Computer-asisted proof of theorem

We consider triplets (e, L, p), where e=1,2,3,4 and 2 is a primitive root modulo L.
The parity of h-p were checked by the method of Lemma 1(II) for ∀p∈Pe or ∀p∈(a superset of Pe). ¬(2|h-p) was verified in all cases.

e 1 2 3 4
Me 24=16 212=4096 232=4294967296 280
computation for ∀p<Me(*4) Only 1 (L, p) prime number pair exists. At the pair, 2 is a primitive root modulo L, and ¬(2|h-p). [computation](*1) 20 (L, p) pairs found. In 12 of them, 2 is a primitive root modulo L. By [computation](*2) ¬(2|h-p) were verified. 916835 (L, p) pairs found. In 268427 of them, 2 is a primitive root modulo L. By [computation(20MB)](*3) ¬(2|h-p) were verified.
me 5 81 97393 542909003297
computation for ∀p<me(*4) (included in *1,*2,*3) Hard job. In the partial range ∀p<233, 888235 (L, p) pairs found. In 392821 of them, 2 is a primitive root modulo L. For them ¬(2|h-p) were verified by [computation(31MB)].
Pe [computation of Pe] ∅ {41} {593, 977} {97, 353, 929,…,194600255393, 205620281249} (|Pe|=2193)
Computer-asisted proof of Theorem: check of the parity of h-p for ∀p ∈ Pe (Pe=∅) The computations had been included in (*2) and (*3).
¬(2|h-p) holds for ∀p ∈ Pe.		 ¬(2|h-p) holds for ∀p ∈ Pe. [computation]

*4: In these computations, cases of p ∈ Pe constitute the proof. The residual cases, p ∉ Pe, are considered to be computational verification of Proposition 3.

Note on the class number of the p th cyclotomic field, II
Shoichi FUJIMA and Humio ICHIMURA