--- In

primenumbers@yahoogroups.com,

"WarrenS" <warren.wds@...> wrote:

> max prime involved in either 2573827

Definition: For positive integer n let p be the largest

prime divisor of n*(n+1) and S(n) = log(n)/log(p) be

the figure of merit for the smoothness of the

consecutive integers n and n+1.

Then Warren's 125-digit example had

S(n) =~ log(7.5828465*10^124)/log(2573827) =~ 19.480

Here is a 135-digit example with greater merit:

{f(y)=

(y^2-11^4)*(y^2-35^2)*(y^2-47^2)*

(y^2-94^2)*(y^2-146^2)*(y^2-148^2)/

67440294559676054016000 - 1;}

n = f(12971885307194);

{if(type(n)=="t_INT",F=factor(n*(n+1))[,1];

p=F[#F];print("n has "#Str(n)" digits");

print("max prime is "p);

default(realprecision,5);

print("S(n) =~ "log(n)/log(p)));}

n has 135 digits

max prime is 6244451

S(n) =~ 19.797

David