- Is this an expected property of the number 19 or even 9?

19 digits 9191919191919191919 = 3 * 3 * 1021324354657687991

which has the digits n n-1 n+1 repeating as follows:

= 9 * (n n-1 n+1 (n+1) (n+1)-1 (n+1)+1 ...) / 10

Also note:

23 digits 91919191919191919191919 is prime

17 digits 91919191919191919 is prime.

11 digits 91919191919 is prime.

9 digits 919191919 is prime.

3 digits 919 is prime.

Ali

Prime numbers are God's signature!

www.heliwave.com

[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com, Ali Adams

<alipoland@...> wrote:

> 23 digits 91919191919191919191919 is prime

The next probable prime has 25229 digits:

(91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s)

David >

and was found by Patrick de Geest in july 2004:

> --- In primenumbers@yahoogroups.com, David Broadhurst wrote:

>

> > 23 digits 91919191919191919191919 is prime

>

> The next probable prime has 25229 digits:

>

> (91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s)

>

> David

>

>

>

http://www.primenumbers.net/prptop/searchform.php?form=%3F%2F99

Lélio

[Non-text portions of this message have been removed]- On 2010/09/10 21:20, Lélio Ribeiro de Paula wrote:
>> --- In primenumbers@yahoogroups.com, David Broadhurst wrote:

According to Patrick de Geest's website, Hans Rosenthal found it.

>>

>> The next probable prime has 25229 digits:

>>

>> (91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s)

>

> and was found by Patrick de Geest in july 2004:

>

> http://www.primenumbers.net/prptop/searchform.php?form=%3F%2F99

http://www.worldofnumbers.com/undulat.htm#supp919

Factorizations of (91*10^(2n+1)-19)/99 are here:

http://www.asahi-net.or.jp/~kc2h-msm/mathland/aba/aba919.htm

Makoto Kamada > 23 digits 91919191919191919191919 is prime

The 15 digit number 151515151515151 is prime, too ;

> 17 digits 91919191919191919 is prime.

> 11 digits 91919191919 is prime.

> 9 digits 919191919 is prime.

and it is the only such prime (undulating : aba...ba

with ab = 10*a+b or ba = 10*b+a digits.

M.