## RE twin prim conjecture extended

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• ... From: Sebastian Martin ... Counterexample [contraejemplo]: p = 3, q = 11 z = sqrt( (p^2+q^2)/2 -1 ) = = sqrt( (9+121)/2 -1 ) = =
Message 1 of 2 , Jul 7, 2006
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----- Original Message -----
From: "Sebastian Martin" <sebi_sebi@...>

>I have extended the conjecture:
>p, q consecutive primes p<q
>are equivalents:
>1) p q are twin primes
>2) z=sqrt[(p^2+q^2)/2-1] is integer

Counterexample [contraejemplo]:

p = 3, q = 11

z = sqrt( (p^2+q^2)/2 -1 ) =

= sqrt( (9+121)/2 -1 ) =

= sqrt( 130/2 -1 ) =

= sqrt(64) = 8

There are plenty more... [Hay muchos más...]
(3,31), (7,59), (11,23), (11,41)...

Dude, I thought you had done an extended search! :-( [Tío, ¡creía que habías hecho una
búsqueda exhaustiva! :-(]

Pari-GP code:
forprime(p=3,100,forprime(q=3,100,if(issquare((p^2+q^2)/2-1),print(i","j)))

3,5
3,11
3,31
5,3
5,7
7,5
7,59
11,3
11,13
11,23
11,41
11,67
13,11
17,19
19,17
23,11
29,31
31,3
31,29
31,79
31,97
41,11
41,43
43,41
59,7
59,61
59,83
61,59
67,11
71,73
73,71
79,31
83,59
97,31

Regards. Jose Brox
• ... From: Jose Ramón Brox ... Ooops... as Paul Jobling noted to me, I missed the condition of p and q being _consecutive_. Sorry. Jose
Message 2 of 2 , Jul 7, 2006
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----- Original Message -----
From: "Jose Ramón Brox" <ambroxius@...>

>Counterexample [contraejemplo]:
>p = 3, q = 11
>(...)

Ooops... as Paul Jobling noted to me, I missed the condition of p and q being
_consecutive_. Sorry.

Jose Brox
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