- In a message dated 01/02/03 07:01:00 GMT Standard Time,

miltbrown@... writes:

> PPR of the form 10^x+y

So 10^1+9933 (= 9943 =61*163) is a PRP?

> x y x y

> =========== =========

> 1 9933 16 38353

>

Mike

[Non-text portions of this message have been removed] - --- mikeoakes2@... wrote:
> In a message dated 01/02/03 07:01:00 GMT Standard Time,

Mike,

> miltbrown@... writes:

>

>

> > PPR of the form 10^x+y

> > x y x y

> > =========== =========

> > 1 9933 16 38353

> >

>

> So 10^1+9933 (= 9943 =61*163) is a PRP?

GP first, conclusions second.

(13:41) gp > Mod(548,9943)^9942

%1 = Mod(1, 9943)

(13:42) gp > Mod(977,9943)^9942

%4 = Mod(1, 9943)

In fact,

(13:44) gp > Mod(548,9943)^(9942/2)

%6 = Mod(9942, 9943)

Therefore it's a _SPRP_ too.

Phil

=====

Is that free as in Willy or as in bird?

__________________________________________________

Do you Yahoo!?

Yahoo! Mail Plus - Powerful. Affordable. Sign up now.

http://mailplus.yahoo.com - Of course it should say:

PRP of the form 10^(10000+x) + y

Milton L. Brown

miltbrown@...

-----Original Message-----

From: Milton Brown [mailto:miltbrown@...]

Sent: Friday, January 31, 2003 6:24 PM

To: primenumbers@yahoogroups.com

Cc: miltbrown@...

Subject: [PrimeNumbers] Interpreting Another Prime Puzzle

Corresponding to my posting of January 13, the following PRP's,

from my list may help you see the patterns and discover the

meaning:

PPR of the form 10^x+y

x y x y

=========== =========

1 9933 16 38353

2 7341 17 26371

3 63091 18 3631

4 28333 19 20007

5 13629 20 46291

6 4659 21 3663

7 9001 22 52783

8 3909 23 58333

9 49521 24 15679

10 59689 25 105417

11 55971 26 12379

12 170781

13 29247

14 25291

15 116961

What does the following 50 digit prime number represent:

98199 63091 11696 12833 31362 \

94629 15833 31169 61981 99927

If you need additional discussion, you may contact me

on or off-list.

Milton L. Brown

miltbrown@...

[Non-text portions of this message have been removed]

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

The Prime Pages : http://www.primepages.org/

Your use of Yahoo! Groups is subject to

http://docs.yahoo.com/info/terms/ - The 50 digit prime was

98199 63091 11696 12833 31362 \

94629 15833 31169 61981 99927

The PRP's of the form 10^(10000+x) + y, (smallest y)

transform x :: 1 to 26 corresponding to A to Z

into y which are all unique. This allows English

words to be encoded as patterns in the prime.

To decode the message you must recognize the patterns

and reverse the process. These variable length encodings

also make it more difficult. This corresponds to a

"trap-door" function which is easy to do, but hard

to reverse.

The letter C or 3 corresponds to 63091, and so the message

can be decoded.

Milton L. Brown

miltbrown@...

-----Original Message-----

From: Milton Brown [mailto:miltbrown@...]

Sent: Friday, January 31, 2003 6:24 PM

To: primenumbers@yahoogroups.com

Cc: miltbrown@...

Subject: [PrimeNumbers] Interpreting Another Prime Puzzle

Corresponding to my posting of January 13, the following PRP's,

from my list may help you see the patterns and discover the

meaning:

PPR of the form 10^(10000+x) + y

x y x y

=========== ==================

1 9933 16 38353

2 7341 17 26371

3 63091 18 3631

4 28333 19 20007

5 13629 20 46291

6 4659 21 3663

7 9001 22 52783

8 3909 23 58333

9 49521 24 15679

10 59689 25 105417

11 55971 26 12379

12 170781

13 29247

14 25291

15 116961

What does the following 50 digit prime number represent:

98199 63091 11696 12833 31362 \

94629 15833 31169 61981 99927

If you need additional discussion, you may contact me

on or off-list.

Milton L. Brown

miltbrown@...

[Non-text portions of this message have been removed]

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

The Prime Pages : http://www.primepages.org/

Your use of Yahoo! Groups is subject to

http://docs.yahoo.com/info/terms/

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

The Prime Pages : http://www.primepages.org/

Your use of Yahoo! Groups is subject to

http://docs.yahoo.com/info/terms/