Given the 1,2,15 seed, or 1,2,12 seed etc

Couldn't we check for a 4th element using ECM, and a 5th element (e) such

that we can form a 5-carm of the form N = e*1*2*15*ECMFactor

Carms of that form

5,7,13,193,439,9637697

5,7,13,193,499,2657,42829

5,19,37,547,1009,3211937

7,19,37,541,601,58741

7,79,157,2341,3541,9181

13,19,37,541,631,2689

13,19,37,541,739,811,1231

13,19,37,541,1009,2311

17,37,73,1093,2081,65521

17,37,73,1093,93809

With my dataset i will have 4 billion possible e values and 350 titanic

seeds of whatever 3 part seed that is picked. Is it possible to create a

carm by extending a "seed" at both ends. IE creating a custom formula for

each e*1*2*15 which is then ecm'd. to get a prime that

makes e*1*2*15*ECMFactor PRP

Markus

>But Markus is stuck with his NewPgen output and so

>can't use CRT. So I thought it would be useful

>to give {1,2,12} a proof in principle by beating the

>4-Carmichael 4th factor record.

>

>In fact I did it twice over:

>

>2763260532*((1591638066432*3061#+19)^2-1)*3061#/

>286610757607008951353515277095+1 3909 p44 03

>4-Carmichael factor (4)

>

>757849549*((72753556704*3061#+19)^2-1)*3061#/

>56731664597567983567442428202862519351615138+1 3891 p44 03

>4-Carmichael factor (4)

>

>finding ECM factors at about twice

>the rate for this seed as compared with

>the other seeds in my plantpot.

>

>OK, it's a trivial [and suspect] use of Dickman.

>

>But it was funny that you should mention him

>just after I had commented on another such seed

>{1,2,15}. But Markus can't use that

>Dickman-enhanced seed, since he

>can't get x=1 mod 5 in

>

>? print(factor((1+x)*(1+2*x)*(1+15*x)-1))

>[x, 1; 3*x + 2, 1; 10*x + 9, 1]

>

>because he used primorial mode in NewPgen.

>

>David

>

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