--- In

primenumbers@yahoogroups.com, "Mark" <mark.underwood@...> wrote:

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> --- In primenumbers@yahoogroups.com, "Dimiter Skordev" <skordev@> wrote:

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> > Let A be the least set of natural numbers with the following two properties:

> > (i) the number 1 belongs to A;

> > (ii) whenever x belongs to A, and y is a prime divisor of x+1, the product x*y also belongs to A.

> > Let us call a prime number Euclid-style accessible if it is a divisor of some number belonging to A. Are there prime numbers that are not Euclid-style accessible, and if there are such ones, which is the least among them?

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> I can't think of a reason why any prime would be excluded from being a factor of numbers in the set. I've only gone 5 'deep', and thus far 19 is the only prime < 29 that hasn't shown up yet. 11 and 17 were late to the party, but they eventually surfaced at depth 5. Have you gone further?

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> Mark

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No, I have not gone even to that depth.