las --adjust-strategy 2 does not properly sieve projective primes [was: las outputs relation with composite factor]
Reported by Robert Balfour on the mailing-list:
I've found a case where las produces a relation where one of the factors is the square of a prime. This was picked up by msieve filtering; I haven't tried CADO filtering on this dataset. Is this expected behaviour or a bug?
The relation is: 2511674949,47519:2,2,2,2,2,2f,3d,359,587b,253c69,91b17f,107ef81:2,2,2,3,3,3,5,5,7,b,59,2f41,2fa5,25a29,cb45f,1b1a87,b35a35,4dcef0f,146baa23 where 0x107ef81 = 17297281 = 4159^2 = (0x103f)^2. This number was correctly factored as 103f,103f in other relations. Both the latest revision and revision dbdb6eb5 fail to split 107ef81 in this relation.
Number and polynomials are:
n:
295050353250969949275638952676190854099143197890400946947699613474117769236877135613197953075573082247700069221444132611618998393933743532422465257
# f(x) = -3003840*x^5+957820236360*x^4+1389898521545792753*x^3-322967502530987876578342*x^2-83629655633967437555949973621*x+3423180581131422410334670590644010
# g(x) = 164665144403235916141*x-15113634718431527142364842527
Parameters used for sieving:
tasks.I = 14
tasks.qmin = 4000000
tasks.lim0 = 13000000
tasks.lim1 = 25000000
tasks.lpb0 = 29
tasks.lpb1 = 29
tasks.sieve.mfb0 = 54
tasks.sieve.mfb1 = 57
tasks.sieve.lambda0 = 2.06
tasks.sieve.lambda1 = 2.165
tasks.sieve.ncurves0 = 15
tasks.sieve.ncurves1 = 20
tasks.sieve.qrange = 10000
tasks.sieve.adjust_strategy = 2
tasks.sieve.rels_wanted = 60000000
The relation was found in the range 11750000-11760000 (q=11754037).