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• ... 29 = 4.7+1, and 7 is prime 5.29 = 145 = 1mod4 so your move is not legal. ... I will assume that you misunderstood the rules, and allow you another chance.
Message 1 of 28 , Sep 4, 2002
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>If k is prime or 1, then the next person must respond with a prime q such
>that pq=-1mod4

29 = 4.7+1, and 7 is prime

5.29 = 145 = 1mod4

so your move is not legal.

>This game is very intolerant - a false move results in immediate expulsion
>from the game.

I will assume that you misunderstood the rules, and allow you another
chance.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• ... Jon, I analyzed your game, and you should note that in a 2-player game, an opening move of 29 is a losing move. After a 29, these are all winning moves for
Message 2 of 28 , Sep 4, 2002
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--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:
>
> 29
>

Jon, I analyzed your game, and you should note that in a 2-player
game, an opening move of 29 is a losing move.

After a 29, these are all winning moves for the second player:

23, 31, 47, 59, 71, 79, 83

(any prime of the form 4k-1 with k composite)

So if you want to play...

29 -> 23 -> your turn...
• Hmmm... deep thought involved: 29 - 23 - 3 23=4.6-1, 6 is composite, therefore 23.3 must be 1mod4 (1 is prime) Jon Perry perry@globalnet.co.uk
Message 3 of 28 , Sep 4, 2002
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Hmmm... deep thought involved:

29 -> 23 -> 3

23=4.6-1, 6 is composite, therefore 23.3 must be 1mod4

(1 is prime)

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• ... To which I respond: 29 - 23 - 3 - 5
Message 4 of 28 , Sep 4, 2002
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--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

> 29 -> 23 -> 3

To which I respond:

29 -> 23 -> 3 -> 5
• ##To which I respond: ##29 - 23 - 3 - 5 29 - 23 - 3 - 5 - 83 (p.s. post to the list, as anyone can join it at any time, thus smashing your I m going to
Message 5 of 28 , Sep 5, 2002
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##To which I respond:

##29 -> 23 -> 3 -> 5

29 -> 23 -> 3 -> 5 -> 83

(p.s. post to the list, as anyone can join it at any time, thus smashing
your 'I'm going to win 'coz I went second' into unimaginably little pieces)

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: jbrennen [mailto:jack@...]
Sent: 04 September 2002 21:38

--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

> 29 -> 23 -> 3
• ... First, 29 - 23 - 3 - 5 - 83 - 31 Second, that s not what I said... What I said was that *in a two player game*, 29 is a losing play to start the game.
Message 6 of 28 , Sep 5, 2002
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--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:
>
> 29 -> 23 -> 3 -> 5 -> 83
>
> (p.s. post to the list, as anyone can join it at any time, thus
> smashing your 'I'm going to win 'coz I went second' into
> unimaginably little pieces)

First,

29 -> 23 -> 3 -> 5 -> 83 -> 31

Second, that's not what I said...
What I said was that *in a two player game*, 29 is a losing
play to start the game. Note that any prime of the form 4k+/-1
with k composite is a winning opening (the smallest such number
being 17). All other openings are losing openings.

Third, if anyone can join at any time, the concept of winning or
losing is nonsensical. Is the 'winner' the last person able to
add a number? If so, it's just a race to see who can post first
after the penultimate number is posted. And there is no 'loser'
of course, since nobody is obligated to 'go next' ...

The following applies to the 2-player game only...

Note that the opening strategy varies depending on the upper limit
of primes we're allowed to use.

A = 4k-1, where k is 1 or prime
B = 4k+1, where k is composite
C = 4k+1, where k is 1 or prime
D = 4k-1, where k is composite

Prime limit: winning play to start

3: A
5: any opening loses
7: A
11: A
13: A
17: B or C
19: B or C
23: B or D
29: B or D
31: B or C
37: A
41: B or C
43: B or C
47: B or D
53: B or D
59: B or C
61: A
67: A
71: A
73: B or D
79: B or C
83: B or D
89: A
97: B or D

An obvious question -- is limit=5 the only game for which the
opening player has no forced win?
• ... I just answered this for myself... If the limit is 389, the opening player has no winning play.
Message 7 of 28 , Sep 5, 2002
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--- In primenumbers@y..., "jbrennen" <jack@b...> wrote:
>
> An obvious question -- is limit=5 the only game for which the
> opening player has no forced win?

I just answered this for myself...

If the limit is 389, the opening player has no winning play.
• 29 - 23 - 3 - 5 - 83 - 31 - 7 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML and JavaScript
Message 8 of 28 , Sep 6, 2002
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29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13
Message 9 of 28 , Sep 6, 2002
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29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 97 (imagine this was a C++ object!) Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths
Message 10 of 28 , Sep 6, 2002
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29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 97

(imagine this was a C++ object!)

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• ... A problem -- 97 is not a valid successor to 13. 13 is of the form 4k+1, with k prime, so you must respond with a prime q such that 13q = -1 (mod 4).
Message 11 of 28 , Sep 6, 2002
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--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

> 29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 97

A problem -- 97 is not a valid successor to 13.

13 is of the form 4k+1, with k prime, so you must respond
with a prime q such that 13q = -1 (mod 4).
• Sorry - I must have been sleep surfing. ... Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML and
Message 12 of 28 , Sep 7, 2002
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Sorry - I must have been sleep surfing.

> 29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 79

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: jbrennen [mailto:jack@...]
Sent: 06 September 2002 22:05

--- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

> 29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 97

A problem -- 97 is not a valid successor to 13.

13 is of the form 4k+1, with k prime, so you must respond
with a prime q such that 13q = -1 (mod 4).

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
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• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47
Message 13 of 28 , Sep 9, 2002
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29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 79 -> 47
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for
Message 14 of 28 , Sep 9, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53
Message 15 of 28 , Sep 9, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths
Message 16 of 28 , Sep 9, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17
Message 17 of 28 , Sep 9, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 Jon Perry perry@globalnet.co.uk
Message 18 of 28 , Sep 10, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37
Message 19 of 28 , Sep 10, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97 ->
37
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 Jon Perry perry@globalnet.co.uk
Message 20 of 28 , Sep 11, 2002
• 0 Attachment
29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97 ->
37 -> 61

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 - 41
Message 21 of 28 , Sep 11, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97 ->
37 -> 61 -> 41
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 - 41 - 73 Jon Perry perry@globalnet.co.uk
Message 22 of 28 , Sep 11, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97 ->
37 -> 61 -> 41 -> 73

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• 29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 - 41 - 73 - 89 Checkmate.
Message 23 of 28 , Sep 11, 2002
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29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97 ->
37 -> 61 -> 41 -> 73 -> 89

Checkmate.
• Jack is hereby declared the Winner. How about we go again? - only this time if the k is prime, then the mod must be opposite to the last mod, otherwise the
Message 24 of 28 , Sep 11, 2002
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Jack is hereby declared the Winner.

How about we go again? - only this time if the k is prime, then the mod must
be opposite to the last mod, otherwise the same.

e.g. 13 -> (anything, say...) 17 ->

17 is 4.4+1, 4 is composite, therefore reply with a number that when
multiplied by 17 is the same sign as 13*17 (=1mod4), i.e. reply with a
1mod4.

If the second go was 19, then 13.19=3mod4, therefore as the k for 19 is 5,

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: jbrennen [mailto:jack@...]
Sent: 11 September 2002 19:27

29 -> 23 -> 3 -> 5 -> 83 ->
31 -> 7 -> 13 -> 79 -> 47 ->
11 -> 53 -> 19 -> 17 -> 97 ->
37 -> 61 -> 41 -> 73 -> 89

Checkmate.

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• I forgot to go first: 89 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML and JavaScript
Message 25 of 28 , Sep 11, 2002
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I forgot to go first:

89

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
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