Wolfram Cloud Document

In[]:=

m3M

Out[]=

m3M

In[]:=

CloseKernels[]

Out[]=

{}

In[]:=

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

LinkObject

:Unable to communicate with closed link LinkObject[55669@192.168.1.237,55670@192.168.1.237,229,30].

LinkObject

:Unable to communicate with closed link LinkObject[55673@192.168.1.237,55674@192.168.1.237,231,32].

Parallel`Developer`ConnectKernel

::failinit

:2 of 16 kernels failed to initialize.

LightweightGridClient`RemoteKernelClose

::nokernel

:Kernel could not be closed because no kernel was found for the given link "

PC-7C61205847

LightweightGridClient`RemoteKernelClose

::nokernel

:Kernel could not be closed because no kernel was found for the given link "

PC-7C61205847

Out[]=

{KernelObject[1,local],KernelObject[2,local],KernelObject[3,local],KernelObject[4,local],KernelObject[5,local],KernelObject[6,local],KernelObject[7,local],KernelObject[8,local],KernelObject[9,local],KernelObject[10,local],KernelObject[11,local],KernelObject[12,local],KernelObject[13,local],KernelObject[14,local],KernelObject[15,local],KernelObject[16,local],KernelObject[17,PC-7C61205847],KernelObject[18,PC-7C61205847],KernelObject[19,PC-7C61205847],KernelObject[20,PC-7C61205847],KernelObject[22,PC-7C61205847],KernelObject[24,PC-7C61205847],KernelObject[25,PC-7C61205847],KernelObject[26,PC-7C61205847],KernelObject[27,PC-7C61205847],KernelObject[28,PC-7C61205847],KernelObject[29,PC-7C61205847],KernelObject[30,PC-7C61205847],KernelObject[31,PC-7C61205847],KernelObject[32,PC-7C61205847]}

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 Sat 6 Apr 2024 12:19:34.

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 9.372 seconds. Should take 1.439×

days or 1.243×

s, finish Wed 28 Mar 2418 05:10:07.

2048 iterations done in 18.86 seconds. Should take 0.01414 days or 1222.s, finish Sat 6 Apr 2024 12:39:55.

4096 iterations done in 28.10 seconds. Should take 0.01053 days or 910.1s, finish Sat 6 Apr 2024 12:34:44.

6144 iterations done in 37.49 seconds. Should take 0.009370 days or 809.5s, finish Sat 6 Apr 2024 12:33:03.

8192 iterations done in 47.18 seconds. Should take 0.008843 days or 764.1s, finish Sat 6 Apr 2024 12:32:18.

10240 iterations done in 56.70 seconds. Should take 0.008502 days or 734.6s, finish Sat 6 Apr 2024 12:31:48.

12288 iterations done in 65.96 seconds. Should take 0.008242 days or 712.1s, finish Sat 6 Apr 2024 12:31:26.

14336 iterations done in 75.51 seconds. Should take 0.008087 days or 698.7s, finish Sat 6 Apr 2024 12:31:12.

16384 iterations done in 84.75 seconds. Should take 0.007942 days or 686.2s, finish Sat 6 Apr 2024 12:31:00.

18432 iterations done in 94.14 seconds. Should take 0.007842 days or 677.5s, finish Sat 6 Apr 2024 12:30:51.

20480 iterations done in 104.2 seconds. Should take 0.007815 days or 675.2s, finish Sat 6 Apr 2024 12:30:49.

22528 iterations done in 113.6 seconds. Should take 0.007739 days or 668.7s, finish Sat 6 Apr 2024 12:30:42.

24576 iterations done in 122.9 seconds. Should take 0.007679 days or 663.5s, finish Sat 6 Apr 2024 12:30:37.

26624 iterations done in 132.3 seconds. Should take 0.007627 days or 659.0s, finish Sat 6 Apr 2024 12:30:32.

28672 iterations done in 141.5 seconds. Should take 0.007578 days or 654.7s, finish Sat 6 Apr 2024 12:30:28.

30720 iterations done in 150.7 seconds. Should take 0.007534 days or 651.0s, finish Sat 6 Apr 2024 12:30:24.

32768 iterations done in 159.9 seconds. Should take 0.007493 days or 647.4s, finish Sat 6 Apr 2024 12:30:21.

34816 iterations done in 169.7 seconds. Should take 0.007485 days or 646.7s, finish Sat 6 Apr 2024 12:30:20.

36864 iterations done in 179.0 seconds. Should take 0.007453 days or 644.0s, finish Sat 6 Apr 2024 12:30:17.

38912 iterations done in 188.4 seconds. Should take 0.007433 days or 642.2s, finish Sat 6 Apr 2024 12:30:16.

40960 iterations done in 197.6 seconds. Should take 0.007407 days or 639.9s, finish Sat 6 Apr 2024 12:30:13.

43008 iterations done in 207.0 seconds. Should take 0.007390 days or 638.5s, finish Sat 6 Apr 2024 12:30:12.

45056 iterations done in 216.6 seconds. Should take 0.007382 days or 637.8s, finish Sat 6 Apr 2024 12:30:11.

47104 iterations done in 226.0 seconds. Should take 0.007365 days or 636.4s, finish Sat 6 Apr 2024 12:30:10.

49152 iterations done in 235.4 seconds. Should take 0.007354 days or 635.4s, finish Sat 6 Apr 2024 12:30:09.

51200 iterations done in 244.9 seconds. Should take 0.007345 days or 634.6s, finish Sat 6 Apr 2024 12:30:08.

53248 iterations done in 254.3 seconds. Should take 0.007332 days or 633.5s, finish Sat 6 Apr 2024 12:30:07.

55296 iterations done in 263.6 seconds. Should take 0.007320 days or 632.5s, finish Sat 6 Apr 2024 12:30:06.

57344 iterations done in 272.9 seconds. Should take 0.007307 days or 631.3s, finish Sat 6 Apr 2024 12:30:05.

59392 iterations done in 282.5 seconds. Should take 0.007302 days or 630.9s, finish Sat 6 Apr 2024 12:30:04.

61440 iterations done in 291.7 seconds. Should take 0.007290 days or 629.9s, finish Sat 6 Apr 2024 12:30:03.

63488 iterations done in 301.3 seconds. Should take 0.007286 days or 629.5s, finish Sat 6 Apr 2024 12:30:03.

65536 iterations done in 310.4 seconds. Should take 0.007273 days or 628.4s, finish Sat 6 Apr 2024 12:30:02.

67584 iterations done in 319.8 seconds. Should take 0.007266 days or 627.8s, finish Sat 6 Apr 2024 12:30:01.

69632 iterations done in 329.4 seconds. Should take 0.007263 days or 627.5s, finish Sat 6 Apr 2024 12:30:01.

71680 iterations done in 338.6 seconds. Should take 0.007253 days or 626.6s, finish Sat 6 Apr 2024 12:30:00.

73728 iterations done in 347.9 seconds. Should take 0.007245 days or 626.0s, finish Sat 6 Apr 2024 12:30:00.

75776 iterations done in 357.3 seconds. Should take 0.007241 days or 625.6s, finish Sat 6 Apr 2024 12:29:59.

77824 iterations done in 366.7 seconds. Should take 0.007234 days or 625.0s, finish Sat 6 Apr 2024 12:29:59.

79872 iterations done in 376.0 seconds. Should take 0.007228 days or 624.5s, finish Sat 6 Apr 2024 12:29:58.

81920 iterations done in 385.4 seconds. Should take 0.007224 days or 624.1s, finish Sat 6 Apr 2024 12:29:58.

83968 iterations done in 395.1 seconds. Should take 0.007224 days or 624.2s, finish Sat 6 Apr 2024 12:29:58.

86016 iterations done in 404.8 seconds. Should take 0.007226 days or 624.3s, finish Sat 6 Apr 2024 12:29:58.

88064 iterations done in 414.4 seconds. Should take 0.007225 days or 624.3s, finish Sat 6 Apr 2024 12:29:58.

90112 iterations done in 423.6 seconds. Should take 0.007218 days or 623.6s, finish Sat 6 Apr 2024 12:29:57.

92160 iterations done in 433.0 seconds. Should take 0.007214 days or 623.3s, finish Sat 6 Apr 2024 12:29:57.

94208 iterations done in 442.5 seconds. Should take 0.007212 days or 623.1s, finish Sat 6 Apr 2024 12:29:57.

96256 iterations done in 451.7 seconds. Should take 0.007206 days or 622.6s, finish Sat 6 Apr 2024 12:29:56.

98304 iterations done in 461.0 seconds. Should take 0.007200 days or 622.1s, finish Sat 6 Apr 2024 12:29:56.

100352 iterations done in 470.3 seconds. Should take 0.007196 days or 621.7s, finish Sat 6 Apr 2024 12:29:55.

102400 iterations done in 479.4 seconds. Should take 0.007188 days or 621.1s, finish Sat 6 Apr 2024 12:29:55.

104448 iterations done in 488.7 seconds. Should take 0.007183 days or 620.6s, finish Sat 6 Apr 2024 12:29:54.