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Old 2020-10-18, 23:35   #1
charybdis
 
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Apr 2020

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Default NFS cofactorization with 3LP

When sieving with 2 large primes, one tends to find that the optimal value of mfb is slightly less than 2*lpb. Presumably this is because a composite cofactor close to 2^(2*lpb) is unlikely to split into two primes that are both smaller than 2^lpb. For example, for lpb=32 the optimum value of mfb with CADO-NFS appears to be 60.

Similarly, when sieving with 3 large primes, the optimum value of mfb is slightly less than 3*lpb. However, what happens if we get a cofactor that is just below 2^(2*lpb)? Such a cofactor is still unlikely to contribute to a relation: as in the 2LP case, it is probably not the product of two primes both smaller than 2^lpb, and it will also be too small to be the product of three large primes. So again it should make sense to set a double large prime bound smaller than 2^(2*lpb).

Neither GGNFS nor CADO appear to have an option to set a double large prime bound separately from mfb when using 3LP. Does anyone here know what is actually done? Is a value computed automatically, perhaps from the mfb given?
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