## 11221Re: [PrimeNumbers] RE: Estimating log (B^pi(B))

Expand Messages
• Feb 1, 2003
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
>
>
>Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
>The Prime Pages : http://www.primepages.org/
>
>
>
>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
• Show all 19 messages in this topic