pcf2 back data : e = 33, L = 219−1 = 524287

Definition of the polynomial G

The order of polynomial G is L−1. For each u ( 0 ≤ u ≤ L-1 ), the coefficient xu to T u is

xu = ∑0≤v≤2e-1 sp(gLv + 2e+1u).

Computation

The computation of polynomial G was separated into 4096 parts. The i th part (0 ≤ i ≤ 4095) computed

xu(i) = ∑v1≤v≤v2 sp(gLv + 2e+1u) for 0 ≤ u ≤ L-1,

where v1 = 2e×(i/4096), v2 = 2e×((i+1)/4096)-1. These had been computed in 2014-2015, which required totally 125,800 hours using several personal computers.

We can execute the procedure of Lemma 1(I) by assembling partitioned data into G mod 2, and computing GCD(G mod 2, Φ mod 2).
Obtained result is ¬(2 | h-p). [computation log]

Data files

The result of i th part, xu(i)mod 2 (0 ≤ u ≤ L-1) were packed into a bit array. Each 64 bits in the bit array were converted to a long integer (-263 ≤ l ≤ 263-1) and stored in the data file "partiof4096.bitpoly".

In the table below, one can see the data file by clicking "D", and can see the corresponding computation log file. by clicking "L". One can also see these files by direct specification of URLs on browsers, e.g.
"http://fujima.sci.ibaraki.ac.jp/pcf2/e=33-L=524287/part123of4096.bitpoly"
and
"http://fujima.sci.ibaraki.ac.jp/pcf2/e=33-L=524287/part123of4096.bitpoly.log".

i+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
0 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
20 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
40 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
60 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
80 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
100 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
120 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
140 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
160 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
180 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
200 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
220 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
240 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
260 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
280 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
300 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
320 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
340 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
360 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
380 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
400 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
420 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
440 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
460 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
480 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
500 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
520 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
540 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
560 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
580 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
600 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
620 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
640 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
660 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
680 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
700 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
720 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
740 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
760 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
780 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
800 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
820 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
840 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
860 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
880 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
900 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
920 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
940 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
960 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
980 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
1000 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1020 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1040 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1060 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1080 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1100 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1120 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1140 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1160 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1180 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1200 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1220 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1240 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1260 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1280 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1300 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1320 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1340 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1360 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1380 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1400 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1420 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1440 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1460 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1480 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
1500 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1520 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1540 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1560 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1580 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1600 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1620 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1640 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1660 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1680 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1700 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1720 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1740 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1760 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1780 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1800 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1820 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1840 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1860 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1880 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1900 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1920 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1940 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1960 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
1980 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
2000 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2020 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2040 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2060 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2080 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2100 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2120 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2140 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2160 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2180 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2200 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2220 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2240 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2260 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2280 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2300 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2320 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2340 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2360 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2380 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2400 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2420 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2440 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2460 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2480 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
2500 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2520 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2540 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2560 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2580 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2600 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2620 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2640 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2660 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2680 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2700 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2720 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2740 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2760 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2780 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2800 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2820 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2840 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2860 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2880 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2900 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2920 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2940 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2960 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
2980 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
3000 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3020 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3040 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3060 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3080 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3100 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3120 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3140 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3160 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3180 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3200 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3220 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3240 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3260 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3280 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3300 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3320 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3340 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3360 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3380 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3400 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3420 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3440 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3460 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3480 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
3500 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3520 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3540 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3560 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3580 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3600 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3620 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3640 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3660 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3680 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3700 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3720 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3740 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3760 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3780 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3800 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3820 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3840 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3860 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3880 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3900 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3920 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3940 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3960 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
3980 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19
4000 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
4020 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
4040 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
4060 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL
4080 DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL DL

pcf2: Note on the class number of the p th cyclotomic field, II,
Shoichi Fujima and Humio Ichimura, 2015