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2014-04-29, 10:45
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#1 |
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Apr 2011
2·5 Posts |
Which unfactorable natural composite has had the most ECM?
I want to generate a short list of composite numbers ordered by the expected lower bound on the smallest factor based on ECM factoring effort.
A composite numbers which is the product of generated primes is in a sense an "artificial" composite as if the primes had not been forgotten then factorizing it would be trivial. I'm only interested in "natural" composites which commonly have a short description. By "unfactorable" I mean that if a factor is not found using ECM then the number is so large that it is expected that a NFS factorization is impractical for the forseeable future. A short search shows that 2^1753-1 might be a good champion as it has over 500 digits, no factors known and over 63k curves at B1=800M Does anyone have any non-mersenne and non-cunningham candidates? |
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2014-04-29, 14:53
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#3 |
Sep 2008
Kansas
3×1,129 Posts |
C561
I can submit one.
235^235+236^236 34988 at B1=110000000 61988 at B1=260000000 71212 at B1=850000000 75372 at B1=2900000000 77640 at B1=7600000000 80488 at B1=10000000000 79688 at B1=25000000000 Plus -pm1 at B1=200000000000 (2e11) |
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