- Trying to factor 134^131+131^134, I obtained:

GMP-ECM 5.1-beta [powered by GMP 4.1] [P-1]

Input number is 25865447487363725783122634349075395812340400623026024679130966646043807574550805573958725860457194408072135499668441003308474484944428943584532115942895847887759143649437935379122607964373488754857613201155063924520774277362143078736973209926360612163137002918023001 (266 digits)

Using B1=10000000, B2=732940912, polynomial x^24, x0=2101091962

Step 1 took 102255ms

Step 2 took 29094ms

********** Factor found in step 2: 1713776305533792578182169122961

Found probable prime factor of 31 digits: 1713776305533792578182169122961

Composite cofactor 15092662562695062190247830140515451896766513154868853489965873041122539539760189456815505401475408896982253689154264478030985178890080361607674298468006609898425851973638515015599202280707306886386928007775058770877765909292554751405641 has 236 digits

All is OK, because

P-1 = 1713776305533792578182169122960 = 2*2*2*2*5*7*17*17*89*401*290827*1497107*681469339

But then I found the same factorization among my P+1 results:

GMP-ECM 5.1-beta [powered by GMP 4.1] [P+1]

Input number is 25865447487363725783122634349075395812340400623026024679130966646043807574550805573958725860457194408072135499668441003308474484944428943584532115942895847887759143649437935379122607964373488754857613201155063924520774277362143078736973209926360612163137002918023001 (266 digits)

Using B1=10000000, B2=1967819029, polynomial x^1, x0=461132087

Step 1 took 132377ms

Step 2 took 62497ms

Line=1/1 Curves=2/3 B1=10000000 factors=0

C266 Using B1=10000000, B2=1967819029, polynomial x^1, x0=1494475138

Step 1 took 132816ms

Step 2 took 62399ms

[factor found by P-1]

********** Factor found in step 2: 1713776305533792578182169122961

Found probable prime factor of 31 digits: 1713776305533792578182169122961

Composite cofactor 15092662562695062190247830140515451896766513154868853489965873041122539539760189456815505401475408896982253689154264478030985178890080361607674298468006609898425851973638515015599202280707306886386928007775058770877765909292554751405641 has 236 digits

Line=1/1 Curves=3/3 B1=10000000 factors=1

C236 Using B1=10000000, B2=1967819029, polynomial x^1, x0=3018874033

Step 1 took 110956ms

Step 2 took 54854ms

Is it normal? Using B1 = 10^7, we find the factor P with

P+1 = 1713776305533792578182169122962 = 2*3*285629384255632096363694853827

Andrey

[Non-text portions of this message have been removed] > The first item is in the ECM-GMP documentation. It states that you

Understand. I should be more attentive before asking a question, as usual...

> need to run P+1 a total of 3 times since it has roughly a 50/50

> chance of actually executing a P-1 instead of a P+1. I don't know the

> math behind it, I just know what the document states.

>

> The second item is that if you look carefully in the ECM-GMP output,

> you'll see a line within brackets saying that this factor was found

> via P-1.

:-)

Thanks,

Andrey> Trying to factor 134^131+131^134, I obtained:

...

> ********** Factor found in step 2: 1713776305533792578182169122961

...

> Found probable prime factor of 31 digits:

> 1713776305533792578182169122961

> All is OK, because

>

> P-1 = 1713776305533792578182169122960 =

> 2*2*2*2*5*7*17*17*89*401*290827*1497107*681469339

>

> But then I found the same factorization among my P+1 results:

> Is it normal? Using B1 = 10^7, we find the factor P with

Yes, it is normal. If you don't happen upon a lucky starting number for P+1, you end up doing a (very slow) P-1.

>

> P+1 = 1713776305533792578182169122962 =

> 2*3*285629384255632096363694853827

Paul- I made the same identical mistake myself. You have to take into

account two items of information.

The first item is in the ECM-GMP documentation. It states that you

need to run P+1 a total of 3 times since it has roughly a 50/50

chance of actually executing a P-1 instead of a P+1. I don't know the

math behind it, I just know what the document states.

The second item is that if you look carefully in the ECM-GMP output,

you'll see a line within brackets saying that this factor was found

via P-1. (Look 4 lines into the clip below). This signifies that

while you executed a P+1 pass, the factor was found via P-1. To

determine if there exists a factor via P+1, you must run a total of 3

passes of P+1 and check for a factor to be found without the P-1

statement within the output.

> C266 Using B1=10000000, B2=1967819029, polynomial x^1, x0=1494475138

1713776305533792578182169122961

> Step 1 took 132816ms

> Step 2 took 62399ms

> [factor found by P-1]

> ********** Factor found in step 2: 1713776305533792578182169122961

> Found probable prime factor of 31 digits:

> Composite cofactor

1509266256269506219024783014051545189676651315486885348996587304112253

9539760189456815505401475408896982253689154264478030985178890080361607

6742984680066098984258519736385150155992022807073068863869280077750587

70877765909292554751405641 has 236 digits