Computation for Proposition 3(I) - part 2: e≥5

Table of c1-c2[-c3] for each Ae,s

s range of L e=5 6 7 8 9 10 11 12 13 14 15 16
2 2-4*1 1-0 1-0 1-0
3 4-8 1-1 1-0 0-0 0-0 0-0 0-0 0-0 1-0 1-1 1-0 0-0 0-0
4 8-16*2 1-01-0 1-0
5 16-32 1-0 0-0 1-1 1-1 1-0 1-0 0-0 1-1 0-0 1-1 0-0 0-0
6 32-64 1-1 0-0 1-0 0-0 1-0 2-1 3-1 0-0 0-0 0-0 1-0 1-0
7 26-27 3-2 2-1 0-0 3-2 1-1 0-0 1-1 1-1 4-3 0-0 1-1 1-0
8 27-28 2-1 3-2 5-3 3-1 1-1 3-1 3-2 4-2 3-2 5-1 0-0 4-3
9 28-29 7-6 7-3 8-7 7-4 4-3 4-1 3-2 2-1 3-1 3-1 5-4 3-2
10 29-210 9-5 6-6 8-3 12-10 5-2 3-3 7-6 8-6 3-3 4-3 7-6 5-4
accumulated total 25-16 20-12 25-14 26-18 14-7 13-6 18-12 17-11 14-10 14-6 14-11 14-9
11 210-211 11-8 12-7 13-8 17-11 12-9 15-8 13-9 10-4 13-11 9-5 9-4 10-6
12 211-212 30-21 20-12 27-13 20-8 20-7 23-12 26-18 22-14 19-14 19-15 21-13 14-9
13 212-213 46-31 46-25 48-35 41-24 40-25 38-22 38-27 30-18 37-25 29-17 21-16 26-13
14 213-214 68-45 91-53 76-53 69-39 77-53 61-35 58-39 61-37 53-42 47-30 54-36 56-29
15 214-215 147-102 144-84 133-97 111-68 135-96 120-62 117-84 105-65 96-67 110-57 83-61 101-55
16 215-216 254-173 260-160 235-166 220-120 235-177 222-131 216-146 210-117 207-142 210-128 168-115 182-105
17 216-217 485-345 486-256 424-299 438-247 410-291 382-201 381-268 371-210 376-257 363-204 327-245 321-175
18 217-218 846-569 834-469 797-558 813-475 712-506 729-400 707-479 697-399 676-472 632-358 644-467 616-357
(31h)
19 218-219 1664-1128 1514-851 1450-1022 1408-807 1339-936 1319-731 1245-892 1156-648 1180-822 1148-637 1114-798
(84h)		 1080-601
(107h)
20 219-220 2831-1943 2758-1542 2697-1921 2588-1454 2450-1664 2503-1405 2258-1611 2280-1287 2176-1515 2090-1172
(5d)		 2037-1409
(15d)		 2032-1136
Finished finally on Dec22,2015
(16.6days)
accumulated total 6407-4381 6185-3471 5925-4186 5751-3271 5444-3771 5425-3013 5077-3585 4959-2810 4847-3377 4671-2629 4492-3175 4452-2495
24,268 - 15,309 20,905 - 13,179 18,462 - 11,676
63,635 - 40,164

s range of L e=17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
2 2-4*1 1-0 1-0
3 4-8 0-0 0-0 1-1-1 0-0 0-0 0-0 0-0 1-0 1-1 0-0 0-0 0-0 0-0 0-0 0-0 0-0 0-0 0-0
4 8-16*2 1-01-01-0 1-0 0-0
5 16-32 0-0 0-0 0-0 0-0 0-0 0-0 0-0 0-0 0-0 2-1 0-0 1-1 0-0 0-0 0-0 0-0
6 32-64 1-1 1-1 0-0 1-0 1-0 0-0 0-0 0-0 2-1 1-0 0-0 0-0 0-0 0-0 0-0
7 26-27 2-2 1-1 2-1 2-1 0-0 2-1 2-2 0-0 0-0 3-1 0-0 0-0 2-2 0-0
8 27-28 2-1 4-1 2-1 1-0 2-1 0-0 3-3 2-1 0-0 2-1 2-1 1-1 3-2
9 28-29 5-5 2-0 2-2 2-2 1-1 2-1 4-3 2-1 5-3 2-0 3-3 2-2
10 29-210 6-3 5-4 6-4 3-3 5-2 2-1 4-3 2-2 3-2 5-3 6-4
accumulated total 17-12 14-7 14-9-1 10-6 9-4 6-3 13-11 7-4 11-7 15-6
11 210-211 8-7 12-9 11-9 8-7 10-8 5-4 5-5 12-5 8-7
12 211-212 14-10 24-12 10-7 24-11 13-9 11-8 14-7 15-8 19-14
13 212-213 24-15 33-17 33-21 32-16 25-20 19-11 24-18 34-17
14 213-214 48-35 45-23 42-34 50-28 56-35 46-23 56-41
15 214-215 83-64 99-52 90-67 74-46 88-54
(19h)		 87-49
16 215-216 180-129 161-91 165-118 152-93
(33h)		 201-130
17 216-217 324-229 321-169
(29h)		 313-213
(74h)		 350-207
18 217-218 577-399
(69h)		 610-360
(127h)		 678-478-1
19 218-219 1082-759
(265h)		 1319-740
20 219-220 2357-1659
accumulated total 4704 - 3084 - 1 378 - 237 45 - 28
5,127 - 3,349 - 1

c1 = |Ae,s|, c2 = |Ae,s-B|,
where
Ae,s = { (L,p) | 2s-1<L<2s, L is a prime number, p = 2e+1L+1 is a prime number },
B = { (L,p) | 2 is a primitive root modulo L }.

c3 is the number of the cases of 2 | h-p.

*1: One prime number, 3, exists in this range. Since 2 is a primitive root modulo 3, no data in the row.
*2: Two prime numbers, 11 and 13, exist in this range. Since 2 is a primitive root modulo each of them, no data in the row.

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