--- In

primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>

wrote:

> If z= p1^2 * p2^2 * p3^2 * ... * pn^2 +1 (where p1, p2, p3, etc.

form

> the ordered prime number sequence 2, 3, 5, etc.), then either

> z or z-2 must contain one and only one twin prime factor > pn.

>

> Can anyone find a counter-example? I check it up to pn= 89.

>

Well, if pn = 61,

then z = 13756564401909684622656803563109083750619892901

And neither z nor z-2 contains any twin prime factor.

z = 96973 * 141859738297357868918738242223186698881337

z - 2 = 223 * 1193 * 85738903 * 1146665184811 * 525956867082542470777

Unless of course, your definition of "twin prime factor" is

different than mine???