Re: Question on the Limiting Value of Ratios of Consecuative Primes...

*To*: mathgroup at smc.vnet.net*Subject*: [mg88523] Re: Question on the Limiting Value of Ratios of Consecuative Primes...*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 7 May 2008 07:09:09 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <fvpcpn$mge$1@smc.vnet.net>

Richard Palmer wrote: > Is there some analytic limit to the ratio of consecuative primes? The > expression Limit[Prime[i]/Prime[i+1],{i,->Infinity}] returns unevaluated. > Plotting Table[ Prime[i]/Prime[i+1],{i,1,20000}] shows a lot of structure > with a minimum of 3/5. You could use something like the expression below to explore numerically the limit on a wider range of prime numbers. (Table build a list, i.e. consume more and more memory, whereas For will just iterate and change only one value when required.) In[142]:= Timing@ Module[{rat, lowest = 1}, For[i = 1, i <= 10^7, i++, rat = Prime[i]/Prime[i + 1]; If[rat < lowest, lowest = rat]]; lowest] Out[142]= {139.046, 3/5} Regards, -- Jean-Marc