yet, attached is also my previous first occurence list (4.5e15 to 5e15) with the count of the single primes.
Attached Files
File Type: txt 1st occ - 45e14-50e14 - incl #single_primes.txt (6.2 KB, 18 views)
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Old 2019-10-13, 19:34   #135
Bobby Jacobs
 
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What is the list of all new maximal twin prime gaps you have found in order?
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Old 2019-10-16, 16:26   #136
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Sorry. I'm traveling at the mo. Do plan to update at some stage
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Old 2019-12-09, 21:03   #137
mart_r
 
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Default 6.5e15 to 6.6e15

I'd like to continue here with the range 6.5e15 to 6.6e15.
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Old 2019-12-24, 16:30   #138
mart_r
 
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Default New results & The search goes on

Results 6.5e15 to 6.6e15 (only new entries):
Code:
gap     k                   # single primes
4333    6533135369970037    609
4464    6558949607080003    637
4498    6532616565216252    650
4565    6571276803702410    684
4593    6556530616266752    670
4599    6562341576429613    705
4612    6509617279610035    712
4632    6517377286609478    721
4965    6513798244437545    711
And taking 6.6e15 to 6.7e15.
Attached Files
File Type: txt output_6500-6600e15_new.txt (268 Bytes, 12 views)
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Old 2019-12-27, 16:10   #139
mart_r
 
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Question faster searching possible?

On a whim, I sat down this morning and within two hours, I built from scratch a twin gap search routine in Pari that's already almost half as fast as the Perl code.
I'm not an expert programmer, so I'm pretty sure with a few adjustments and in a language other than Pari, it should be possible to speed things up considerably.

Here's my crummy code:
Code:
{
k=6422555400000000;
g=3900;
j=832;
u=128;
r=9699690;
z=378675;
v=vector(z);
w=vector(1485);
x=1;
forprime(y=23,887,x*=y);
a=0;
print("twins matrix 13#");
for(b=1,5005,
    if(gcd(6*b-1,30030)==1&&gcd(6*b+1,30030)==1,a+=1;w[a]=6*b)
);
print("twins matrix 19#");
l=0;
for(m=0,r/30030-1,
    for(b=1,a,
        if(gcd(30030*m+w[b]-1,r)==1&&gcd(30030*m+w[b]+1,r)==1,l+=1;v[l]=30030*m+w[b])
    )
);
if(l==z,print("OK, "gettime()"ms"));
print("searching, k="k);
k*=6;
k=r*floor(k/r);
a=1;
i=1;
while(i,
    p=k+v[a];
    a+=1;
    if(a>z,a=1;k+=r);
    if(gcd(p-1,x)==1&&gcd(p+1,x)==1,
        if(ispseudoprime(p-1)&&ispseudoprime(p+1),i=0)
    )
);
while(1,
    h=1;
    while(h,
        a+=j;
        if(a>z,a-=z;k+=r);
        b=0;
        c=k;d=a;
        i=1;
        while(i,
            p=k+v[a];
            a+=1;
            b+=1;
            if(a>z,a=1;k+=r;print("searching, k="k/6));
            if(gcd(p-1,x)==1&&gcd(p+1,x)==1,
                if(ispseudoprime(p-1)&&ispseudoprime(p+1),i=0)
            )
        );
        if(b>u,h=0)
    );
    q=p;
    e=k;f=a;
    i=1;
    k=c;a=d;
    while(i,
        a-=1;
        if(a<1,a=z;k-=r);
        p=k+v[a];
        if(gcd(p-1,x)==1&&gcd(p+1,x)==1,
            if(ispseudoprime(p-1)&&ispseudoprime(p+1),i=0)
        )
    );
    if(q-p>6*g,
        print((q-p)/6" "p/6);
        write("twins_output.txt",(q-p)/6" "p/6,Strchr(13))
    );
    k=e;a=f
)
}
k is the start value (=p/6, as in the current Perl code)
g: gap reporting threshold (likewise)
j: jumping value (see below) - this is manually set, together with u ("undercount" - had that word in mind while choosing the variable, nevermind:)
I used a variable (y=887#/19#) for a gcd routine (trial division) before an ispseudoprime test, as Pari seems to only check for factors up to 101 in the order of magnitude k is in. The 887 here seems to be close to optimal for that purpose. I don't know if later versions of Pari use other parameters for an isprime or ispseudoprime test, so that part of the program is open for discussion.

The approach is pretty straightforward (I guess).
A vector of 378675 integers between 6 and 9699690 is built, where values v are stored for which v-1 and v+1 are coprime to 19#. (I did this in two steps, so instead of 11 secs it only takes 3 secs at the beginning of the program.)
Then the search runs through values of k, with a jump of 832 values of v after a twin prime is found, and after every such jump, if a twin prime is found within another 128 values of v, a backward search picks up to look for a twin prime in the interval that has been jumped. (Sounds a bit funny... oh whatever.) That means, in the worst case, 960 values of v have to be without a twin prime to be detected. The largest gap between 960 values of v is 24972, or 6*4162, whereas the smallest not yet recorded maximal gap is 6*4206, so no maximal gap should be missed.

The current version of my code above duly finds the next two gaps >6*3900 in under two minutes on the PC I'm working on.



---> Possible optimizations within the code?
---> How much faster can this work in Perl or C[++]?
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Old 2019-12-29, 15:09   #140
mart_r
 
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With a precalculated interval of 23# (7,952,175 values of v for which a twin prime mod 23# is admissible), and a Mod(3,n)^(n-1) test instead of ispseudoprime(n), I was able to get 54% of the speed of the Perl program.

From what I gather, the customized prime tests in Perl or C are (much?) more efficient than in Pari.

Currently the throughput on my fast PC is about 27e6 k/s/core, and 10.9e6 k/s/core on my laptop, where I get 5.90e6 k/s/core with my own Pari code.

I'd like to continue the search, but before I do that, I'd like to know how much faster the program can get.
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Old 2019-12-29, 22:12   #141
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Quote:
Originally Posted by mart_r View Post
With a precalculated interval of 23# (7,952,175 values of v for which a twin prime mod 23# is admissible), and a Mod(3,n)^(n-1) test instead of ispseudoprime(n), I was able to get 54% of the speed of the Perl program.

From what I gather, the customized prime tests in Perl or C are (much?) more efficient than in Pari.

Currently the throughput on my fast PC is about 27e6 k/s/core, and 10.9e6 k/s/core on my laptop, where I get 5.90e6 k/s/core with my own Pari code.

I'd like to continue the search, but before I do that, I'd like to know how much faster the program can get.
See: https://www.mersenneforum.org/showthread.php?t=24438

You might get more throughput in Pari/GP by aligning your n.
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Old 2019-12-30, 09:26   #142
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Regarding an implementation in C:

I slightly modified Tomás Oliveira e Silva's fast_sieve.c from 2010 in order to search for gaps between twin primes (see attachment).
It seems to be pretty fast already (around 100e6 k/s/core). Perhaps this could be used as a base for further improvements.

Usage example:
Code:
kmin=6422555400000000
kmax=6422560000000000
mingap=3000

./twingaps -k1 $kmin -k2 $kmax -mingap $mingap >> logfile.txt
Attached Files
File Type: zip twingaps.zip (10.0 KB, 19 views)

Last fiddled with by Thomas11 on 2019-12-30 at 09:30
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Old 2019-12-31, 14:16   #143
mart_r
 
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Quote:
Originally Posted by Thomas11 View Post
Regarding an implementation in C:

I slightly modified Tomás Oliveira e Silva's fast_sieve.c from 2010 in order to search for gaps between twin primes (see attachment).
It seems to be pretty fast already (around 100e6 k/s/core). Perhaps this could be used as a base for further improvements.

Usage example:
Code:
kmin=6422555400000000
kmax=6422560000000000
mingap=3000

./twingaps -k1 $kmin -k2 $kmax -mingap $mingap >> logfile.txt
I'm afraid I can't get the program to run.
Code:
// assumptions: Linux, GNU libc, C99-capable compiler
Apparently I have neither of that. I tried to install a C compiler once which didn't work.
Could you provide a Win executable? As long as it's no trouble, of course.




Quote:
Originally Posted by paulunderwood View Post
See: https://www.mersenneforum.org/showthread.php?t=24438

You might get more throughput in Pari/GP by aligning your n.
Hmm, that doesn't seem to work too well for me, and gives different results.




Meanwhile, here's the data for 6.6e15 to 6.684e15:
Code:
gap     k                   # single primes
4206    6650801286755762    619
4320    6603223408106523    657
4359    6629775407330098    628
4450    6628852021999928    681
4462    6601637753498165    698
4624    6669047311697568    711
4649    6602043547162233    703
4658    6678195146158970    709
4695    6622871858769833    673
5211    6647995738937662    801
Now 4206 is there, the next smallest gap TBD is 4239 (i.e. 25434).

BTW, a quad search specifically for (p+0, p+2, p+25434, p+25436) would be faster than the twin search, but probably slower than the twin search in general depending on how many different gaps we want to look at (and maybe duplicating work). Also depends on how much the twin search can be sped up with rising smallest gap. Any thoughts?
Attached Files
File Type: txt output_6600-6684e12_new.txt (295 Bytes, 13 views)
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