--- 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?