Re: Prime[..] slows down

*To*: mathgroup at smc.vnet.net*Subject*: [mg53562] Re: [mg53524] Prime[..] slows down*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Tue, 18 Jan 2005 05:08:02 -0500 (EST)*References*: <200501160207.VAA05705@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

George Szpiro wrote: >My last posting did not have the program listing: > > >can somebody explain why Prime[...] slows down so drastically and so >abruptly at about 105 >million (see below)? > >also: how can I get elapsed time in fractions of seconds? (Timing[...] did >not work inside the loop for some reason.)AboluteTime to give > >Thanks, > >George >george at netvision.net.il > > >Sets=100; > >KK=20000; > >InitValue=105000000; > >Steps=10000; > >For[k=1,k<=Sets,k++, > > TT=AbsoluteTime[]; > > For[j=1,j<=KK,j++, x=2*Prime[InitValue+k*Steps+j];] > > Print["Prime[",InitValue+k*Steps+j-1,"]=",Prime[InitValue+k*Steps+j-1]," >Time ",AbsoluteTime[]-TT]; > > TT=AbsoluteTime[];] > >Prime[105010000]=2145604099 Time 1.00000 > >Prime[105030000]=2146031753 Time 2.00000 > > The jump is explained by the computation below. In[4]:= PrimePi[2^31]-1 Out[4]= 105097564 So between 105090000 and 105100000 we move from machine integers to bignums. Performing arithmetic on these is slower. Daniel Lichtblau Wolfram Research

**References**:**Prime[..] slows down***From:*George Szpiro <george@netvision.net.il>