pcf2 back data : e = 17, 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 64 parts. The i th part (0 ≤ i ≤ 63) computed

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

where v1 = 2e×(i / 64), v2 = 2e×((i + 1) / 64) − 1. Although this case can be computed within one day in one PC, the partitioned computation method was tested in this case.

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 "partiof64.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=17-L=524287/data/part12of64.bitpoly"
and
"http://fujima.sci.ibaraki.ac.jp/pcf2/e=17-L=524287/log/part12of64.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

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