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Old 2020-11-22, 15:48   #1
storm5510
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Default ECM Factors

Question: Where are the majority of factors found in ECM? Stage 1 or Stage 2?
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Old 2020-11-22, 18:20   #2
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Quote:
Originally Posted by storm5510 View Post
Question: Where are the majority of factors found in ECM? Stage 1 or Stage 2?
It depends.


With my workload it is in stage 2.
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Old 2020-11-23, 15:31   #3
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Originally Posted by xilman View Post
It depends.

With my workload it is in stage 2.
Several years ago, a member here told me,"Multiple factors can be found below B1, but only one factor above." I wanted to check the validity of this statement. Apparently, this is not always the case.
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Old 2020-11-23, 16:32   #4
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Quote:
Originally Posted by storm5510 View Post
Several years ago, a member here told me,"Multiple factors can be found below B1, but only one factor above." I wanted to check the validity of this statement. Apparently, this is not always the case.
Something's lost in translation. Rather than explain why you've misunderstood that (oddly phrased) statement, can you explain to us why you think that is not always the case?
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Old 2020-11-23, 16:44   #5
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Quote:
Originally Posted by storm5510 View Post
Several years ago, a member here told me,"Multiple factors can be found below B1, but only one factor above." I wanted to check the validity of this statement. Apparently, this is not always the case.
I think it might mean that if a number has several prime factors stage 1 might find a composite factor, the product of more that 1 prime factor. But stage 2 would not find a composte factor.

But that's not true. A quick search of recent ECM work I've done reveals:
Code:
********** Factor found in step 2: 450447448630040607679056578447
Found composite factor of 30 digits: 450447448630040607679056578447
Prime cofactor 857728978884123546562041187998599433152336542089743038903 has 57 digits
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Old 2020-11-23, 18:00   #6
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Something's lost in translation. Rather than explain why you've misunderstood that (oddly phrased) statement, can you explain to us why you think that is not always the case?
Because of this:

Quote:
Originally Posted by xilman
With my workload, it is in stage 2.
.
"Multiple factors can be found below B1, but only one factor above..."

Oddly phrased? Perhaps the individual who wrote this statement thought I may not understand a more complex response, so he kept it simple. This was probably three years ago, at least. Who wrote it, I cannot remember.
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Old 2020-11-23, 18:39   #7
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Quote:
Originally Posted by storm5510 View Post
Several years ago, a member here told me,"Multiple factors can be found below B1, but only one factor above." I wanted to check the validity of this statement. Apparently, this is not always the case.
I think it is a misunderstanding that comes from P-1, where the method will find a factor p if p-1 is "smooth enough": Meaning that all of p-1 factors are below B1 with at most 1 factor allowed in between B1 and B2. But this requirement of p-1 has nothing to do with the factors p that the method finds.

Besides with ECM it is the group order that has to be smooth and the group order changes with each curves sigma.

Last fiddled with by ATH on 2020-11-23 at 18:43
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Old 2020-11-23, 19:18   #8
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Quote:
Originally Posted by storm5510 View Post
Because of this:

.
"Multiple factors can be found below B1, but only one factor above..."

Oddly phrased? Perhaps the individual who wrote this statement thought I may not understand a more complex response, so he kept it simple. This was probably three years ago, at least. Who wrote it, I cannot remember.
What does finding more factors in stage 2 have to do with that "multiple factors" statement? Those seem completely unconnected, yet you used "because of this". So, I too fear there is a substantial set of misunderstandings here, and a quick correction of one bad assumption won't cure the real problem.
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