Hello,

cheesehead, I will come back to your answer, but atm I have some other problems detectet while finding some more of these factors.

I createt a list with all known factors (for exponents from 1 to 5000) from the GIMPS database and stored it to a text-file. With my own proggy I read out the exponents, createt the M-numbers, divided out the factors and performed a prp-test at the remaining co-factors. The composite cofactors I stored in a table. Then I deletet all those exponents from this table which are still at the ECM-progress page listet with known factors for ECM'ing.

From the remaining exponents in the list I knew this: my proggy says that the last remaing cofactors of these exponents are still composite but the server hasn't listet them anymore at ECM-page, so the server 'thinks' or 'knows' that the last remaining cofactor is prp. It follows that there must be more factors for these exponents. I searched for them (most I got with the Alpertron, some from Brent's, some from Wagstaff's tables etc...). I attached a list with the factors I got.

But there are 3 exponents I have some problem with:

M857 should be deletet from the ECM-page as the last remaining cofactor is prp afaik, 2 factors were added some hours ago (nice to see such long factors found by ECM

)

But the real problems are M3259 and M4729

from both numbers 1 factor is known at the GIMPS-database:

M3259: 21926805872270062496819221124452121

M4729: 61944189981415866671112479477273

my proggy says: the remaining cofactors of these M-numbers are still composite. They are not listet for ECM'ing with known factors, thus I have to assume the server 'thinks' or 'knows' that these cofactors are prp. But there are no more factors to find for these 2 exponents. The Alpertron makes a Rabin Miller prp-test at the cofactors, I haven't finished them as they need much time. But the output of my proggy's prp-test that they are composite is a statement for sure...

I already run curves with B1=1e6 (changing to B1=3e6 soon) on the remaining cofactors, but I need a verification of the prp-test. Are the remaining cofactors of M3259 and M4729 composite or prp?

If they are composite they should be added to the ECM-progress page with known factors. If they are prp and my proggy's prp-test is faulty then I will report some senseless work in a few hours

.

best regards,

Matthias

Code:

M1223 c
31799,439191833149903
M1289 c
108817410937,827446666316953,9580889333063599,16055826953448199975207
M1303 c
1140690503
M1307 c
141196558805510033914433414063,161633497146742177992711798481
M1327 c
6363071161
M1361 c
3397057,137450113,30322542339673,15459763525875943,856450061281312036458486309832227737
M1459 c
93377
M1531 c
14661821742553
M1553 c
354271470446427666439,432076532964254217618937,67625467049371226906709645391,169336513704068271013494661928987033
M1693 c
3 361912
721093432406946778492953,414073707708708359213580367115039,21637859486326546740118800926236362073
M1783 c
59767828889,21991704205191358757046463,60701317462845977755176049,1943163990190458280022304032374692151
M1997 c
2982351597692070261023,342849716969843931264330628335073
M2069 c
1816583,1662927218441,1776510807594595616100267889706057
M2311 c
4514379640917651135021865565129
M2383 c
889865441849036810633962436005361
M2447 c
2771915076094391,459390495235738452861593,24700068031700569654277801,3922634957266302331319319913
M2549 c
5490243876052618831,324013067177330948216089046508086969
M2677 c
81699346406928829474760749455463
M2699 c
307687,1187561,7570504839257,1987104667810711
M2837 c
138871151,336396730297
M2909 c
46174737359,29101424767901148287,2810063687215981074703243943
M3041 c
5565031
M3259 c
???
M3547 c
148823192092809407
M3833 c
340789152474053904109001
M4127 c
2080009
M4729 c
???
M4751 c
3274778783,629530076753,81630665742097,1507074535068001
M4871 c
144558074148074062894378117006327