In[]:=

Print["Start time is ",ds=DateString[],"."];prec=300000;(**Numberofrequireddecimals.*.*)ClearSystemCache[];T0=SessionTime[];expM[pre_]:=Module[{x11,z,t,a,d,s,k,bb,c,end,iprec,xvals,x,pc,cores=16(*=4*numberofphysicalcores*),tsize=128,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/64;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=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}]];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[MRB-MRB1,20]

Start time is Mon 21 Nov 2022 17:07:18.

Iterations required: 397978

Will give 195 time estimates, each more accurate than the previous.

Will stop at 399360 iterations to ensure precsion of around 301499 decimal places.

As of Mon 21 Nov 2022 17:08:52 there were 2048 iterations done in 94.697 seconds. That is 21.627 iterations/s. 0.5128205% complete. It should take 0.212986 days or 1.840×s, and finish Mon 21 Nov 2022 22:13:59.

4

10

As of Mon 21 Nov 2022 17:09:43 there were 4096 iterations done in 145.44 seconds. That is 28.163 iterations/s. 1.025641% complete. It should take 0.163558 days or 1.413×s, and finish Mon 21 Nov 2022 21:02:49.

4

10

As of Mon 21 Nov 2022 17:10:29 there were 6144 iterations done in 191.92 seconds. That is 32.014 iterations/s. 1.538462% complete. It should take 0.143882 days or 1.243×s, and finish Mon 21 Nov 2022 20:34:29.

4

10

As of Mon 21 Nov 2022 17:11:15 there were 8192 iterations done in 237.77 seconds. That is 34.453 iterations/s. 2.051282% complete. It should take 0.133697 days or 1.155×s, and finish Mon 21 Nov 2022 20:19:49.

4

10

As of Mon 21 Nov 2022 17:12:07 there were 10240 iterations done in 289.15 seconds. That is 35.414 iterations/s. 2.564103% complete. It should take 0.130069 days or 1.124×s, and finish Mon 21 Nov 2022 20:14:35.

4

10

As of Mon 21 Nov 2022 17:12:53 there were 12288 iterations done in 335.32 seconds. That is 36.646 iterations/s. 3.076923% complete. It should take 0.125695 days or 1.086×s, and finish Mon 21 Nov 2022 20:08:18.

4

10

As of Mon 21 Nov 2022 17:13:45 there were 14336 iterations done in 387.77 seconds. That is 36.970 iterations/s. 3.589744% complete. It should take 0.124593 days or 1.076×s, and finish Mon 21 Nov 2022 20:06:42.

4

10

As of Mon 21 Nov 2022 17:14:33 there were 16384 iterations done in 435.01 seconds. That is 37.664 iterations/s. 4.102564% complete. It should take 0.122299 days or 1.057×s, and finish Mon 21 Nov 2022 20:03:24.

4

10

As of Mon 21 Nov 2022 17:15:20 there were 18432 iterations done in 482.23 seconds. That is 38.223 iterations/s. 4.615385% complete. It should take 0.120511 days or 1.041×s, and finish Mon 21 Nov 2022 20:00:50.

4

10

As of Mon 21 Nov 2022 17:16:11 there were 20480 iterations done in 533.66 seconds. That is 38.376 iterations/s. 5.128205% complete. It should take 0.120028 days or 1.037×s, and finish Mon 21 Nov 2022 20:00:08.

4

10

As of Mon 21 Nov 2022 17:16:59 there were 22528 iterations done in 581.28 seconds. That is 38.756 iterations/s. 5.641026% complete. It should take 0.118852 days or 1.027×s, and finish Mon 21 Nov 2022 19:58:26.

4

10

As of Mon 21 Nov 2022 17:17:50 there were 24576 iterations done in 632.80 seconds. That is 38.837 iterations/s. 6.153846% complete. It should take 0.118605 days or 1.025×s, and finish Mon 21 Nov 2022 19:58:05.

4

10

As of Mon 21 Nov 2022 17:18:38 there were 26624 iterations done in 680.50 seconds. That is 39.124 iterations/s. 6.666667% complete. It should take 0.117734 days or 1.017×s, and finish Mon 21 Nov 2022 19:56:50.

4

10

As of Mon 21 Nov 2022 17:19:25 there were 28672 iterations done in 727.73 seconds. That is 39.399 iterations/s. 7.179487% complete. It should take 0.116911 days or 1.010×s, and finish Mon 21 Nov 2022 19:55:39.

4

10

As of Mon 21 Nov 2022 17:20:13 there were 30720 iterations done in 775.22 seconds. That is 39.627 iterations/s. 7.692308% complete. It should take 0.116239 days or 1.004×s, and finish Mon 21 Nov 2022 19:54:41.

4

10

As of Mon 21 Nov 2022 17:21:00 there were 32768 iterations done in 822.91 seconds. That is 39.820 iterations/s. 8.205128% complete. It should take 0.115677 days or 9994.s, and finish Mon 21 Nov 2022 19:53:52.

As of Mon 21 Nov 2022 17:21:53 there were 34816 iterations done in 875.22 seconds. That is 39.780 iterations/s. 8.717949% complete. It should take 0.115794 days or 1.000×s, and finish Mon 21 Nov 2022 19:54:02.

4

10

As of Mon 21 Nov 2022 17:22:40 there were 36864 iterations done in 922.07 seconds. That is 39.980 iterations/s. 9.230769% complete. It should take 0.115214 days or 9954.s, and finish Mon 21 Nov 2022 19:53:12.

As of Mon 21 Nov 2022 17:23:31 there were 38912 iterations done in 973.88 seconds. That is 39.956 iterations/s. 9.743590% complete. It should take 0.115284 days or 9961.s, and finish Mon 21 Nov 2022 19:53:18.

As of Mon 21 Nov 2022 17:24:19 there were 40960 iterations done in 1021.6 seconds. That is 40.095 iterations/s. 10.25641% complete. It should take 0.114884 days or 9926.s, and finish Mon 21 Nov 2022 19:52:43.

As of Mon 21 Nov 2022 17:25:07 there were 43008 iterations done in 1069.6 seconds. That is 40.209 iterations/s. 10.76923% complete. It should take 0.114557 days or 9898.s, and finish Mon 21 Nov 2022 19:52:15.

As of Mon 21 Nov 2022 17:26:00 there were 45056 iterations done in 1122.1 seconds. That is 40.152 iterations/s. 11.28205% complete. It should take 0.114719 days or 9912.s, and finish Mon 21 Nov 2022 19:52:29.

As of Mon 21 Nov 2022 17:26:48 there were 47104 iterations done in 1170.4 seconds. That is 40.247 iterations/s. 11.79487% complete. It should take 0.114448 days or 9888.s, and finish Mon 21 Nov 2022 19:52:06.

As of Mon 21 Nov 2022 17:27:41 there were 49152 iterations done in 1223.0 seconds. That is 40.189 iterations/s. 12.30769% complete. It should take 0.114614 days or 9903.s, and finish Mon 21 Nov 2022 19:52:20.

As of Mon 21 Nov 2022 17:28:29 there were 51200 iterations done in 1271.5 seconds. That is 40.268 iterations/s. 12.82051% complete. It should take 0.114390 days or 9883.s, and finish Mon 21 Nov 2022 19:52:01.

As of Mon 21 Nov 2022 17:29:17 there were 53248 iterations done in 1319.7 seconds. That is 40.349 iterations/s. 13.33333% complete. It should take 0.114161 days or 9863.s, and finish Mon 21 Nov 2022 19:51:41.

As of Mon 21 Nov 2022 17:30:10 there were 55296 iterations done in 1372.8 seconds. That is 40.278 iterations/s. 13.84615% complete. It should take 0.114360 days or 9881.s, and finish Mon 21 Nov 2022 19:51:58.

As of Mon 21 Nov 2022 17:30:59 there were 57344 iterations done in 1421.0 seconds. That is 40.354 iterations/s. 14.35897% complete. It should take 0.114146 days or 9862.s, and finish Mon 21 Nov 2022 19:51:40.

As of Mon 21 Nov 2022 17:31:52 there were 59392 iterations done in 1474.3 seconds. That is 40.286 iterations/s. 14.87179% complete. It should take 0.114338 days or 9879.s, and finish Mon 21 Nov 2022 19:51:56.

As of Mon 21 Nov 2022 17:32:41 there were 61440 iterations done in 1522.9 seconds. That is 40.343 iterations/s. 15.38462% complete. It should take 0.114176 days or 9865.s, and finish Mon 21 Nov 2022 19:51:42.