--- In

primeform@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:

> I know in some of your previous sets,

> the /5 (or /30, or whatever)

> has been there to shrink a larger pattern to be the

> right size for a tuplet/CPAP

Indeed. This was a consolation prize for a failed triplet

search. I had 175591 singlets, 540 twins and hence the

probability of failure was

exp(-540^2/175591) = 19%

but I drew that short straw. Then I realized that (since I

had triple sieved) there might be ways of turning this

failure into an AP5 success. So I took all threesomes of

the form (a+k*d)*16001#/5+1 for which three of the integers

k=0,1,2,3,4 had given primes and tested for the two holes,

which had not been tested in the triplet search, since

NewPGen had found that the corresponding numbers

(a+k*d)*16001#/5-1 and/or (a+k*d)*16001#/5+5 were composite.

In the AP5 the two holes were at k=1 and k=3 and

have cognate factors that

pfgw -f -e1000000000

can quickly recover

> 2813053969*16001#/5+5 has factors: 25841

> 2839585489*16001#/5-1 has factors: 572332339

Thanks for your interest,

David

PS: There would have been a tedious ECPP job if the triplet

search had succeeded.