## Re: Prime sequence teaser!

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• ... Suggestion: Strip my Sophies ... and then the residual part of his diseased brain :-) resides in ... of Cunningham base-2 [pmain901] David (refusing to
Message 1 of 29 , May 29, 2002
Marcel:

> except 11113. I failed

Suggestion: Strip my Sophies

> 7 23 47 167 263 359 383 479 503 719 839
> 863 887 983 1319 1367 1439 1487 1823

from Phil's perversity:

> 23, 47, 431, 167, 263, 359, 383, 479,
> 503, 719, ...
> 839 863 887 11113 983 1319 1367 1439
> 1487 8831

and then the residual part of
his diseased brain :-)
resides in

> 43 431.9719.2099863

> 463 11113.3407681.448747600991881.239932071009857681156251129.
> 385606580062688087218266143.P62

> 883 8831.63577.258777491057348926546569104663.P228

of Cunningham base-2 [pmain901]

David (refusing to ORDER:-)
• ... And even then the setter can return and say: you got the right answer for a different reason, perhaps. Frankly, I opted out, on the grounds that such
Message 2 of 29 , May 29, 2002
Marcel:
> Each time I try to solve a puzzle, I believe
> that the key is to find _the_
> interesting property which justifies the
> puzzle :-)
And even then the setter can return and say:
you got the right answer for a different reason,
perhaps.
Frankly, I opted out, on the grounds that
such things are not to be encouraged.
David
• PS: I hope you appreciate, dear Marcel, that Phil will probably slap your hand for suggesting that he ever said that 193949641=3863*50207 was part of his ...
Message 3 of 29 , May 29, 2002
PS: I hope you appreciate, dear Marcel, that Phil
will probably slap your hand for suggesting
that he ever said that
193949641=3863*50207
was part of his
> Prime sequence teaser!
..^^^^^
When he asked, "what comes next"
he probably meant: find the next composite.
Sorry about that, but I thought you
should learn of it from a friend
rather than from the teaser himself...
David
• For the truly perverse: 174143*2263847 193949641 = 3863*50207 However I wish it to be recorded that this true statement is in no way to be construed as a
Message 4 of 29 , May 29, 2002
For the truly perverse:

174143*2263847 > 193949641 = 3863*50207

However I wish it to be recorded that
this true statement is in no way to
be construed as a response to Phil's postings;
rather I offer it in deference to Marcel's
great igenuity, which far exceeded mine.

David
• ... The sequence was _generated_ by primes, I never promised it contained only primes. Maybe the fact that I owned up to it including the number 193949641
Message 5 of 29 , May 29, 2002
> PS: I hope you appreciate, dear Marcel, that Phil
> will probably slap your hand for suggesting
> that he ever said that
> 193949641=3863*50207
> was part of his
> > Prime sequence teaser!
> ..^^^^^
> When he asked, "what comes next"
> he probably meant: find the next composite.
> Sorry about that, but I thought you
> should learn of it from a friend
> rather than from the teaser himself...

The sequence was _generated_ by primes, I never promised it contained
only primes. Maybe the fact that I owned up to it including the
number 193949641 would have been enough of a clue that it wasn't
entirely prime in its contents, But maybe not.
How should I know, I'm merely the generator! Erm... Sue me?

Phil

=====
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hard disk." - Prof. Stuart E Madnick, MIT.
So called "expert" witness for Microsoft. 2002/05/02

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• ... It is quite sufficient to shame you. David :-)
Message 6 of 29 , May 29, 2002
Phil:
> Sue me?
It is quite sufficient to shame you.
David :-)
• ... The simple script was: \$ calc p=1;while(p 1)print g;} i.e. you re spot on. Well done. I m reading mail in
Message 7 of 29 , May 29, 2002
--- Marcel Martin <znz@...> wrote:
>
> In short, the sequence is constituded of the gcd's
> (2^p_i-1,3^p_i-1).

The 'simple script' was:

\$ calc
'p=1;while(p<999){p=nextprime(p);g=gcd(2^p-1,3^p-1);if(g>1)print g;}'

i.e. you're spot on.

Well done.
I'm reading mail in reverse, but s far you're the first to have
described it in the terms that I vieed it in. Which makes you a
winner, if there is such a thing. :-|

> As far as I am concerned, it is impossible to find such result.
> Each
> time I try to solve a puzzle, I believe that the key is to find
> _the_
> interesting property which justifies the puzzle :-)
>
> >Bonus question:
> >What comes next in this subsequence of the above?
> > 193949641, ...
>
> 4007,

Hmmm, those looked a little prime to me.

Anyone got any composites that are in the sequence?

Of course, if you obeyed orders, then the answer is p s.t. Order(2,
mod p) = Order(3, mod p). So a coincidence isn't impossible. One
composite was interesting, but I never found a second...

Phil

=====
--
"One cannot delete the Web browser from KDE without
losing the ability to manage files on the user's own
hard disk." - Prof. Stuart E Madnick, MIT.
So called "expert" witness for Microsoft. 2002/05/02

__________________________________________________
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• ... Now that I ve released the answer I have no problem re-posing the question without the obfuscation. The initial sequence I posed was the non-1 values for
Message 8 of 29 , May 29, 2002
--- Insall <montez@...> wrote:
> Phil wrote: ``And I am genuinely interested in the answer to the
> bonus
>
> I am a newbie. Would you mind repeating for me the ``bonus
> question''?

Now that I've released the answer I have no problem re-posing the
question without the obfuscation.

The initial sequence I posed was the non-1 values for gcd(2^p-1,
3^p-2) for prime p. I calculated about something like 5000 terms, and
many of them were 1. Some, the ones I posted as the original
sequence, were not 1, and were prime. However _one_ term was a
composite. That was the 'bonus' sequence.

What is the next composite value of gcd(2^p-1,3^p-1)?
Genuinely, I don't know.

Phil

=====
--
"One cannot delete the Web browser from KDE without
losing the ability to manage files on the user's own
hard disk." - Prof. Stuart E Madnick, MIT.
So called "expert" witness for Microsoft. 2002/05/02

__________________________________________________
Do You Yahoo!?
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• It get s even more boring: 213407*2774279
Message 9 of 29 , May 29, 2002
It get's even more boring:
213407*2774279
• ... 3^p-1, that is And yes, I deny any inginuity in coming up with the sequence, and ascribe all whatevers to whomever. Phil ===== -- One cannot delete the
Message 10 of 29 , May 29, 2002
--- Phil Carmody <thefatphil@...> wrote:
>
> --- Insall <montez@...> wrote:
> > Phil wrote: ``And I am genuinely interested in the answer to the
> > bonus
> >
> > I am a newbie. Would you mind repeating for me the ``bonus
> > question''?
>
> Now that I've released the answer I have no problem re-posing the
> question without the obfuscation.
>
> The initial sequence I posed was the non-1 values for gcd(2^p-1,
> 3^p-2) for prime p. I calculated about something like 5000 terms,

3^p-1, that is

And yes, I deny any inginuity in coming up with the sequence, and
ascribe all whatevers to whomever.

Phil

=====
--
"One cannot delete the Web browser from KDE without
losing the ability to manage files on the user's own
hard disk." - Prof. Stuart E Madnick, MIT.
So called "expert" witness for Microsoft. 2002/05/02

__________________________________________________
Do You Yahoo!?
Yahoo! - Official partner of 2002 FIFA World Cup
http://fifaworldcup.yahoo.com
• ... gcd(2^1931-1,3^1931-1) trivially factors as: 3863*50207 gcd(2^87071-1,3^87071-1) has factors: 174143*2263847 gcd(2^106703-1,3^106703-1) has factors:
Message 11 of 29 , May 30, 2002
> Anyone got any composites that are in the sequence?
gcd(2^1931-1,3^1931-1) trivially factors as: 3863*50207
gcd(2^87071-1,3^87071-1) has factors: 174143*2263847
gcd(2^106703-1,3^106703-1) has factors: 213407*2774279
gcd(2^215863-1,3^215863-1) has factors: 2158631*5180713
gcd(2^305219-1,3^305219-1) has factors: 610439*29911463
gcd(2^327779-1,3^327779-1) has factors: 655559*16388951
gcd(2^453983-1,3^453983-1) has factors: 907967*10895593
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