In[]:=

Print["Start time is ",ds=DateString[],"."];prec=100000;(**Numberofrequireddecimals.*.*)ClearSystemCache[];T0=SessionTime[];expM[pre_]:=Module[{a,d,s,k,bb,c,end,iprec,xvals,x,pc,cores=16(*=4*numberofphysicalcores*),tsize=2^7,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=Ceiling[pr/6912];Do[xvals=Flatten[Parallelize[Table[Table[ll=start+j*tsize+l;x=N[E^(Log[ll]/(ll)),iprec];pc=iprec;While[pc<pr/1024,pc=Min[3pc,pr/1024];x=SetPrecision[x,pc];y=x^ll-ll;x=x(1-2y/((ll+1)y+2llll));];(**N[Exp[Log[ll]/ll],pr/1024]**)x=SetPrecision[x,pr/256];xll=x^ll;z=(ll-xll)/xll;t=2ll-1;t2=t^2;x=x*(1+SetPrecision[4.5,pr/256](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/256]ll(ll-1)1/(3llt2+t^3z));(*N[Exp[Log[ll]/ll],pr/256]*)x=SetPrecision[x,pr/64];xll=x^ll;z=(ll-xll)/xll;t=2ll-1;t2=t^2;x=x*(1+SetPrecision[4.5,pr/64](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/64]ll(ll-1)1/(3llt2+t^3z));(**N[Exp[Log[ll]/ll],pr/64]**)x=SetPrecision[x,pr/16];xll=x^ll;z=(ll-xll)/xll;t=2ll-1;t2=t^2;x=x*(1+SetPrecision[4.5,pr/16](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/16]ll(ll-1)1/(3llt2+t^3z));(**N[Exp[Log[ll]/ll],pr/16]**)x=SetPrecision[x,pr/4];xll=x^ll;z=(ll-xll)/xll;t=2ll-1;t2=t^2;x=x*(1+SetPrecision[4.5,pr/4](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/4]ll(ll-1)1/(3llt2+t^3z));(**N[Exp[Log[ll]/ll],pr/4]**)x=SetPrecision[x,pr];xll=x^ll;z=(ll-xll)/xll;t=2ll-1;t2=t^2;x=x*(1+SetPrecision[4.5,pr](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr]ll(ll-1)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);Print[kc," iterations done in ",N[st,4]," seconds."," Should take ",N[ti,4]," days or ",N[ti*24*3600,4],"s, finish ",DatePlus[ds,ti],"."],{k,0,end-1}];N[-s/d,pr]];t2=Timing[MRBtest2=expM[prec];];Print["Finished on ",DateString[],". Proccessor time was ",t2[[1]]," s."];Print["Actual time was ",st];(*Print[*)MRBtest2(*]*)(*Remove(**)orenterMRBtest2toprintoutput*);Print["Enter MRBtest2 to print ",Floor[Precision[MRBtest2]]," digits"];Print["If you saved m3M, the difference between this and 3,014,991 known digits is ",N[MRBtest2-m3M,10]]

Start time is Wed 7 Dec 2022 00:38:55.

Iterations required: 132658

Will give 65 time estimates, each more accurate than the previous.

Will stop at 133120 iterations to ensure precsion of around 100499 decimal places.

0 iterations done in 9.449 seconds. Should take 1.451× days or 1.253×s, finish Sun 16 Feb 2420 03:16:39.

5

10

10

10

2048 iterations done in 19.28 seconds. Should take 0.01445 days or 1249.s, finish Wed 7 Dec 2022 00:59:43.

4096 iterations done in 29.30 seconds. Should take 0.01098 days or 948.8s, finish Wed 7 Dec 2022 00:54:43.

6144 iterations done in 39.35 seconds. Should take 0.009834 days or 849.7s, finish Wed 7 Dec 2022 00:53:04.

8192 iterations done in 49.36 seconds. Should take 0.009251 days or 799.3s, finish Wed 7 Dec 2022 00:52:14.

10240 iterations done in 59.42 seconds. Should take 0.008910 days or 769.8s, finish Wed 7 Dec 2022 00:51:44.

12288 iterations done in 69.40 seconds. Should take 0.008672 days or 749.2s, finish Wed 7 Dec 2022 00:51:24.

14336 iterations done in 79.38 seconds. Should take 0.008501 days or 734.5s, finish Wed 7 Dec 2022 00:51:09.

16384 iterations done in 89.12 seconds. Should take 0.008352 days or 721.6s, finish Wed 7 Dec 2022 00:50:56.

18432 iterations done in 98.88 seconds. Should take 0.008237 days or 711.7s, finish Wed 7 Dec 2022 00:50:46.

20480 iterations done in 108.6 seconds. Should take 0.008142 days or 703.5s, finish Wed 7 Dec 2022 00:50:38.

22528 iterations done in 118.5 seconds. Should take 0.008076 days or 697.8s, finish Wed 7 Dec 2022 00:50:32.

24576 iterations done in 128.3 seconds. Should take 0.008016 days or 692.5s, finish Wed 7 Dec 2022 00:50:27.

26624 iterations done in 138.2 seconds. Should take 0.007970 days or 688.6s, finish Wed 7 Dec 2022 00:50:23.

28672 iterations done in 148.1 seconds. Should take 0.007931 days or 685.3s, finish Wed 7 Dec 2022 00:50:20.

30720 iterations done in 158.0 seconds. Should take 0.007897 days or 682.3s, finish Wed 7 Dec 2022 00:50:17.

32768 iterations done in 167.9 seconds. Should take 0.007865 days or 679.6s, finish Wed 7 Dec 2022 00:50:14.

34816 iterations done in 177.7 seconds. Should take 0.007838 days or 677.2s, finish Wed 7 Dec 2022 00:50:12.

36864 iterations done in 187.5 seconds. Should take 0.007810 days or 674.8s, finish Wed 7 Dec 2022 00:50:09.

38912 iterations done in 197.3 seconds. Should take 0.007786 days or 672.7s, finish Wed 7 Dec 2022 00:50:07.

40960 iterations done in 207.0 seconds. Should take 0.007760 days or 670.5s, finish Wed 7 Dec 2022 00:50:05.

43008 iterations done in 216.8 seconds. Should take 0.007740 days or 668.7s, finish Wed 7 Dec 2022 00:50:03.

45056 iterations done in 226.5 seconds. Should take 0.007718 days or 666.8s, finish Wed 7 Dec 2022 00:50:01.

47104 iterations done in 236.3 seconds. Should take 0.007702 days or 665.5s, finish Wed 7 Dec 2022 00:50:00.

49152 iterations done in 245.9 seconds. Should take 0.007680 days or 663.6s, finish Wed 7 Dec 2022 00:49:58.

51200 iterations done in 255.5 seconds. Should take 0.007661 days or 661.9s, finish Wed 7 Dec 2022 00:49:56.

53248 iterations done in 265.2 seconds. Should take 0.007647 days or 660.7s, finish Wed 7 Dec 2022 00:49:55.

55296 iterations done in 275.1 seconds. Should take 0.007640 days or 660.1s, finish Wed 7 Dec 2022 00:49:55.

57344 iterations done in 284.9 seconds. Should take 0.007628 days or 659.0s, finish Wed 7 Dec 2022 00:49:54.

59392 iterations done in 294.8 seconds. Should take 0.007621 days or 658.4s, finish Wed 7 Dec 2022 00:49:53.

61440 iterations done in 304.7 seconds. Should take 0.007613 days or 657.8s, finish Wed 7 Dec 2022 00:49:52.

63488 iterations done in 314.5 seconds. Should take 0.007606 days or 657.2s, finish Wed 7 Dec 2022 00:49:52.

65536 iterations done in 324.2 seconds. Should take 0.007595 days or 656.2s, finish Wed 7 Dec 2022 00:49:51.

67584 iterations done in 334.0 seconds. Should take 0.007589 days or 655.7s, finish Wed 7 Dec 2022 00:49:50.

69632 iterations done in 343.7 seconds. Should take 0.007578 days or 654.8s, finish Wed 7 Dec 2022 00:49:49.

71680 iterations done in 353.5 seconds. Should take 0.007573 days or 654.3s, finish Wed 7 Dec 2022 00:49:49.

73728 iterations done in 363.2 seconds. Should take 0.007564 days or 653.5s, finish Wed 7 Dec 2022 00:49:48.

75776 iterations done in 373.0 seconds. Should take 0.007558 days or 653.0s, finish Wed 7 Dec 2022 00:49:48.

77824 iterations done in 382.7 seconds. Should take 0.007550 days or 652.3s, finish Wed 7 Dec 2022 00:49:47.

79872 iterations done in 392.4 seconds. Should take 0.007543 days or 651.7s, finish Wed 7 Dec 2022 00:49:46.

81920 iterations done in 402.0 seconds. Should take 0.007535 days or 651.1s, finish Wed 7 Dec 2022 00:49:46.

83968 iterations done in 411.8 seconds. Should take 0.007529 days or 650.5s, finish Wed 7 Dec 2022 00:49:45.

86016 iterations done in 421.5 seconds. Should take 0.007523 days or 650.0s, finish Wed 7 Dec 2022 00:49:45.

88064 iterations done in 431.2 seconds. Should take 0.007518 days or 649.6s, finish Wed 7 Dec 2022 00:49:44.

90112 iterations done in 440.7 seconds. Should take 0.007510 days or 648.8s, finish Wed 7 Dec 2022 00:49:43.

92160 iterations done in 450.4 seconds. Should take 0.007504 days or 648.3s, finish Wed 7 Dec 2022 00:49:43.

94208 iterations done in 460.0 seconds. Should take 0.007497 days or 647.7s, finish Wed 7 Dec 2022 00:49:42.

96256 iterations done in 469.8 seconds. Should take 0.007493 days or 647.4s, finish Wed 7 Dec 2022 00:49:42.

98304 iterations done in 479.3 seconds. Should take 0.007486 days or 646.8s, finish Wed 7 Dec 2022 00:49:41.

100352 iterations done in 489.0 seconds. Should take 0.007481 days or 646.4s, finish Wed 7 Dec 2022 00:49:41.

102400 iterations done in 498.6 seconds. Should take 0.007476 days or 645.9s, finish Wed 7 Dec 2022 00:49:40.

104448 iterations done in 508.4 seconds. Should take 0.007473 days or 645.7s, finish Wed 7 Dec 2022 00:49:40.

106496 iterations done in 518.2 seconds. Should take 0.007471 days or 645.5s, finish Wed 7 Dec 2022 00:49:40.

108544 iterations done in 527.9 seconds. Should take 0.007468 days or 645.2s, finish Wed 7 Dec 2022 00:49:40.

110592 iterations done in 537.7 seconds. Should take 0.007465 days or 644.9s, finish Wed 7 Dec 2022 00:49:39.

112640 iterations done in 547.3 seconds. Should take 0.007460 days or 644.5s, finish Wed 7 Dec 2022 00:49:39.

114688 iterations done in 556.9 seconds. Should take 0.007455 days or 644.1s, finish Wed 7 Dec 2022 00:49:39.

116736 iterations done in 566.4 seconds. Should take 0.007450 days or 643.7s, finish Wed 7 Dec 2022 00:49:38.

118784 iterations done in 575.8 seconds. Should take 0.007443 days or 643.1s, finish Wed 7 Dec 2022 00:49:38.

120832 iterations done in 585.4 seconds. Should take 0.007439 days or 642.7s, finish Wed 7 Dec 2022 00:49:37.

122880 iterations done in 594.9 seconds. Should take 0.007433 days or 642.2s, finish Wed 7 Dec 2022 00:49:37.

124928 iterations done in 604.4 seconds. Should take 0.007429 days or 641.8s, finish Wed 7 Dec 2022 00:49:36.

126976 iterations done in 614.1 seconds. Should take 0.007425 days or 641.6s, finish Wed 7 Dec 2022 00:49:36.

129024 iterations done in 623.6 seconds. Should take 0.007421 days or 641.2s, finish Wed 7 Dec 2022 00:49:36.

131072 iterations done in 632.8 seconds. Should take 0.007413 days or 640.5s, finish Wed 7 Dec 2022 00:49:35.

Finished on Wed 7 Dec 2022 00:49:28. Proccessor time was 282.266 s.

Actual time was 632.8139346

Enter MRBtest2 to print 100493 digits

If you saved m3M, the difference between this and 3,014,991 known digits is 0.×

-100494

10

In[]:=

632/60.

Out[]=

10.5333

In[]:=

282/60.

Out[]=

4.7