downloadthisnotebookforfullfunctionality»
EvaluateNoteBook
MRBTrue=MRB1;
In[]:=
(*MRBconstantcomputationwithverification!Theconstant'sdecimalapproximationissavedasMRBtest*)prec=10000;(*Numberofrequireddecimals.*)ClearSystemCache[];T0=SessionTime[];expM[pre_]:=Module[{a,d,s,k,bb,c,n,end,iprec,xvals,x,pc,cores=4,tsize=2^7,chunksize,start=1,ll,ctab,pr=Floor[1.02pre]},chunksize=cores*tsize;n=Floor[1.32pr];end=Ceiling[n/chunksize];d=N[(3+Sqrt[8])^n,pr+10];d=Round[1/2(d+1/d)];{b,c,s}={SetPrecision[-1,1.1*n],-d,0};iprec=Ceiling[pr/27];Do[xvals=Flatten[ParallelTable[Table[ll=start+j*tsize+l;x=N[E^(Log[ll]/(ll)),iprec];pc=iprec;While[pc<pr,pc=Min[3pc,pr];x=SetPrecision[x,pc];y=x^ll-ll;x=x(1-2y/((ll+1)y+2llll));];(*N[Exp[Log[ll]/ll],pr]*)x,{l,0,tsize-1}],{j,0,cores-1},Method"EvaluationsPerKernel"1]];ctab=Table[c=b-c;ll=start+l-2;b*=2(ll+n)(ll-n)/((ll+1)(2ll+1));c,{l,chunksize}];s+=ctab.(xvals-1);start+=chunksize;,{k,0,end-1}];etaMs=N[-s/d-(EulerGammaLog[2]-Log[2]^2/2),pr]];t2=Timing[MRBtest2=expM[prec];];Print["The MRB constant was computed and checked to ",prec," digits in ",t1=t2[[1]]+Timing[eta[s_]:=(1-2^(1-s))Zeta[s];eta1=Limit[D[eta[s],s],s1];MRBtrue=mm;MRBtest=eta1+etaMs;check=MRBtest-MRBtrue][[1]]," seconds"];check
The MRB constant was computed and checked to 10000 digits in 3.26563 seconds
Out[]=
0.×
-10196
10