Difference between revisions of "Proth prime small bases least n"

Latest revision as of 11:32, 12 October 2024

Description

Here are shown the least n ≥ 1 generating a Proth prime of the form k•bⁿ+1 for 2 ≤ b ≤ 1030 and 2 ≤ k ≤ 12.

History

2024-09-10: Found 2•836⁷⁹⁸⁴³¹+1, Predrag Kurtovic
2024-07-21: Found 8•558⁴⁴⁷⁰⁴⁷+1, Kyle Gingrich
2024-05-04: Found 5•308³⁰⁹⁷⁵⁵+1, Predrag Kurtovic
2023-10-20: Found 12•978³¹²³⁴⁶+1, Predrag Kurtovic
2022-07-30: Found 3•912¹³²¹⁷³+1, (Anonymous)
2022-06-05: Found 8•785⁹⁰⁰³²⁵+1, Dennis Sydekum
2022-03-29: Found 10•744¹³⁷⁰⁵⁵+1, (Anonymous)
2021-10-06: Found 8•908²⁴³⁴³⁹+1, (Anonymous)
2021-07-04: Found 10•977¹²⁵⁸⁷²+1, Mark Rodenkirch
2019-12-10: Found 6•522⁵²⁶⁰³+1, Gary Barnes
2019-12-10: Found 8•254⁶⁷⁷¹⁵+1, Gary Barnes
2019-12-10: Found 10•786⁶⁸¹⁶⁸+1, Gary Barnes
2019-12-10: Found 10•986⁴⁸²⁷⁸+1, Gary Barnes
2019-12-10: Found 12•230⁹⁴⁷⁵⁰+1, Gary Barnes
2019-12-10: Found 12•359⁶¹²⁹⁴+1, Gary Barnes
2019-12-10: Found 12•481⁴⁵⁹⁴⁰+1, Gary Barnes
2019-12-10: Found 12•593⁴²⁷⁷⁸+1, Gary Barnes
2019-12-10: Found 12•700⁹¹⁹⁵²+1, Gary Barnes
2019-12-10: Found 12•923⁶⁴³⁶⁴+1, Gary Barnes
2019-09-29: Found 5•326⁴⁰⁰⁷⁸⁵+1, Dennis Sydekum
2019-09-23: Found 4•789¹⁴⁹¹³⁹+1, (whizbang)
2019-09-11: Found 11•878²²⁷⁴⁸¹+1, (CharityEngine2)
2019-06-26: Found 10•743²⁸⁵⁴⁷⁸+1, Douglas Grosvenor

Wanted values given as base

`k` = 2

365 (500K)
383 (1M)
461 (600K)
542 (500K)
647 (300K)
773 (500K)
801 (100K)
878 (400K)
908 (300K)
914 (400K)
917 (600K)
947 (400K)
1004 (600K)

`k` = 3

718 (500K)

`k` = 4

53 (3.15M)
155 (1.875M)
174 (1M)
204 (1M)
212 (1.3M)
230 (1M)
332 (1M)
334 (500K)
335 (1M)
395 (1.0043M)
467 (1M)
593 (1M)
767 (1M)
803 (600K)
848 (1M)
875 (1M)

`k` = 5

512 (1M)
824 (100K)

`k` = 6

212 (1.6M)
509 (100K)
579 (600K)
625 (300K)
774 (300K)
894 (500K)
993 (520K)
999 (100K)

`k` = 7

none for base ≤ 1030

`k` = 8

86 (1M)
140 (1M)
182 (1M)
263 (1M)
353 (700K)
368 (500K)
389 (100K)
395 (500K)
422 (500K)
426 (600K)
428 (1M)
434 (100K)
443 (500K)
488 (300K)
497 (600K)
572 (300K)
575 (100K)
593 (500K)
606 (100K)
698 (300K)
710 (500K)
746 (300K)
758 (600K)
770 (300K)
773 (500K)
824 (100K)
828 (600K)
866 (600K)
911 (300K)
930 (400K)
953 (600K)
957 (500K)
983 (400K)
993 (520K)
1014 (100K)

`k` = 9

724 (600K)
884 (100K)

`k` = 10

185 (1M)
338 (300K)
417 (1M)
432 (100K)
614 (100K)
668 (100K)
773 (500K)
863 (100K)
935 (400K)

`k` = 11

560 (100K)
770 (300K)
968 (400K)

`k` = 12

163 (500K)
207 (100K)
354 (500K)
362 (100K)
368 (500K)
480 (600K)
620 (500K)
692 (100K)
697 (100K)
736 (600K)
753 (300K)
792 (300K)
998 (400K)
1019 (100K)
1022 (100K)

Data

The data file can be found here.

For all values given with '-' there is no prime possible or are Generalized Fermat numbers.
All unknown values are listed with "0".
For k = 2 there is the sequence A253178 in OEIS.

Base	k = 2	k = 3	k = 4	k = 5	k = 6	k = 7	k = 8	k = 9	k = 10	k = 11	k = 12
2	1	1	2	1	1	2	1	1	2	1	3
3	1	-	1	-	1	-	2	-	1	-	1
4	-	1	1	-	2	1	-	1	1	-	2
5	1	-	2	-	1	-	1	-	2	-	1
6	1	1	-	1	1	1	4	-	1	1	1
7	-	-	1	-	1	-	-	-	1	-	4
8	1	2	2	1	-	2	-	1	2	1	1
9	1	-	1	-	2	-	1	-	2	-	1
10	-	1	1	-	1	1	-	3	1	-	2
11	1	-	-	-	1	-	1	-	10	-	2
12	3	1	2	1	1	2	1	1	-	3	-
13	-	-	1	-	1	-	-	-	1	-	1
14	1	1	-	1	6	2	1	1	6	-	-
15	1	-	1	-	-	-	2	-	1	-	1
16	-	2	-	-	1	1	-	-	3	-	1
17	47	-	6	-	1	-	1	-	1356	-	2
18	1	3	1	2	1	1	2	1	1	1	2
19	-	-	3	-	14	-	-	-	1	-	1
20	1	1	2	1	15	2	-	1	2	3	1
21	1	-	-	-	1	-	2	-	1	-	10
22	-	1	1	-	-	2	-	1	15	-	4
23	1	-	342	-	1	-	119215	-	-	-	1
24	2	1	1	12	2	3	1	5	1	2	42
25	-	-	1	-	1	-	-	-	1	-	9
26	1	1	-	1	1	2	35	-	2	3	1
27	2	-	1	-	1	-	-	-	1	-	-
28	-	7	1	-	3	1	-	2	1	-	1
29	1	-	-	-	-	-	1	-	4	-	1
30	1	3	6	1	1	1	1	1	2	1	1023
31	-	-	-	-	4	-	-	-	1	-	1
32	3	1	-	3	1	4	1	13	-	1	2
33	1	-	2	-	1	-	2	-	1	-	1
34	-	1	1	-	-	1	-	1	-	-	1
35	1	-	42	-	1	-	1	-	2	-	1
36	1	1	-	1	-	3	2	-	3	1	1
37	-	-	1	-	1	-	-	-	2	-	3
38	2729	3	10	1	1	4	7	21	4	1	1
39	1	-	1	-	2	-	1	-	4	-	2
40	-	2	5	-	1	1	-	2	1	-	-
41	1	-	-	-	3	-	-	-	2	-	2
42	2	1	2	1	3	4	1	1	1	1	2
43	-	-	1	-	-	-	-	-	1	-	2
44	1	9	-	15	2	2	1	1	6	-	3
45	2	-	1	-	1	-	8	-	-	-	1
46	-	1	-	-	1	2	-	-	1	-	6
47	175	-	2	-	1	-	-	-	2	-	3
48	1	3	1	1	27	1	2	1	2	7	1
49	-	-	1	-	2	-	-	-	1	-	2
50	1	1	10	1	-	516	1	2	4	9	1
51	1	-	-	-	1	-	1	-	3	-	1
52	-	1	10	-	1	15	-	2	1	-	3
53	1	-	0	-	143	-	227183	-	16	-	-
54	1	1	3	1	2	1	1	1	1	2	4
55	-	-	2	-	1	-	-	-	9	-	1
56	1	5	-	1	1	6	1	-	-	1	1
57	3	-	1	-	-	-	1	-	1	-	3
58	-	2	1	-	1	2	-	1	2	-	4
59	3	-	-	-	2	-	5	-	36	-	1
60	3	1	1	42	2	1	14	1	1	1	2
61	-	-	-	-	1	-	-	-	165	-	1
62	43	12	2	1	1	308	-	3	66	1	27
63	1	-	2	-	1	-	8	-	1	-	1
64	-	1	1	-	-	1	-	1	1	-	1
65	1	-	2	-	5	-	1	-	-	-	684
66	2	1	-	1	1	1	2	-	1	1	-
67	-	-	1	-	4532	-	-	-	-	-	135
68	1	2	6	29	1	2	319	1	6	3947	656921
69	1	-	1	-	-	-	20	-	1	-	1
70	-	1	1	-	1	1	-	1	1	-	7
71	3	-	-	-	-	-	1	-	2	-	1
72	2	14	3	7	1	10	1	6	12	32	28
73	-	-	1	-	1	-	-	-	3	-	1
74	1	1	-	3	4	2	1	65	138	-	2
75	1	-	2	-	2	-	1	-	1	-	57
76	-	1	-	-	1	2	-	-	1	-	2
77	3	-	6098	-	1	-	1	-	4	-	3
78	1	2	1	3	-	1	2	3	-	1	1
79	-	-	1	-	2	-	-	-	5	-	-
80	11	1	2	1	3	12	1	2	4	1	2
81	1	-	-	-	1	-	2	-	1	-	50
82	-	2	6	-	3	4	-	1	1	-	107
83	1	-	5870	-	1	-	-	-	2	-	1
84	4	2	1	1	2	2	1	1	5	2	1
85	-	-	2	-	-	-	-	-	2	-	1
86	1	2	-	1	40	12	0	-	2	1	1
87	2	-	1	-	1	-	112	-	3	-	1214
88	-	4	1	-	7	1	-	2	1	-	9
89	1	-	-	-	2	-	5	-	-	-	1
90	1	1	2	6	1	1	14	1	2	1	3
91	-	-	-	-	1	-	-	-	1	-	1
92	3	1	2	1	-	6	109	1	24	1	-
93	2	-	1	-	520	-	2	-	2	-	1
94	-	1	3	-	2	1	-	263	1	-	1
95	1	-	6	-	1	-	1	-	42	-	2
96	1	3	-	3	1	1	1	-	7	2	1
97	-	-	1	-	3	-	-	-	1	-	2
98	1	2	294	1	32	8	119	1	-	19	2
99	1	-	1	-	-	-	10	-	1	-	30
100	-	5	1	-	1	1	-	2	-	-	1
101	192275	-	-	-	1	-	1	-	1506	-	1
102	2	1	1	2	1	3	2	1	1	1	2739
103	-	-	2	-	1	-	-	-	1	-	1
104	1233	1	-	1	-	8	-	1	2	-	1
105	1	-	1	-	1	-	10	-	1	-	-
106	-	3	-	-	-	1	-	-	1	-	138
107	3	-	32586	-	1	-	1	-	42	-	4
108	5	270	1	1	16317	1	4	3	3	189	1
109	-	-	3	-	2	-	-	-	1	-	2
110	51	1	10	3	1	2	1	1	2	161	1
111	1	-	-	-	3	-	62	-	-	-	2
112	-	1	1	-	1	3	-	1	2	-	10
113	1	-	2958	-	-	-	47	-	2	-	4
114	1	12	1	1	2	3	2	5	3	10	15
115	-	-	1	-	1	-	-	-	1	-	1
116	1	1	-	3	2	4	1	-	4	1	47
117	286	-	101	-	3	-	1	-	1	-	6
118	-	46	2	-	1	1	-	1	1	-	-
119	1	-	-	-	2	-	1	-	6	-	1
120	1	2	2	1	-	2	2	3	1	1	2
121	-	-	-	-	1	-	-	-	5	-	1
122	755	1	358	135	1	6	1	3	-	13	2
123	2	-	6	-	1	-	16	-	1	-	2
124	-	1	471	-	10	3	-	1	18	-	1
125	1	-	2	-	1	-	-	-	4	-	6
126	4	1	-	1	1	1	1	-	2	2	5
127	-	-	1	-	-	-	-	-	4	-	2
128	1	27	2	1	1	2	-	1	2	1	4
129	6	-	19	-	16796	-	1	-	1	-	1
130	-	21	1	-	7	1	-	1	1	-	6
131	1	-	-	-	1	-	1	-	-	-	-
132	2	1	2	1	5	3	2	2	1	1	2
133	-	-	5	-	3	-	-	-	-	-	1
134	1	4	-	3	-	2	2795	183	42	-	1
135	1	-	1	-	1	-	8	-	54	-	1
136	-	1	-	-	2	1	-	-	1	-	2
137	327	-	18	-	1	-	1	-	102	-	3
138	1	8	3	1	1	1	10	3	1	32	1
139	-	-	1	-	-	-	-	-	18	-	1
140	1	1	2	1	5	2	0	2	24	37	3
141	1	-	-	-	-	-	1	-	2	-	1
142	-	2	1	-	1	23	-	1	407	-	-
143	5	-	10	-	1	-	491	-	10	-	2
144	5	1	1	2	782	1	1	1	-	2	-
145	-	-	21	-	2	-	-	-	1	-	1
146	1	1	-	3	1	2	-	-	6	1	1
147	154	-	3	-	1	-	4	-	1	-	2
148	-	2	1	-	-	5	-	2	1	-	1
149	3	-	-	-	10	-	1	-	2	-	1
150	3	3	1	1	13	1	1	3	9	2	1
151	-	-	-	-	1	-	-	-	1	-	2
152	3	1	18	1	27	2	1	7	2	837	4
153	1	-	1	-	1	-	2	-	1	-	2
154	-	1	1	-	2	2	-	15	2	-	2
155	1	-	0	-	-	-	5	-	-	-	1
156	1	2	-	6	1	1	1	-	15	3	1
157	-	-	2	-	4	-	-	-	1	-	-
158	1	4	874	51	17	2	123475	1	4	3	2
159	3	-	29	-	2	-	5	-	3	-	121
160	-	2	1	-	3	4	-	4	1	-	2
161	7	-	-	-	1	-	1	-	2	-	1
162	2	1	13	1	-	2	1	1	1	1	20
163	-	-	1	-	1303	-	-	-	3	-	0
164	3	4	-	1	2	2	2399	3	-	-	2826
165	1	-	1	-	1	-	1	-	3	-	2
166	-	1	-	-	1	1	-	-	-	-	1
167	6547	-	10	-	25	-	-	-	2	-	31
168	1	2	1	2	1	2	26	18	2	3	1
169	-	-	1	-	-	-	-	-	2	-	1
170	3	3	2	175	1	178	1	1	2	1	-
171	8	-	-	-	2	-	4	-	3	-	1
172	-	4	6	-	1	3	-	1	1	-	2
173	1	-	10	-	1	-	323	-	264234	-	4
174	1	1	0	2	-	2	68	1	1	12	1
175	-	-	1	-	1	-	-	-	3	-	2
176	1	3	-	1	-	12	1	-	146	3	1
177	2	-	1	-	1	-	64	-	-	-	3810
178	-	4	25	-	1	5	-	3	3	-	1
179	1	-	-	-	4	-	1	-	336	-	3
180	8	1	66	6	4	3	2	1	1	54	1
181	-	-	-	-	1	-	-	-	1	-	3
182	15	1	70	1	1	4	0	263	2	1	2
183	1	-	1	-	-	-	2	-	1	-	-
184	-	11	29	-	40	1	-	1	9	-	10
185	3	-	414	-	170	-	1	-	0	-	1
186	1	12	-	2	1	1	1	-	1	2	2
187	-	-	11	-	1	-	-	-	1	-	6
188	9	2	26	1	1	2	-	1	-	1	2
189	1	-	1	-	34	-	7	-	2	-	1
190	-	1	1	-	-	43	-	2	1	-	1
191	1	-	-	-	2	-	17	-	1314	-	1
192	3	1	1	2	1	4	4	2	34	1	7
193	-	-	1	-	148	-	-	-	1	-	113
194	1	2	-	1	10	280	1	1	18	-	7
195	6	-	3	-	1	-	16	-	1	-	1
196	-	2	-	-	3	1	-	-	3	-	-
197	3	-	6	-	-	-	5	-	-	-	6
198	1	11	2	1	5	5	7	1	47664	1	1
199	-	-	1	-	2	-	-	-	-	-	1
200	1	1	2	767	1	2	1	1	6036	7	14
201	2	-	-	-	3	-	1	-	1	-	6
202	-	1	1	-	1	2	-	30	2	-	22
203	105	-	2	-	3	-	7	-	2956	-	1
204	1	1	0	1	-	1	79	5	3	50	4586
205	-	-	1	-	1	-	-	-	9	-	3
206	46205	1	-	1	1	4	13	-	4	1	1
207	6	-	1	-	5	-	1	-	3	-	0
208	-	2	10	-	1	69	-	1	1	-	22
209	1	-	-	-	-	-	-	-	2	-	-
210	1	1	2	1	2	1	94	55	-	1	1
211	-	-	-	-	-	-	-	-	1	-	2
212	7	6	0	1	0	12	1	2	2	1	16
213	14	-	1	-	1	-	2	-	1	-	1
214	-	1	1	-	2	1	-	3	1	-	2
215	1	-	2	-	1	-	1	-	6	-	40
216	1	2	-	49	1	2	-	-	1	1	1
217	-	-	6	-	1	-	-	-	2	-	2
218	333925	2	2	1	-	14	115	2	4	1	1
219	1	-	1	-	4	-	1	-	5	-	29230
220	-	1	1	-	1	25	-	3	3	-	5
221	1	-	-	-	1	-	5	-	-	-	3
222	66	2	2	3	5	7	1	1	1	100	-
223	-	-	6	-	3	-	-	-	2	-	1
224	1	1	-	71	2	688	5	1	4	-	1
225	4	-	87	-	-	-	1	-	1	-	4
226	-	8	-	-	2	1	-	-	11	-	1
227	3	-	13346	-	20	-	5	-	84	-	2
228	1	12	3	14	8	1	2	1	1	15	8
229	-	-	21	-	308	-	-	-	2	-	1
230	1	1	0	1	1	6	-	2	-	1	94750
231	1	-	-	-	8	-	2	-	1	-	2
232	-	4	1	-	-	2	-	1	-	-	2
233	1	-	2	-	1	-	35	-	2	-	1
234	6	3	1	1	4	4	1	9	1	2	5
235	-	-	1	-	4	-	-	-	1	-	-
236	161229	1	-	1	2	346	1	-	2046	153	1
237	2	-	2	-	1	-	2	-	1	-	206
238	-	2	1	-	1	1	-	1	1	-	1
239	1	-	-	-	-	-	1	-	2	-	2
240	2	2	5	1	2	6	5	1	2	3	1243
241	-	-	-	-	1	-	-	-	1	-	14
242	11	1	4206	45	1	6	-	1	6	1	11
243	1	-	3	-	1	-	2	-	-	-	1
244	-	1	1	-	-	1	-	1835	1	-	4
245	1	-	2	-	1	-	23	-	4	-	2
246	3	1	-	1	-	1	2	-	3	1	1
247	-	-	3	-	1	-	-	-	24	-	7
248	321	7	2	261	1	30	43	39510	4	1	-
249	1	-	1	-	4	-	1	-	7	-	6
250	-	1	3	-	4	2	-	1	127	-	1
251	1	-	-	-	17	-	-	-	12	-	3
252	3	1	1	3	7	2	1	1	1	3	2
253	-	-	1	-	-	-	-	-	1	-	1
254	1	2	-	9	4	30	67715	1	-	-	1
255	2	-	1	-	1	-	7	-	1	-	1
256	-	1	-	-	5	15	-	-	3	-	2
257	12183	-	160422	-	1	-	29	-	12	-	3
258	5	8	1	1	1	20	10	59	3	3	6
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896	3	1	-	1	2	4	7	-	436	1	1
897	2	-	2	-	-	-	1	-	1	-	2
898	-	6	1	-	29	1	-	15	2	-	-
899	15731	-	-	-	16	-	1	-	12	-	1
900	1	3	3	3	47	1	2270	1	1	1	-
901	-	-	-	-	1	-	-	-	1	-	-
902	3	1	6	15	1	2	-	2	16	1	50
903	40	-	1	-	1	-	7	-	-	-	1
904	-	1	1	-	-	1	-	3	1	-	33
905	1	-	6	-	1	-	31	-	5154	-	1
906	3	1	-	3	1	1	199	-	18	1	23
907	-	-	5	-	1	-	-	-	3	-	2
908	0	6	2	5	1	10	243439	1069	6	9855	4
909	10	-	1	-	-	-	2	-	1	-	1
910	-	1	125	-	4	5	-	1	23	-	4
911	1	-	-	-	-	-	0	-	336	-	-
912	3	132173	2	1	8	3	1	1	21	3	6
913	-	-	3	-	1	-	-	-	88	-	1
914	0	12	-	3	2	10	31	9	-	-	2
915	1	-	27	-	3	-	1	-	1	-	207
916	-	1	-	-	3	9	-	-	1	-	1
917	0	-	22	-	1	-	53	-	2	-	4
918	2	7	1	1	-	1	2	1	1	1	2
919	-	-	1	-	5092	-	-	-	8	-	45358
920	221	3	103686	15	1	490	107821	2	4	3	8
921	5	-	-	-	1	-	1	-	3	-	2
922	-	1	1179	-	3	2	-	2	1	-	183
923	1	-	10	-	41	-	-	-	-	-	64364
924	4	3	1	1	10	1	1	1	1	2	-
925	-	-	1	-	-	-	-	-	-	-	3
926	765	71	-	40035	1	522	199	-	4998	11	1
927	6	-	1	-	1	-	1	-	4752	-	2355
928	-	19	7	-	1	2	-	1	1	-	2
929	99	-	-	-	9148	-	1	-	13064	-	1
930	1	1	2	1	1	217	0	24	2	7	1
931	-	-	-	-	2	-	-	-	1	-	1
932	13643	1	262	31	-	22	1	1	2	1	56
933	1	-	1	-	77	-	20	-	3	-	1
934	-	1	101403	-	4	6	-	429	1	-	44
935	1	-	2	-	8	-	1	-	0	-	3
936	1	5	-	54	3	1	1	-	-	4	7
937	-	-	6	-	1	-	-	-	1	-	-
938	1	6	2	1	29	4	3083	1	16	5	1
939	1	-	3	-	-	-	520	-	1	-	20
940	-	14	1	-	1	1	-	1	56	-	103
941	3	-	-	-	1	-	1	-	8508	-	11
942	7	13	1	2	1	3	1	3	1	5	3
943	-	-	3	-	1	-	-	-	1	-	1
944	1	1	-	1	-	42	-	97	4	-	1
945	40	-	9	-	4	-	1	-	3	-	2
946	-	2	-	-	-	2	-	-	1	-	1
947	0	-	2	-	1	-	1	-	-	-	4
948	1242	3	1	18	1	1	11	194	79	1	69
949	-	-	1	-	4	-	-	-	1	-	2
950	1	1	14	1	1	12	305	2	26	113	-
951	2	-	-	-	3	-	2	-	1	-	32
952	-	1	35	-	5	26	-	3	1	-	4
953	1	-	18	-	-	-	0	-	2	-	1
954	8100	12	3	3	158	1	26	55	1506	24	3
955	-	-	1	-	3	-	-	-	1	-	2087
956	1	3	-	9	1	2	1	-	-	3	710
957	182	-	3	-	1	-	0	-	2	-	3
958	-	6	1	-	1	168	-	1	-	-	1
959	5	-	-	-	4	-	1	-	388	-	3
960	2	8	2	1	-	127	1	1	1	7	2
961	-	-	-	-	2	-	-	-	12	-	225
962	59	1	84234	7	7	6	47221	5	6	9	7
963	2	-	1	-	1	-	7	-	1	-	-
964	-	33	3	-	2	8	-	1	2	-	3
965	1	-	62	-	1	-	-	-	6	-	2
966	1	2	-	1	18	1	8	-	1	1	1
967	-	-	3	-	-	-	-	-	5	-	2
968	917	2	90	3	40	8	7	1	162	0	1
969	4	-	1	-	5888	-	1	-	-	-	8
970	-	3	1	-	1	1	-	1	9	-	2
971	79	-	-	-	1	-	391	-	2	-	11
972	103	1	1	1	27	8	2992	2	1	9	2
973	-	-	239	-	1	-	-	-	2	-	1
974	1	7	-	1	-	1588	1	2015	2	-	1
975	1	-	3	-	1	-	5	-	18	-	1
976	-	3	-	-	1	1	-	-	41	-	-
977	7	-	10	-	6404	-	1	-	125872	-	3
978	2	156	3	9	1	2	2	1	1	3	312346
979	-	-	1	-	-	-	-	-	1	-	3
980	3	3	182	11	1	2	1	1	-	1	2
981	3	-	-	-	-	-	7	-	1	-	557
982	-	2	1	-	13	312	-	1	72	-	3
983	5	-	2	-	20	-	0	-	6	-	141
984	8	1	1663	3	16	6	1	315	21	6	41
985	-	-	2	-	291	-	-	-	1	-	1
986	1	3	-	1	21633	6	-	-	48278	1	1
987	3	-	2	-	1	-	2	-	1	-	11
988	-	42	3	-	-	1	-	1	2	-	2
989	1	-	-	-	22	-	25	-	-	-	-
990	2	1	2	1	2	2	139	3	1	1	3
991	-	-	-	-	4	-	-	-	-	-	8
992	1179	8	10	2165	1	10	1	1	152	4413	10299
993	1	-	39	-	0	-	0	-	1	-	2
994	-	4	3	-	122	1	-	3	1	-	3
995	3	-	2	-	-	-	35	-	2	-	1
996	1	6549	-	28	5	3	7	-	2	1	1
997	-	-	1	-	3	-	-	-	15	-	8
998	1	87	14	3	19	2	81239	74	88	1	0
999	1	-	389	-	0	-	1	-	12	-	9
1000	-	1	1	-	3	1	-	1	-	-	-
1001	1	-	-	-	1	-	1	-	14	-	8
1002	4	169	6	1	-	2	1	11	-	3	-
1003	-	-	1	-	8	-	-	-	2	-	1
1004	0	19	-	1	10	54848	125	839	10644	-	1
1005	1	-	1	-	2	-	2	-	49	-	2
1006	-	1	-	-	1	1	-	-	1	-	1
1007	7	-	6	-	1	-	-	-	6	-	3
1008	1	36	15	185	7	1	2	6	3	5	1
1009	-	-	39	-	-	-	-	-	1	-	1
1010	5	2	6	1	23	2	1	1	2	13	4
1011	2	-	-	-	1	-	1	-	1	-	8
1012	-	1	1	-	1	40	-	1	426	-	254
1013	1	-	2	-	1	-	43871	-	-	-	1
1014	1	3	1	3	-	9	0	1	1	2	264
1015	-	-	10	-	1	-	-	-	1	-	-
1016	119	1	-	1	-	2	5	-	6	1	4
1017	2	-	2	-	1165	-	2	-	3	-	58
1018	-	4	1	-	9943	1	-	2	1	-	2
1019	1	-	-	-	2	-	293	-	4	-	0
1020	2	1	29	1	1	2	1	1	23	2	1
1021	-	-	-	-	15	-	-	-	1	-	1
1022	727	1	6	5	1	36	-	1	-	1	0
1023	33	-	1	-	-	-	2	-	110	-	1
1024	-	3	-	-	4	2	-	323	-	-	1
1025	15	-	2	-	1	-	11	-	22	-	1
1026	1	1	-	6	4	25	1	-	7	1	5097
1027	-	-	2	-	1	-	-	-	1	-	3
1028	669	8	2	9	1437	16	-	30	14	55	-
1029	4	-	55	-	6	-	1	-	2	-	2
1030	-	9	3	-	-	1	-	941	1	-	10

External link

Thread "k=1 thru k=12" at MersenneForum

@@ Line 4: / Line 4: @@
 ==History==
+{{HistF|2024-09-10|&nbsp;{{T5000|138513|{{Kbn|+|2|836|798431}}}}|Predrag Kurtovic|1053318}}
+{{HistF|2024-07-21|&nbsp;{{T5000|138328|{{Kbn|+|8|558|447047}}}}|Kyle Gingrich|662924}}
+{{HistF|2024-05-04|&nbsp;{{T5000|138060|{{Kbn|+|5|308|309755}}}}|Predrag Kurtovic|656421}}
+{{HistF|2023-10-20|&nbsp;{{T5000|136544|{{Kbn|+|12|978|312346}}}}|Predrag Kurtovic|641052}}
+{{HistF|2022-07-30|&nbsp;{{Kbn|+|3|912|132173}}|(Anonymous)|610485}}
+{{HistF|2022-06-05|&nbsp;{{T5000|134013|{{Kbn|+|8|785|900325}}}}|Dennis Sydekum|607141}}
 {{HistF|2022-03-29|&nbsp;{{Kbn|+|10|744|137055}}|(Anonymous)|602803}}
-{{HistF|2021-10-06|&nbsp;{{Kbn|+|8|908|243439}}|(Anonymous)|589662}}
+{{HistF|2021-10-06|&nbsp;{{T5000|132800|{{Kbn|+|8|908|243439}}}}|(Anonymous)|589662}}
 {{HistF|2021-07-04|&nbsp;{{Kbn|+|10|977|125872}}|Mark Rodenkirch|582601}}
 {{HistF|2019-12-10|&nbsp;{{Kbn|+|6|522|52603}}|Gary Barnes|532521}}
@@ Line 22: / Line 28: @@
 {{HistF|2019-06-26|&nbsp;{{T5000|126594|{{Kbn|+|10|743|285478}}}}|Douglas Grosvenor|520190}}
-==Wanted values==
+==Wanted values given as base==
-===k = 2===
+==={{Vk}} = 2===
-<div style="-webkit-column-count: 6; -moz-column-count: 6; column-count: 6;">
+<div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*2*365^n+1 (300K)
+*{{CRUSLink|S365|365}} ({{HistLink|500K|613191}})
-*2*383^n+1 (1M)
+*{{CRUSLink|S383|383}} ({{HistLink|1M|560850}})
-*2*461^n+1 (600K)
+*{{CRUSLink|S461|461}} (600K)
-*2*542^n+1 (300K)
+*{{CRUSLink|S542|542}} ({{HistLink|500K|620133}})
-*2*647^n+1 (300K)
+*{{CRUSLink|S647|647}} (300K)
-*2*773^n+1 (350K)
+*{{CRUSLink|S773|773}} ({{HistLink|500K|634453}})
-*2*801^n+1 (100K)
+*{{CRUSLink|S801|801}} (100K)
-*2*836^n+1 (400K)
+*{{CRUSLink|S878|878}} (400K)
-*2*878^n+1 (400K)
+*{{CRUSLink|S908|908}} ({{HistLink|300K|589663}})
-*2*908^n+1 (200K)
+*{{CRUSLink|S914|914}} (400K)
-*2*914^n+1 (400K)
+*{{CRUSLink|S917|917}} ({{HistLink|600K|1054995}})
-*2*917^n+1 (400K)
+*{{CRUSLink|S947|947}} (400K)
-*2*947^n+1 (400K)
+*{{CRUSLink|S1004|1004}} ({{HistLink|600K|604721}})
-*2*1004^n+1 (400K)
 </div>
-===k = 3===
+==={{Vk}} = 3===
-<div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
+*{{CRUSLink|S718|718}} ({{HistLink|500K|1052918}})
-*3*718^n+1 (300K)
-*3*912^n+1 (100K)
-</div>
-===k = 4===
+==={{Vk}} = 4===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*4*53^n+1 ([https://www.mersenneforum.org/showpost.php?p=582494 1.8M])
+*{{CRUSLink|S53|53}} ({{HistLink|3.15M|1055605}})
-*4*155^n+1 ([https://www.mersenneforum.org/showpost.php?p=582495 1.375M])
+*{{CRUSLink|S155|155}} ({{HistLink|1.875M|1053796}})
-*4*174^n+1 (850K)
+*{{CRUSLink|S174|174}} ({{HistLink|1M|603737}})
-*4*204^n+1 (1M)
+*{{CRUSLink|S204|204}} (1M)
-*4*212^n+1 (1.0058M)
+*{{CRUSLink|S212|212}} ({{HistLink|1.3M|1055312}})
-*4*230^n+1 (1M)
+*{{CRUSLink|S230|230}} (1M)
-*4*332^n+1 (770K)
+*{{CRUSLink|S332|332}} ({{HistLink|1M|656491}})
-*4*334^n+1 (300K)
+*{{CRUSLink|S334|334}} ({{HistLink|500K|611152}})
-*4*335^n+1 (1M)
+*{{CRUSLink|S335|335}} (1M)
-*4*395^n+1 (500K)
+*{{CRUSLink|S395|395}} ({{HistLink|1.0043M|658506}})
-*4*467^n+1 (750K)
+*{{CRUSLink|S467|467}} ({{HistLink|1M|616839}})
-*4*593^n+1 (300K)
+*{{CRUSLink|S593|593}} ({{HistLink|1M|627769}})
-*4*767^n+1 (300K)
+*{{CRUSLink|S767|767}} ({{HistLink|1M|638880}})
-*4*803^n+1 (500K)
+*{{CRUSLink|S803|803}} ({{HistLink|600K|648594}})
-*4*848^n+1 ([https://www.mersenneforum.org/showpost.php?p=554542 500000])
+*{{CRUSLink|S848|848}} ({{HistLink|1M|613893}})
-*4*875^n+1 (1M)
+*{{CRUSLink|S875|875}} (1M)
 </div>
-===k = 5===
+==={{Vk}} = 5===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*5*308^n+1 (300K)
+*{{CRUSLink|S512|512}} (1M)
-*5*512^n+1 (1M)
+*824 (100K)
-*5*824^n+1 (100K)
 </div>
-===k = 6===
+==={{Vk}} = 6===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*6*212^n+1 ([https://www.mersenneforum.org/showpost.php?p=556221 500K])
+*{{CRUSLink|S212|212}} ({{HistLink|1.6M|1054242}})
-*6*509^n+1 (100K)
+*509 (100K)
-*6*579^n+1 (400K)
+*{{CRUSLink|S579|579}} (600K)
-*6*625^n+1 (200K)
+*{{CRUSLink|S625|625}} (300K)
-*6*774^n+1 (200K)
+*{{CRUSLink|S774|774}} (300K)
-*6*894^n+1 (100K)
+*{{CRUSLink|S894|894}} ({{HistLink|500K|641055}})
-*6*993^n+1 (520K)
+*{{CRUSLink|S993|993}} (520K)
-*6*999^n+1 (100K)
+*{{CRUSLink|S999|999}} (100K)
 </div>
-===k = 7===
+==={{Vk}} = 7===
-*none below b = 1030
+*none for base &le; 1030
-===k = 8===
+==={{Vk}} = 8===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*8*86^n+1 (1M)
+*{{CRUSLink|S86|86}} ({{HistLink|1M|436290}})
-*8*140^n+1 (500K)
+*{{CRUSLink|S140|140}} ({{HistLink|1M|567743}})
-*8*182^n+1 (1M)
+*{{CRUSLink|S182|182}} ({{HistLink|1M|463721}})
-*8*263^n+1 (1M)
+*{{CRUSLink|S263|263}} ({{HistLink|1M|478272}})
-*8*353^n+1 (400K)
+*{{CRUSLink|S353|353}} ({{HistLink|700K|586166}})
-*8*368^n+1 (200K)
+*{{CRUSLink|S368|368}} ({{HistLink|500K|618511}})
-*8*389^n+1 (100K)
+*389 (100K)
-*8*395^n+1 (500K)
+*{{CRUSLink|S395|395}} (500K)
-*8*422^n+1 (400K)
+*{{CRUSLink|S422|422}} (500K)
-*8*426^n+1 (400K)
+*{{CRUSLink|S426|426}} (600K)
-*8*428^n+1 (500K)
+*{{CRUSLink|S428|428}}  ({{HistLink|1M|664605}})
-*8*434^n+1 (100K)
+*434 (100K)
-*8*443^n+1 (500K)
+*{{CRUSLink|S443|443}} (500K)
-*8*488^n+1 (100K)
+*{{CRUSLink|S488|488}} (300K)
-*8*497^n+1 (400K)
+*{{CRUSLink|S497|497}} (600K)
-*8*558^n+1 (300K)
+*{{CRUSLink|S572|572}} (300K)
-*8*572^n+1 (100K)
+*{{CRUSLink|S575|575}} (100K)
-*8*575^n+1 (100K)
+*{{CRUSLink|S593|593}} ({{HistLink|500K|627856}})
-*8*593^n+1 (300K)
+*{{CRUSLink|S606|606}} (100K)
-*8*606^n+1 (100K)
+*{{CRUSLink|S698|698}} (300K)
-*8*698^n+1 (100K)
+*{{CRUSLink|S710|710}} ({{HistLink|500K|641055}})
-*8*710^n+1 (300K)
+*{{CRUSLink|S746|746}} (300K)
-*8*746^n+1 (300K)
+*{{CRUSLink|S758|758}} ({{HistLink|600K|648817}})
-*8*758^n+1 (500K)
+*{{CRUSLink|S770|770}} (300K)
-*8*770^n+1 (300K)
+*{{CRUSLink|S773|773}} ({{HistLink|500K|634453}})
-*8*773^n+1 (200K)
+*824 (100K)
-*8*785^n+1 (400K)
+*{{CRUSLink|S828|828}} ({{HistLink|600K|648595}})
-*8*824^n+1 (100K)
+*{{CRUSLink|S866|866}} ({{HistLink|600K|663586}})
-*8*828^n+1 (500K)
+*{{CRUSLink|S911|911}} (300K)
-*8*866^n+1 (400K)
+*{{CRUSLink|S930|930}} (400K)
-*8*911^n+1 (300K)
+*{{CRUSLink|S953|953}} ({{HistLink|600K|1052250}})
-*8*930^n+1 (400K)
+*{{CRUSLink|S957|957}} ({{HistLink|500K|641391}})
-*8*953^n+1 (400K)
+*{{CRUSLink|S983|983}} (400K)
-*8*957^n+1 (100K)
+*{{CRUSLink|S993|993}} (520K)
-*8*983^n+1 (400K)
+*1014 (100K)
-*8*993^n+1 (520K)
-*8*1014^n+1 (100K)
 </div>
-===k = 9===
+==={{Vk}} = 9===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*9*724^n+1 (400K)
+*{{CRUSLink|S724|724}} ({{HistLink|600K|647955}})
-*9*884^n+1 (100K)
+*884 (100K)
 </div>
-===k = 10===
+==={{Vk}} = 10===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*10*185^n+1 (1M)
+*{{CRUSLink|S185|185}} (1M)
-*10*338^n+1 (100K)
+*{{CRUSLink|S338|338}} (300K)
-*10*417^n+1 (400K)
+*{{CRUSLink|S417|417}} ({{HistLink|1M|659095}})
-*10*432^n+1 (100K)
+*{{CRUSLink|S432|432}} (100K)
-*10*614^n+1 (100K)
+*614 (100K)
-*10*668^n+1 (100K)
+*668 (100K)
-*10*773^n+1 (200K)
+*{{CRUSLink|S773|773}} ({{HistLink|500K|634453}})
-*10*863^n+1 (100K)
+*863 (100K)
-*10*935^n+1 (400K)
+*{{CRUSLink|S935|935}} (400K)
 </div>
-===k = 11===
+==={{Vk}} = 11===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*11*560^n+1 (100K)
+*560 (100K)
-*11*770^n+1 (300K)
+*{{CRUSLink|S770|770}} (300K)
-*11*968^n+1 (400K)
+*{{CRUSLink|S968|968}} (400K)
 </div>
-===k = 12===
+==={{Vk}} = 12===
 <div style="column-count:6;-moz-column-count:6;-webkit-column-count:6">
-*12*163^n+1 (400K)
+*{{CRUSLink|S163|163}} ({{HistLink|500K|584533}})
-*12*207^n+1 (100K)
+*{{CRUSLink|S207|207}} (100K)
-*12*354^n+1 (200K)
+*{{CRUSLink|S354|354}} ({{HistLink|500K|618565}})
-*12*362^n+1 (100K)
+*362 (100K)
-*12*368^n+1 (200K)
+*{{CRUSLink|S368|368}} ({{HistLink|500K|618511}})
-*12*480^n+1 (500K)
+*{{CRUSLink|S480|480}} ({{HistLink|600K|604469}})
-*12*620^n+1 (300K)
+*{{CRUSLink|S620|620}} ({{HistLink|500K|637630}})
-*12*692^n+1 (100K)
+*692 (100K)
-*12*697^n+1 (100K)
+*{{CRUSLink|S697|697}} (100K)
-*12*736^n+1 (400K)
+*{{CRUSLink|S736|736}} ({{HistLink|600K|647783}})
-*12*753^n+1 (200K)
+*{{CRUSLink|S753|753}} ({{HistLink|300K|561665}})
-*12*792^n+1 (300K)
+*{{CRUSLink|S792|792}} (300K)
-*12*978^n+1 (300K)
+*{{CRUSLink|S998|998}} (400K)
-*12*998^n+1 (400K)
+*1019 (100K)
-*12*1019^n+1 (100K)
+*1022 (100K)
-*12*1022^n+1 (100K)
 </div>
@@ Line 180: / Line 178: @@
 *For all values given with '-' there is no prime possible or are [[Generalized Fermat number]]s.
 *All unknown values are listed with "0".
-*For ''k'' = 2 there is the {{OEIS|l|A253178}}.
+*For {{Vk}} = 2 there is the {{OEIS|l|A253178}}.
 {{#get_web_data:url=https://www.rieselprime.de/z/images/0/0c/Proth_prime_small_bases_least_n.csv|format=csv with header|data=b=Base,k2=k2,k3=k3,k4=k4,k5=k5,k6=k6,k7=k7,k8=k8,k9=k9,k10=k10,k11=k11,k12=k12}}
 <div style="width: 56em; height:50em; overflow:auto;">

Difference between revisions of "Proth prime small bases least n"

Latest revision as of 11:32, 12 October 2024

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Wanted values given as base

`k` = 2

`k` = 3

`k` = 4

`k` = 5

`k` = 6

`k` = 7

`k` = 8

`k` = 9

`k` = 10

`k` = 11

`k` = 12

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