Parameters From Realistic Example
To illustrate typical parameter choices for a realistic example on a real implementation including the multiple polynomial and large prime optimizations, the tool msieve was run on a 267-bit semiprime, producing the follow parameters:
- Trial factoring cutoff: 27 bits
- Sieve interval (per polynomial): 393216 (12 blocks of size 32768)
- Smoothness bound: 1300967 (50294 primes)
- Number of factors for polynomial A coefficients: 10 (see Multiple polynomials above)
- Large prime bound: 128795733 (26 bits) (see Large primes above)
- Smooth values found: 25952 by sieving directly, 24462 by combining numbers with large primes
- Final matrix size: 50294 × 50414, reduced by filtering to 35750 × 35862
- Nontrivial dependencies found: 15
- Total time (on a 1.6 GHz UltraSparc III): 35 min 39 seconds
- Maximum memory used: 8 MB
Read more about this topic: Quadratic Sieve
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