I developed a new 19-tuple search algorithm with a minimum diameter of 252 from consecutive primes and wrote a program in PARI/GP language.

The program

\l res_17tuple.txt
{m=[4223,19693,19847,21563,29417,29963,30403,38257,39973,40127,45433,55597,56143,63997,64283,69743,79753,79907,80453,81623,88307,89477,90023,90463,95923,98317,100187,103777,105493,105647,114487,115657,116203,124057,129803,139967,140513,148367,150083,155983,163837,165553,165707,174547,176263,184117,189863,200573,208427,210143,215603,216043,223897,224443,225613,225767,226313,234167,234607,236323,241783,244177,249637,249923,260347,260633,266093,268487,273947,275663,276103,283957,284503,284657,285827,286373,294227,294667,300127,301843,309697,320407,326153,334007,335723,344563,344717,346433,354287,360187,361903,369757,370303,380467,386213,394067,394613,395783,404623,404777,406493,410083,411953,414347,419807,420247,420793,421963,428647,429817,430363,430517,440527,445987,446273,454127,454673,464837,470143,470297,472013,479867,480307,480853,488707,490423,490577,506047];
pat=[0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240];
pat1=vector(17); w=vector(25);
pat3=[114, 120, 126];
pat5=[90, 114, 120, 126, 150];
pat7=[84, 90, 114, 120, 126, 150, 156];
pat9=[66, 84, 90, 114, 120, 126, 150, 156, 174];
pat11=[36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204];
pat13=[24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216];
pat15=[6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234];
w13=vector(13); w15=vector(15); w11=vector(11); w9=vector(9); w7=vector(7); w5=vector(5); w3=vector(3);
i1=20115164930439000001+355*10^10;
i2=i1-1+5*10^10;
print("range of search");
print(i1," (p=", i1*510510," )");
print(i2," (p=", i2*510510," )");
forstep (i=i1,i2, 9999,
x=510510*i;
for (n=1, 128,
v=x+m[n];
if(ispseudoprime(v) && ispseudoprime(v+240),
k=0; 
forprime(p=v,v+240, k++; w[k]=p; );
if(k==17,
for(j=1,17, pat1[j]=w[j]-w[1]; );
for(m=1,3, w3[m]=pat1[m+7]; );
for(m=1,5, w5[m]=pat1[m+6]; );
for(m=1,7, w7[m]=pat1[m+5]; );
for(m=1,9, w9[m]=pat1[m+4]; );
for(m=1,11, w11[m]=pat1[m+3]; );
for(m=1,13, w13[m]=pat1[m+2]; );
for(m=1,15, w15[m]=pat1[m+1]; );
if(w3==pat3, print(w[8],": ",w3); print(w[1],": ",pat1); );
if(w5==pat5, print(w[7],": ",w5); print(w[1],": ",pat1); );
if(w7==pat7, print(w[6],": ",w7); print(w[1],": ",pat1);  );
if(w9==pat9, print(w[5],": ",w9); print(w[1],": ",pat1); );
if(w11==pat11, print(w[4],": ",w11); print(w[1],": ",pat1); );
if(w13==pat13, print(w[3],": ",w13); print(w[1],": ",pat1); );
if(w15==pat15, print(w[2],": ",w15); print(w[1],": ",pat1); );
););););
}

See message
https://boinc.progger.info/odlk/forum_thread.php?id=237&postid=13007

I suggest programmers optimize the program.

You can take part in the experiment.
Now I am performing this experiment on my computer.

I offer you 20 tasks.
Download the archive from the following link
https://disk.yandex.ru/d/763i7XeLAFVlJw

In the archive you see the gp.exe program and 20 working programs

17tuple_1.txt
17tuple_2.txt
. . . . . . .
17tuple_19.txt
17tuple_20.txt

You can run any of these tasks.
For example, the first task is launched from the command line
gp 17tuple_1.txt

You can also run multiple jobs at once in one folder.
The results will be written to an output file that is opened by each running program.
On my slow computer, one task takes 9 hours to complete.

You can also run this algorithm on the BOINC platform if you have a server and experience with BOINC.

Please write to me at natalimak1@yandex.ru
Let me know if you'll be counting tasks.

Please ask your questions in the thread or in PM.

This problem is being addressed by Dmitriy40 on the dxdy.ru forum.

See, for example, the latest news in the message
https://dxdy.ru/post1613929.html#p1613929

You can participate in this forum if the task interests you.