RSA512:

We assume that a file rsa512.data exists. The following should produce a
good polynomial for this number:

$ ./pol51m0 -b rsa512 -v -v -p 7 -n 6e22 -a 28000 -A 29000
Parameters: number: 1.094e+154, norm_max: 6.000e+22, a5: 2.800e+07 - 2.900e+07
Accected a5-range: 1.000000 - 123897297399046.968750 
Searching in subinterval: 28000020 - 29000000
..........................28172400 207899046817573037944003980721 1431689581421081
490457424114402 207899046817571298429701341940
......28200000 207858335743926583066618629796 14507315380338583
2513405668036628 207858335743889845727447842295
.............................................................................................................28788360 207001685830582539787623092532 277876585108001
67319283658787 207001685830581576549075927732
..................................Statistics:
a5-values: 16673, suitable for 7 primes: 3913
raw checks of (a5,p): 1945962 (1089573),  fine checks of (a5,p): 0
polynomials computed: 547,  survivors: 3
Total number of checked polynomials: 152028281250
success

--------------------------------------
This should have taken around 3 minutes on an 1GHz PIII.
Now a file rsa512.51.m containing the lines:
28172400 1431689581421081 207899046817573037944003980721
28200000 14507315380338583 207858335743926583066618629796
28788360 277876585108001 207001685830582539787623092532
should have been created. After:

$ ./pol51opt -b rsa512 -v -v -n 5e21 -N 2e19 -e 2e-12
28172400 137407314866185 -95421350700438998987 -146557736431495680250776677 40051849155435036583483365067795 20635075642866534027509737103227346009 
1431689581421081 207899045420998506886437834408

area: [-1003520,1003519]x[-100,100]
norm: 1.051e+22  alpha_proj: -1.635  skewness: 825977.864
limit: 8.832998, lim0: 50.707062   cut: 8833
.........................................................................................................................................................................................................28200000 -32490562539851 -9988621726698864150 3602085041663164063242149 441712338043438681590088699558 -52709848224323990818583861168440497 
14507315380338583 207858339086847266158038310486

area: [-1003520,1003519]x[-100,100]
norm: 4.982e+20  alpha_proj: -1.290  skewness: 265718.305
limit: 6.128939, lim0: 47.657574   cut: 6129
..................................................................f...............ffffPff.......f..f.....ff.ffPffffffffffffffffffffffff.ffPfff.fffff.fffffffffffffffff.ffff.fffffPfffffffffffffffffffffffffffPfffffffPfPfffffPffffffffPffffffffffffffffffffffffPffffffffffffffffffPfffffffffffffffffffffffffffffffffffffPffffPffffPfffPfffffffPfffffffffffffffffffffffffffffffffffffffffffffffPfffffffffffffffffffffffffffffff.fffffffffff.fPff..ffffPffffPff....f..Pf..........................................................................................28788360 -38461665456103 341536155051745850040 302940605370508202796022 -1145741667441318786745339894842 -301776673333039763066096285541808 
277876585108001 207001685904831996958236283735

area: [-480658,477805]x[-7,100]
norm: 7.031e+21  alpha_proj: -1.142  skewness: 63688.236
limit: 8.923309, lim0: 50.304673   cut: 8923
............................................................................................................

------------------------------------------
(ca. 4min on 1GHz PIII) a file rsa512.cand with 21 polynomial should exist. 
Among them:
BEGIN POLY #skewness 316769.74 norm 7.82e+20 alpha -5.04 Murphy_E 2.55e-12
X5 28200000
X4 -28360813539851
X3 -13553173634695647906
X2 2564268902978149419168456
X1 415989256480951014687269907996
X0 -28294692934494412681458239834080920
Y1 14507315380338583
Y0 -207858338661942505983301552999
M 3360535699488068065188616076918604440700798249780305704017974532022544629934677045714592688052709846153098285633372058200144914970580706639105648340708817
END POLY

