--- In primenumbers@y..., John McNamara <mistermac39@y...> wrote:

> (1) Let f(x,y) = x^2 - y^2 -2xy.

> f(3511,1093) = 7294949 and is prime P.

>

> (2) 7294950 = 2*3*3*5*5*13*29*43 which made it easy to

> factorise into its 8 factors, of which 5 are less than

> (P+1)^(1/8) and all less than (P+1)^(1/4). This fact

> seem to me to make 7294950 fairly interesting as only

> 6435 previous composites have the property of having 8

> prime factors, one in more than a thousand.

Notice that (1) should be read f(x,y) = x^2 - y^2 -xy

to get f(3511,1093) = 7294949.

Assuming this, other prime pairs (x,y) exist that

satisfy f(x,y) = P (prime) and P+1 have the property

of having 8 prime factors.

As an example, the prime pair (47,2) gives

P=f(47,2)=2111 prime and P+1=2*2*2*2*2*2*3*11.

Regards

Flavio Torasso