20221119, 08:46  #100 
Jan 2007
Germany
1152_{8} Posts 
10^16 complete
Searching up to 10^16 now complete. No new gap record, but one near missing. (k=322493, 9911752981863911)
Continue with triplets https://www.mersenneforum.org/showthread.php?t=28223 Last fiddled with by Cybertronic on 20221119 at 08:46 
20221124, 21:20  #101  
May 2018
2^{3}×5×7 Posts 
Quote:


20221124, 21:28  #102 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{2}·5·7·79 Posts 

20221213, 08:56  #103 
Jan 2007
Germany
2·3·103 Posts 
Status 13th Dec 2022
Up to 1.03e16 ( and double check ) done.
See zipfile for gaps and open gaps Last fiddled with by Cybertronic on 20221213 at 09:15 
20230102, 22:51  #104 
Dec 2008
you know...around...
2^{4}×53 Posts 
An update
New first occurrence gaps between prime quadruplets, 1030e13 to 1278e13, see attachment.
One new maximal gap: 334884 (*30)  see also https://pzktupel.de/RecordGaps/GAP04.php (Thanks Norman! ) Smallest first occurrence not yet found: 171032 (*30). 
20230109, 19:43  #105  
Dec 2008
you know...around...
2^{4}×53 Posts 
Statistics that (almost surely) noone had considered yet
Quote:
Code:
Column A: number of gaps found <= maximal gap Column B: number of all admissible gaps <= maximal gap Column C: ratio Taken at all points < 1e16 where a new maximal gap was found. A B C 1 2 50.00% 2 15 13.33% 3 16 18.75% 6 28 21.43% 7 52 13.46% 8 90 8.89% 18 153 11.76% 20 213 9.39% 32 215 14.88% 38 316 12.03% 44 392 11.22% 61 575 10.61% 105 686 15.31% 156 705 22.13% 158 952 16.60% 235 1347 17.45% 263 1355 19.41% 309 1705 18.12% 327 1987 16.46% 419 2251 18.61% 588 2725 21.58% 658 3758 17.51% 956 3787 25.24% 1125 4076 27.60% 1185 4223 28.06% 1258 4536 27.73% 1472 4712 31.24% 1533 6382 24.02% 1846 7520 24.55% 2882 9417 30.60% 4082 10363 39.39% 4353 10498 41.47% 4363 12228 35.68% 4692 12762 36.77% 4886 12841 38.05% 4944 13270 37.26% 5243 15122 34.67% 6093 20144 30.25% 9614 20965 45.86% 9798 21768 45.01% 10583 21973 48.16% 11953 23909 49.99% 12156 25488 47.69% 12698 25891 49.04% 12906 26032 49.58% 13403 28530 46.98% 13762 31820 43.25% 15568 31821 48.92% 15906 32106 49.54% 16058 32625 49.22% 16992 35713 47.58% 17904 36920 48.49% 19148 60732 31.53% 29070 60995 47.66% 34375 69427 49.51% 36178 69620 51.96% 38463 70373 54.66% 40129 81488 49.25% 45330 82303 55.08% 46326 92492 50.09% 52329 100675 51.98% 56087 108046 51.91% 57173 109605 52.16% 58840 116307 50.59% 65192 139317 46.79% 86077 154755 55.62% 88233 155827 56.62% 98733 156395 63.13% 99917 160722 62.17% 100516 166279 60.45% 104025 187737 55.41% 111457 193135 57.71% 118534 194895 60.82% 123449 199898 61.76% 124321 210599 59.03% 131102 215472 60.84% 132495 222533 59.54% 137907 234190 58.89% [120, 215370, 392820, 979320, 1561440]. Currently the 27th smallest gap not yet found as first occurrence is the first that's not 2 or 5 mod 7, corroborating that the above list of five numbers may be finite. 

20230110, 09:47  #106 
Jan 2007
Germany
26A_{16} Posts 
Gaps between prime quadruplets , zipfile
Under
https://pzktupel.de/RecordGaps/GAP04.php you get at end of the page the current status as zipfile Last fiddled with by Cybertronic on 20230110 at 09:55 
20230126, 18:57  #107 
Dec 2008
you know...around...
350_{16} Posts 
Memento numeri
Results 1.278e16 to 2.08e16 are attached.
Smallest first occurrence not yet found: 184584 (*30). If a volunteer or two could join in, the search may be carried out to 1e17 within a week or two. In any case, I'll reserve up to 2.4e16 for now. This Pari program reaches a speed of more than 2e9 per second per core on my more than seven years old PC with an Intel i74790 @ 3.6 GHz, I'd guess more than twice the speed is possible on a more modern machine. Just enter interval start (k) and interval end (t) at the beginning. (Note that for test runs with smaller numbers, not all gaps may be found due to the "jump" parameters (j,u) below; these may also be altered if one feels comfortable enough with that.) Code:
{ \\ interval start, interval end: k=24000*10^12; t=24100*10^12; fn="quadgaps_output.txt"; \\ filename for output \\ parameters that may be tweaked as search progresses: g=184580*30; \\ min gap size for output j=14080; \\ jump #offsets u=3200; \\ check #offsets before backtracking gap \\ (j+u)*r/z  particularly the largest difference between (j+u) offsets  must be smaller than g ! \\ compute offsets mod 23# gettime(); r=223092870; z=700245; v=vector(z);w=v;w[1]=11;a=1;n=30;o=5; while(n<r, o=nextprime(o+1); l=0; for(m=0,o1, for(b=1,a, if(gcd(n*m+w[b],n*o)==1&&gcd(n*m+w[b]+2,n*o)==1&&gcd(n*m+w[b]+6,n*o)==1&&gcd(n*m+w[b]+8,n*o)==1,l++;v[l]=n*m+w[b]) ) ); w=v; n*=o; a=l; print("quads coprime to "o"#: "l) ); if(l==z&&n==r,print("OK, "gettime()" ms"),print("Error, check parameters r,z!");break()); c=vector(131072); \\ array for tracking which gaps have been found s=1;forprime(y=29,3089,s*=y); \\ for 1st gcd check x=1;forprime(y=3109,11399,x*=y); \\ for 2nd gcd check print("searching, k="k); k=r*floor(k/r); \\ find first quadruplet > k a=1; i=1; while(i, p=k+v[a]; a++; if(a>z,a=1;k+=r); if(gcd(p,s)==1,if(gcd(p+2,s)==1,if(gcd(p+6,s)==1,if(gcd(p+8,s)==1, if(gcd(p,x)==1,if(gcd(p+2,x)==1,if(gcd(p+6,x)==1,if(gcd(p+8,x)==1, if(ispseudoprime(p),if(ispseudoprime(p+2),if(ispseudoprime(p+6),if(ispseudoprime(p+8),i=0)))) )))) )))) ); \\ find quadruplet gaps > g in range (k,t), output every gap size once (but all gaps > #c*30+g) while(k<t, h=1; while(h, a+=j; if(a>z,a=z;k+=r); b=0; o=k;d=a; i=1; while(i, p=k+v[a]; a++; b++; if(a>z,a=1;k+=r); if(gcd(p,s)==1,if(gcd(p+2,s)==1,if(gcd(p+6,s)==1,if(gcd(p+8,s)==1, if(gcd(p,x)==1,if(gcd(p+2,x)==1,if(gcd(p+6,x)==1,if(gcd(p+8,x)==1, if(ispseudoprime(p),if(ispseudoprime(p+2),if(ispseudoprime(p+6),if(ispseudoprime(p+8),i=0)))) )))) )))) ); if(b>u,h=0) ); q=p; e=k;f=a; i=1; k=o;a=d; while(i, a=1; if(a<1,a=z;k=r); p=k+v[a]; if(gcd(p,s)==1,if(gcd(p+2,s)==1,if(gcd(p+6,s)==1,if(gcd(p+8,s)==1, if(gcd(p,x)==1,if(gcd(p+2,x)==1,if(gcd(p+6,x)==1,if(gcd(p+8,x)==1, if(ispseudoprime(p),if(ispseudoprime(p+2),if(ispseudoprime(p+6),if(ispseudoprime(p+8),i=0)))) )))) )))) ); if(qp>g, n=(qpg)/30; if(n>#c,n=#c); if(!c[n], print((qp)/30", "p" ("floor(gettime()/1000)" s)"); write(fn,(qp)/30", "p); if(n<#c,c[n]=1) ) ); k=e;a=f ) } 
20230126, 20:02  #108 
Jan 2007
Germany
1152_{8} Posts 
Thanks Martin !
" The First Occurrence Gap Between Prime Quadruplets"  list up to 2.08e16 now... https://pzktupel.de/RecordGaps/GAP04.php Last fiddled with by Cybertronic on 20230126 at 20:03 
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