Wasting time at 100 digits

[fivemack]

In search of a polynomial of unreasonable splendor, I searched C4=0..400k for the 99-digit number

138085380262017373391847464640141690192010578238288085140109139681731008586729833372478334305456977

This took eleven hours, which is much longer than the sieving and linear algebra took; as I said, I was wasting time. But I might as well make some observations, having wasted that much time:

* The yield of adequate polynomials drops off quite quickly with C4 (391 in 0..100k, 75 in 100k..200k, 46 in 200k..300k, 35 in 300k..400k)
* The distribution of scores was (*1e8)

1.0-1.1 235
1.1-1.2 182
1.2-1.3 66
1.3-1.4 51
1.4-1.5 12
1.5-1.6 1

* The best polynomial had score 1.543e-8 and came from c4=66000, the second-best had 1.494e-8 and came from c4=120 right at the start of the run
* Sieving with the best polynomial (12e, 24-bit large primes, alim=400k, sieve Q=200k..600k) took 5495 seconds for 1782015 relations and a matrix size of 114k. 1650k relations is enough to run with a matrix size of 132k (1600 is not); so say 5100 seconds for sieving just-enough. Duplication rate at the end is about 20%
* Sieving with the worst polynomial, of score 1.035e-8 (12e, 24-bit large primes, alim=400k, sieve Q=200k..1000k) took 9555 seconds for 1918123 relations and a matrix size of 155k; 1850k is not enough to get a matrix, 1875k is (matrix size 168k); say 9340s for just enough sieving. Duplication rate at the end is 27%

So a polynomial of score 0.67*B produces a matrix of size 1.27*M_B and takes 1.83*t_B to get there.