In[]:=

Needs["SubKernels`LocalKernels`"];Needs["SubKernels`RemoteKernels`"];Block[{$mathkernel=$mathkernel<>" -threadpriority=2"},LaunchKernels[]]

2600:1700:71d0:fd50:0:0:0:49

.

2600:1700:71d0:fd50:0:0:0:49

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2600:1700:71d0:fd50:0:0:0:48

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Out[]=

{$Failed,$Failed,KernelObject[1,2600:1700:71d0:fd50:0:0:0:48],KernelObject[2,2600:1700:71d0:fd50:0:0:0:48],KernelObject[3,2600:1700:71d0:fd50:0:0:0:48],KernelObject[4,2600:1700:71d0:fd50:0:0:0:48],KernelObject[5,2600:1700:71d0:fd50:0:0:0:48],KernelObject[6,2600:1700:71d0:fd50:0:0:0:48],KernelObject[8,2600:1700:71d0:fd50:0:0:0:48],KernelObject[9,2600:1700:71d0:fd50:0:0:0:48],KernelObject[10,2600:1700:71d0:fd50:0:0:0:48],KernelObject[11,2600:1700:71d0:fd50:0:0:0:48],KernelObject[12,2600:1700:71d0:fd50:0:0:0:48],KernelObject[13,2600:1700:71d0:fd50:0:0:0:48],KernelObject[14,2600:1700:71d0:fd50:0:0:0:48],KernelObject[15,2600:1700:71d0:fd50:0:0:0:48],KernelObject[16,2600:1700:71d0:fd50:0:0:0:48],KernelObject[17,local],KernelObject[18,local],KernelObject[19,local],KernelObject[20,local],KernelObject[21,local],KernelObject[22,local],KernelObject[23,local],KernelObject[24,local],KernelObject[25,local],KernelObject[26,local],KernelObject[27,local],KernelObject[28,local],KernelObject[29,local],KernelObject[30,local],KernelObject[31,local],KernelObject[32,local]}

In[]:=

Print["Start time is ",ds=DateString[],"."];prec=50000;(**Numberofrequireddecimals.*.*)ClearSystemCache[];T0=SessionTime[];expM[pre_]:=Module[{x11,z,t,a,d,s,k,bb,c,end,iprec,xvals,x,pc,cores=100(*=4*numberofphysicalcores*),tsize=75,chunksize,start=1,ll,ctab,pr=Floor[1.005pre]},chunksize=cores*tsize;n=Floor[1.32pr];end=Ceiling[n/chunksize];Print["Iterations required: ",n];Print["Will give ",end," time estimates, each more accurate than the previous."];Print["Will stop at ",end*chunksize," iterations to ensure precsion of around ",pr," decimal places."];d=ChebyshevT[n,3];{b,c,s}={SetPrecision[-1,1.1*n],-d,0};iprec=pr/16;Do[xvals=Flatten[ParallelTable[Table[ll=start+j*tsize+l;x=N[E^(Log[ll]/(ll)),iprec];pc=iprec;While[pc<pr,pc=Min[4pc,pr];x=SetPrecision[x,pc];xll=Power[x,ll];z=(ll-xll)/xll;t=2ll-1;t2=t^2;x*=(1+SetPrecision[4.5,pc](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pc]ll(ll-1)/(3llt2+t^3z))];(**N[Exp[Log[ll]/ll],pr]**)x,{l,0,tsize-1}],{j,0,cores-1},Method"FinestGrained"]];ctab=ParallelTable[Table[c=b-c;ll=start+l-2;b*=2(ll+n)(ll-n)/((ll+1)(2ll+1));c,{l,chunksize}],Method"Automatic"];s+=ctab.(xvals-1);start+=chunksize;st=SessionTime[]-T0;kc=k*chunksize;ti=(st)/(kc+10^-4)*(n)/(3600)/(24);If[kc>1,Print["As of ",DateString[]," there were ",kc," iterations done in ",N[st,5]," seconds. That is ",N[kc/st,5]," iterations/s. ",N[kc/(end*chunksize)*100,7],"% complete."," It should take ",N[ti,6]," days or ",N[ti*24*3600,4],"s, and finish ",DatePlus[ds,ti],"."]];Print[];,{k,0,end-1}];N[-s/d,pr]];t2=Timing[MRB1=expM[prec];];Print["Finished on ",DateString[],". Proccessor and actual time were ",t2[[1]]," and ",SessionTime[]-T0," s. respectively"];Print["Enter MRB1 to print ",Floor[Precision[MRB1]]," digits. The error from a 6,500,000 or more digit calculation that used a different method is "];N[m3M-MRB1,20]

Start time is Fri 12 Apr 2024 05:22:45.

Iterations required: 66328

Will give 9 time estimates, each more accurate than the previous.

Will stop at 67500 iterations to ensure precsion of around 50249 decimal places.

As of Fri 12 Apr 2024 05:23:10 there were 7500 iterations done in 24.647 seconds. That is 304.29 iterations/s. 11.11111% complete. It should take 0.00252286 days or 218.0s, and finish Fri 12 Apr 2024 05:26:22.

As of Fri 12 Apr 2024 05:23:22 there were 15000 iterations done in 36.914 seconds. That is 406.35 iterations/s. 22.22222% complete. It should take 0.00188924 days or 163.2s, and finish Fri 12 Apr 2024 05:25:28.

As of Fri 12 Apr 2024 05:23:34 there were 22500 iterations done in 49.219 seconds. That is 457.14 iterations/s. 33.33333% complete. It should take 0.00167932 days or 145.1s, and finish Fri 12 Apr 2024 05:25:10.

As of Fri 12 Apr 2024 05:23:47 there were 30000 iterations done in 61.580 seconds. That is 487.17 iterations/s. 44.44444% complete. It should take 0.00157580 days or 136.1s, and finish Fri 12 Apr 2024 05:25:01.

As of Fri 12 Apr 2024 05:23:59 there were 37500 iterations done in 73.659 seconds. That is 509.10 iterations/s. 55.55556% complete. It should take 0.00150792 days or 130.3s, and finish Fri 12 Apr 2024 05:24:55.

As of Fri 12 Apr 2024 05:24:11 there were 45000 iterations done in 85.892 seconds. That is 523.91 iterations/s. 66.66667% complete. It should take 0.00146529 days or 126.6s, and finish Fri 12 Apr 2024 05:24:51.

As of Fri 12 Apr 2024 05:24:23 there were 52500 iterations done in 98.041 seconds. That is 535.49 iterations/s. 77.77778% complete. It should take 0.00143361 days or 123.9s, and finish Fri 12 Apr 2024 05:24:48.

As of Fri 12 Apr 2024 05:24:34 there were 60000 iterations done in 109.45 seconds. That is 548.22 iterations/s. 88.88889% complete. It should take 0.00140033 days or 121.0s, and finish Fri 12 Apr 2024 05:24:45.

Finished on Fri 12 Apr 2024 05:24:35. Proccessor and actual time were 98.0781 and 109.4753188 s. respectively

Enter MRB1 to print 50243 digits. The error from a 6,500,000 or more digit calculation that used a different method is

Out[]=

1.9641481062269221664×

-50188

10