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My insane pursuit of highly abundant numbers …

The latest PARI/gp command-line and first few lines of ouput are copied below.  Note that Keith Briggs has already published in Experimental Mathematics around 2006 on superabundant and colossally abundant numbers out to ~~~ 10^(10^10) or so, using a sieve technique to locate the first ~ 10^9 or 10^10 primes, and making use of the Erdos-Alaoglu formula for the exponents of primes appearing in superabundant and/or colossally abundant numbers …

 

? for(YYY = 1, 16   ,   for(ZZZZ=1,5,   thebest = 0; www3=vector(100);for(Y=1,100,www3[Y]=www[Y]);stdwww3=vector(dimo);for(Y=1,dimo, stdwww3[Y] = sum(Z=1,30, www3[Z] > (Y-1)));for(Y= ymini+1,yleste , stdwww3[Y] = 0);        cst=ratiott(stdwww3); cst=cst-0.00008;   for(WW = 1,     1     ,   for(X=1,   lastx  ,  www2=vector(100);for(Y=1,100,www2[Y]=www[Y]);www2[X]=www2[X]+delta[X];  stdwww2=vector(dimo);for(Y=1,dimo, stdwww2[Y] = sum(Z=1,30,www2[Z] > (Y-1)));  for(Y=ymini+1,yleste,stdwww2[Y]=0); newr2 = ratiott(stdwww2);  if(newr2>   cst        ,  print(X,”         “, newr2));   if(newr2>cst, cst=newr2; thebest = X)                  ) ) ; print(“Best:  “,thebest,”  Score:  “,cst); if(thebest>0, www[thebest]=www[thebest]+delta[thebest] ;   if(thebest<2,    kol = yleste+ delta[1]; sigcpp78k = sigcpp68k*prod(X=yleste+1, kol  , 1+prime(X));cpp78k = cpp68k*prod(X= yleste+1 ,  kol  , prime(X));yleste = kol ; sigcpp68k = sigcpp78k; cpp68k = cpp78k)                              ); dimo = www[1]+ delta[1]+5 ;   ) ; print(www) )      
1         9999.8161367318480050236360103309064966
Best:  1  Score:  9999.8161367318480050236360103309064966
1         9999.8178667635945587062955380966504143
Best:  1  Score:  9999.8178667635945587062955380966504143
1         9999.8192606775009892371578980177968621
Best:  1  Score:  9999.8192606775009892371578980177968621
1         9999.8210399050758762349397650799650059
Best:  1  Score:  9999.8210399050758762349397650799650059
1         9999.8217474792913918975813952689434803
Best:  1  Score:  9999.8217474792913918975813952689434803
[550805, 495, 55, 19, 10, 7, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
1         9999.8225536547315697620028168239359823
Best:  1  Score:  9999.8225536547315697620028168239359823
1         9999.8229723292895749648920781493140060
Best:  1  Score:  9999.8229723292895749648920781493140060
1         9999.8240274542489694132168978863775870
Best:  1  Score:  9999.8240274542489694132168978863775870
1         9999.8259825043472576022761466011125380

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Written by meditationatae

July 19, 2013 at 3:26 pm

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