2007 fun

[Edwin Clark]

On Wed, 3 Jan 2007, Rainer Rosenthal wrote:

> Nick Hobson schrieb:
> >Ed Pegg wrote:
> >>20071 is prime
> >>200713 is prime 
> >>2007133 is prime
> >>20071333 is prime
> >>200713333 is prime
> >>2007133333 is prime
> >>20071333333 is prime
> 
> > The simple PARI/GP script below found ... 
> > 2007333...333 prime for n = number of 3s =
> > 
> > 1, 2, 3, 4, 5, 6, 26, 73, 87, 220, 248, ...
> > 
> > ... before I cancelled it after about 10 minutes.
> > 
> > for(n=1, 500, x=20071*(10^n) + (10^n)\3; if(isprime(x), print1(n, ", ")))
> 
> 
> Maple is said to be slow but good old Maple 6 with a
> comparable simple loop came up with two more terms in
> less than a minute:
> 
>  1, 2, 3, 4, 5, 6, 26, 73, 87, 220, 248, 349, 410
> 

If you are willing to use Maple's isprime (which is just
a probabilistic primality test) with little extra effort
you can find these terms up to 2007--a good time to stop:  

0, 1, 2, 3, 4, 5, 6, 26, 73, 87, 220, 248, 349, 410, 1208, 1238, 1459, 
1709