> > CONJECTURE ON PRIMES (Z. W. Sun, March 17-18, 2012). For k=1,2,3,... let

> > P_k denote the product of the first k primes p_1,...,p_k.

> >

> > (i) For n=1,2,3,... define w_1(n) as the least integer m>1 such that m

> > divides none of P_i-P_j with i,j distinct and not more than n. Then

> > w_1(n) is always a prime.

>

> Isn't it self evident that the first (least) integer which doesn't divide into another integer, is a prime number? Or am I misunderstanding something here ...

Ignoring Sun's definition of P_i, if we set <P1, P2, P3> = <1, 3, 4>, the

corresponding value of w_1(3) would be equal to 4; not a prime. Thus,

there must be something special about his definition of P_i, which makes

the resulting ones primes [or his conjecture is false :-) ].

Peter

[Non-text portions of this message have been removed]