xu = ∑0≤v≤2e-1 sp(gLv + 2e+1u).
xu(i) = ∑v1≤v≤v2 sp(gLv + 2e+1u) for 0 ≤ u ≤ L-1,
where v1 = 2e×(i / 8), v2 = 2e×((i + 1) / 8) − 1. Although this case can be computed within 10 minutes 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).
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 "partiof8.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.
Obtained result is ¬(2 | h-p).
[computation log]
Data files
"http://fujima.sci.ibaraki.ac.jp/pcf2/e=19-L=8191/data/part2of8.bitpoly"
and
"http://fujima.sci.ibaraki.ac.jp/pcf2/e=19-L=8191/log/part2of8.bitpoly.log".
i +0 +1 +2 +3 +4 +5 +6 +7
0
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