Basic extension of original table Current overall limits
k n k n
3-9 8000-43000 3-7 470000
11-49 8000-32000 9-61 200000
51-99 8000-16000 63-299 100000
101-199 6000-16000
201-299 1-16000
k Further intervals & Contributors
3 43000-51400 Lifchitz, 51400-194200 Keller & Buechel,
194200-3270000 Project 3*2^n-1 Search (in progress)
5 43000-191500 Keller & Buechel, 191500-200000 Harvey,
200000-470000 Carmody
7 43000-191500 Keller & Buechel, 191500-193500 Shepherd,
193500-195000 Harvey, 195000-2055000 Minovic (in progress)
9 43000-191500 Keller & Buechel, 191500-200000 Harvey
11 32000-48000 Graef, 48000-95000 Harvey, 95000-110000 Ritschel,
110000-120000 Harvey, 120000-145000 Ritschel, 145000-150000 Harvey,
150000-1200000 Ritschel (in progress)
13 32000-48000 Graef, 48000-60000 Harvey, 60000-110000 Minovic,
110000-120000 Harvey, 120000-1000000 Minovic
15 32000-48000 Graef, 48000-110000 Pfoertner, 110000-120000 Harvey,
120000-502000 Smith
17 32000-48000 Graef, 48000-110000 Walker, 110000-120000 Harvey,
120000-205000 Walker
19 32000-48000 Graef, 48000-517700 Harvey
21 32000-48000 Graef, 48000-500000 Harvey, 500000-1000000 Minovic
23 32000-48000 Graef, 48000-60000 Harvey, 60000-110000 Pfoertner,
110000-120000 Harvey, 120000-151000 Ritschel, 151000-226600 Harvey
25 32000-48000 Graef, 48000-167000 Broadhurst, 167000-200000 Harvey,
200000-300000 Walker, 300000-400000 Harvey
27 32000-58000 Broadhurst, 58000-175900 Roth, 175900-276100 Harvey [ ]
302500-500000 Harvey
29 32000-67400 Keller, 67400-154500 Keller & Buechel,
154500-286300 Harvey, 286300-1600000 Ritschel (in progress)
31 32000-500000 Harvey
33 32000-43200 Broadhurst, 43200-250000 Harvey
35 32000-100000 Broadhurst, 100000-110000 Pfoertner, 110000-120000 Harvey,
120000-200000 Ritschel, 200000-210000 Harvey, 210000-420000 Minovic
37 32000-33000 Keller, 33000-48000 Kuechler, 48000-200000 Masser,
200000-210000 Harvey
39 32000-62200 Herranen, 62200-500000 Ritschel
41 32000-56000 Kuechler, 56000-110000 Ritschel, 110000-120000 Harvey,
120000-500000 Ritschel
43 32000-66000 Kuechler, 66000-100000 Broadhurst, 100000-110000 Pfoertner,
110000-120000 Harvey, 120000-200000 Ritschel, 200000-210000 Harvey
45 32000-50000 Lifchitz, 50000-500000 Sun
47 32000-100000 Broadhurst, 100000-110000 Ritschel, 110000-120000 Harvey,
120000-200000 Ritschel, 200000-210000 Harvey
49 32000-110000 Rodenkirch, 110000-120000 Harvey, 120000-417500 Rodenkirch
51 16000-40000 Andrews, 40000-110000 Walker, 110000-120000 Harvey,
120000-200000 Walker, 200000-210000 Harvey
53 16000-32000 Carmody, 32000-89850 Broadhurst, 89850-110000 Minovic,
110000-120000 Harvey, 120000-520000 Minovic
55 16000-100000 Andrews, 100000-110000 Pfoertner, 110000-120000 Harvey,
120000-200000 Ritschel, 200000-210000 Harvey, 210000-520000 Minovic
57 16000-40000 Andrews, 40000-100000 Broadhurst, 100000-110000 Ritschel,
110000-120000 Harvey, 120000-200000 Ritschel, 200000-210000 Harvey,
210000-400000 Minovic
59 16000-60000 Kuechler, 60000-100000 Broadhurst, 100000-110000 Ritschel,
110000-120000 Harvey, 120000-200000 Ritschel, 200000-210000 Harvey,
210000-1000000 Minovic
61 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-110000 Ritschel,
110000-120000 Harvey, 120000-200000 Ritschel, 200000-210000 Harvey,
210000-400000 Minovic
63 16000-40000 Andrews, 40000-100000 Broadhurst [ ] 200000-500000 Minovic
65 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey,
210000-420000 Goudt
67 16000-31000 Keller, 31000-66000 Kuechler, 66000-100000 Broadhurst,
100000-110000 Ritschel, 110000-120000 Harvey, 100000-200000 Ritschel,
200000-210000 Harvey, 210000-400000 Minovic
69 16000-100000 Andrews, 100000-186000 Sun
71 16000-61000 Keller, 61000-200000 Broadhurst, 200000-210000 Harvey,
210000-736000 Broadhurst
73 16000-28000 Keller, 28000-65000 Kuechler, 65000-200000 Masser,
200000-1000000 Minovic
75 16000-32000 Carmody, 32000-48000 Broadhurst, 48000-250000 PKeller,
250000-500000 Ritschel
77 16000-32000 Carmody, 32000-80000 Broadhurst,
80000-1340000 Minovic [ ] 1455000-1500000 Minovic
79 16000-51000 Kuechler, 51000-740000 Minovic
81 16000-50000 Kuechler, 50000-100000 Broadhurst
83 16000-66000 Kuechler, 66000-210000 Harvey, 210000-400000 Minovic
[ ] 536800-740000 Minovic
85 16000-66000 Kuechler, 66000-200000 Masser, 200000-210000 Harvey,
210000-1080000 Minovic
87 16000-50000 Kuechler, 50000-210000 Harvey, 210000-1000000 Minovic
89 16000-66000 Kuechler, 66000-80000 Broadhurst, 80000-740000 Minovic
91 16000-66000 Kuechler, 66000-300000 Harvey [ ] 600000-740000 Minovic
93 16000-50000 Kuechler, 50000-74600 Broadhurst, 74600-210000 Harvey
95 16000-66000 Kuechler, 66000-200000 Ritschel, 200000-210000 Harvey,
210000-700000 Minovic
97 16000-66000 Kuechler, 66000-200000 Masser, 200000-800000 Broadhurst,
800000-930000 Minovic
99 16000-66000 Kuechler, 66000-200000 Ritschel, 200000-210000 Harvey
101 16000-66000 Keller, 66000-100000 Broadhurst
103 16000-65000 Kuechler, 65000-100000 Broadhurst
105 16000-32000 Carmody, 32000-100000 Broadhurst
107 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey
109 16000-66000 Keller, 66000-100000 Broadhurst, 100000-350000 Barnes
111 16000-17000 Keller, 17000-37800 Lifchitz, 37800-151200 Keller & Buechel,
151200-700000 Masser
113 16000-32000 Carmody, 32000-500000 Ritschel
115 16000-32000 Carmody, 32000-70400 Broadhurst, 70400-210000 Harvey
117 16000-32000 Carmody, 32000-100000 Broadhurst
119 16000-66300 Keller, 66300-178400 Keller & Buechel, 178400-200000 Masser
121 16000-32000 Carmody, 32000-2800000 Project 12121 Search (in progress)
123 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-700000 Masser
(in progress)
125 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey
127 16000-45000 Keller, 45000-48000 Broadhurst, 48000-200000 Masser
129 16000-47800 Carmody, 47800-100000 Broadhurst [ ] 200000-210000 Harvey
131 16000-65000 Kuechler, 65000-100000 Broadhurst [ ] 200000-210000 Harvey
133 16000-56000 Kuechler, 56000-100000 Broadhurst [ ] 200000-210000 Harvey
135 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey
137 16000-32000 Carmody, 32000-2000000 Broadhurst
139 16000-46500 de Water, 46500-100000 Broadhurst [ ] 200000-210000 Harvey,
210000-400000 Galvan
141 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey,
210000-500000 Ritschel
143 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey
145 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey
147 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey
149 16000-32000 Keller, 32000-66000 Kuechler, 66000-100000 Broadhurst [ ]
200000-210000 Harvey
151 16000-32000 Keller, 32000-48000 Broadhurst, 48000-200000 Masser,
200000-210000 Harvey, 210000-500000 Ritschel
153 16000-52000 de Water, 52000-250000 Ritschel, 250000-700000 Masser
(in progress)
155 16000-32000 Carmody, 32000-500000 Ritschel
157 16000-66000 Kuechler, 66000-500000 Ritschel
159 16000-18000 Keller, 18000-32000 Carmody, 32000-250000 Ritschel,
250000-700000 Masser
161 16000-51000 Kuechler, 51000-500000 Ritschel
163 16000-35000 Keller, 35000-55000 Kuechler, 55000-200000 Masser,
200000-210000 Harvey, 210000-500000 Ritschel
165 16000-32000 Carmody, 32000-100000 Broadhurst [ ] 200000-210000 Harvey,
210000-600000 Minovic
167 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-101060 Ritschel,
101060-200000 Harvey
169 16000-32000 Carmody, 32000-90750 Broadhurst, 90750-210000 Harvey
171 16000-18000 Keller, 18000-32000 Carmody, 32000-48000 Broadhurst,
48000-700000 Masser
173 16000-32000 Carmody, 32000-48000 Broadhurst, 48000-210000 Harvey,
210000-1000000 Minovic
175 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-133600 Ritschel,
133600-210000 Harvey
177 16000-32000 Carmody, 32000-80000 Broadhurst, 80000-210000 Harvey,
210000-1275000 Minovic
179 16000-36000 Keller, 36000-56000 Kuechler, 56000-200000 Masser,
200000-210000 Harvey
181 16000-70000 Andrews, 70000-100000 Broadhurst, 100000-150000 Minovic
(in progress) [ ] 200000-210000 Harvey
183 16000-26000 Keller, 26000-66500 Herranen, 66500-700000 Masser
(in progress)
185 16000-18000 Keller, 18000-32000 Carmody, 32000-100000 Broadhurst,
100000-128100 Ritschel, 128100-210000 Harvey
187 16000-18000 Keller, 18000-66000 Kuechler, 66000-100000 Broadhurst [ ]
200000-210000 Harvey
189 16000-32000 Carmody, 32000-80000 Broadhurst, 80000-200000 Harvey,
200000-700000 Masser, 700000-770000 Minovic
191 16000-65000 Keller, 65000-100000 Andrews, 100000-500000 Ritschel
193 16000-66000 Kuechler, 66000-200000 Masser, 200000-885000 Minovic
195 16000-52000 Lifchitz, 52000-100000 Broadhurst,
100000-267000 Sun & Findley
197 16000-32000 Carmody, 32000-100000 Broadhurst
199 16000-17000 Keller, 17000-36000 Lifchitz, 36000-100000 Broadhurst
201 16000-25000 de Water, 25000-32000 Carmody, 32000-100000 Broadhurst
203 16000-40000 Carmody, 40000-100000 Broadhurst, 100000-260000 Barnes
205 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-250000 Barnes
207 16000-40000 Carmody, 40000-100000 Broadhurst
209 16000-66000 Kuechler, 66000-100000 Broadhurst
211 16000-40000 Carmody, 40000-100000 Broadhurst
213 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-250000 Barnes
215 16000-18000 Keller, 18000-40000 Carmody, 40000-100000 Broadhurst,
100000-110000 Eckhard, 110000-250000 Barnes
217 16000-18000 Keller, 18000-66000 Kuechler, 66000-100000 Broadhurst,
100000-260000 Barnes
219 16000-24000 Keller, 24000-62300 Herranen, 62300-100000 Broadhurst,
100000-200000 Masser, 200000-210000 Harvey, 210000-700000 Masser
(in progress)
221 16000-41000 Keller, 41000-66000 Kuechler, 66000-100000 Broadhurst [ ]
200000-210000 Harvey
223 16000-41000 Keller, 41000-66000 Kuechler, 66000-100000 Broadhurst [ ]
200000-210000 Harvey
225 16000-52800 Carmody, 52800-700000 Masser
227 16000-42500 Carmody, 42500-100000 Broadhurst [ ] 200000-210000 Harvey
229 16000-18000 Keller, 18000-44400 Carmody, 44400-100000 Broadhurst [ ]
160870-210000 Harvey
231 16000-18000 Keller, 18000-50000 Kuechler, 50000-100000 Broadhurst,
100000-150000 Griffin
233 16000-52700 Carmody, 52700-100000 Broadhurst, 100000-150000 Griffin [ ]
200000-230000 Harvey
235 16000-49900 Carmody, 49900-100000 Broadhurst, 100000-150000 Griffin [ ]
200000-230000 Harvey
237 16000-25000 Carmody, 25000-48000 Broadhurst, 48000-200000 Masser,
200000-230000 Harvey, 230000-260000 Barnes
239 16000-45000 Keller, 45000-100000 Andrews, 100000-200000 Masser,
200000-230000 Harvey
241 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-150000 Griffin,
150000-200000 Minovic, 200000-230000 Harvey, 230000-260000 Minovic
243 16000-48000 Andrews, 48000-100000 Broadhurst, 100000-150000 Griffin [ ]
200000-230000 Harvey, 230000-800000 Barnes
245 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-150000 Griffin [ ]
200000-230000 Harvey
247 16000-65000 Keller, 65000-100000 Andrews, 100000-200000 Masser,
200000-230000 Harvey
249 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-150000 Griffin,
150000-200000 Barnes, 200000-230000 Harvey, 230000-260000 Barnes
For k>250 see also Michael Hartley's excellently organized Primesearch,
where the prime table is extended to k<1000
251 16000-53100 Keller, 53100-213000 Keller & Buechel
253 16000-53100 Keller, 53100-213000 Keller & Buechel
[ ] 1165000-1750000 Minovic
255 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-130000 Harvey,
130000-796000 Griffin
257 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-130000 Harvey,
130000-260000 Barnes, 260000-320000 Galvan
259 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-135000 Harvey [ ]
150000-155000 Harvey
261 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-135000 Harvey,
135000-150000 Barnes, 150000-155000 Harvey, 155000-260000 Barnes
263 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-135000 Harvey [ ]
150000-155000 Harvey
265 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-135000 Harvey [ ]
150000-155000 Harvey [ ] 185000-230000 Harvey, 230000-260000 Griffin
267 16000-18000 Keller, 18000-32000 Carmody, 32000-100000 Broadhurst,
100000-135000 Harvey, 135000-150000 Griffin, 150000-155000 Harvey,
155000-160000 Barnes, 160000-180000 Harvey, 180000-205000 Barnes,
205000-260000 Griffin, 260000-300000 Barnes
269 16000-32000 Keller, 32000-56000 Kuechler, 56000-100000 Broadhurst,
100000-120000 Harvey [ ] 130000-260000 Griffin
271 16000-32000 Keller, 32000-130000 Harvey [ ] 140000-160000 Griffin [ ]
165000-175000 Griffin, 175000-180000 Harvey, 180000-195000 Griffin,
195000-200000 Harvey, 200000-260000 Griffin
273 16000-32000 Carmody, 32000-100000 Broadhurst, 100000-120000 Barnes,
120000-130000 Harvey, 130000-150000 Barnes, 150000-155000 Harvey,
155000-170000 Barnes, 170000-175000 Harvey, 175000-180000 Barnes,
180000-195000 Griffin, 195000-230000 Harvey, 230000-260000 Griffin
275 16000-18000 Keller, 18000-32000 Carmody, 32000-100000 Broadhurst [ ]
140000-145000 Griffin, 145000-155000 Harvey [ ] 160000-210000 Griffin,
210000-230000 Harvey, 230000-260000 Griffin
277 16000-18000 Keller, 18000-66000 Kuechler, 66000-100000 Broadhurst,
100000-145000 Minovic, 145000-155000 Harvey, 155000-165000 Minovic,
165000-200000 Harvey, 200000-205000 Minovic, 205000-230000 Harvey,
230000-885000 Minovic
279 16000-24000 Keller, 24000-66900 Herranen, 66900-100000 Broadhurst,
100000-130000 Barnes, 130000-135000 Harvey, 135000-145000 Barnes,
145000-155000 Harvey, 155000-165000 Barnes, 165000-230000 Harvey,
230000-260000 Barnes
281 16000-20000 Keller, 20000-66000 Kuechler, 66000-135000 Harvey,
135000-145000 Minovic, 145000-155000 Harvey, 155000-165000 Minovic,
165000-190000 Harvey, 190000-195000 Minovic, 195000-230000 Harvey,
230000-260000 Minovic
283 16000-20000 Keller, 20000-66000 Kuechler, 66000-100000 Broadhurst,
100000-120000 Minovic, 120000-135000 Harvey, 135000-145000 Minovic,
145000-200000 Harvey, 200000-260000 Minovic
285 16000-70000 Andrews, 70000-135000 Harvey, 135000-145000 Minovic,
145000-155000 Harvey, 155000-170000 Minovic, 170000-230000 Harvey
230000-470000 Minovic
287 16000-56400 Carmody, 56400-120000 Harvey, 120000-130000 Minovic,
130000-135000 Harvey, 135000-150000 Minovic, 150000-155000 Harvey,
155000-165000 Minovic, 165000-230000 Harvey, 230000-260000 Griffin
289 16000-56400 Carmody, 56400-120000 Harvey, 120000-130000 Barnes,
130000-135000 Harvey, 135000-145000 Barnes, 145000-155000 Harvey,
155000-520000 Barnes
291 16000-56400 Carmody, 56400-130000 Harvey, 130000-165000 Barnes,
165000-230000 Harvey, 230000-260000 Griffin
293 16000-56400 Carmody, 56400-100000 Broadhurst, 100000-200000 Minovic,
200000-230000 Harvey, 230000-260000 Griffin
295 16000-40000 Szmidt, 40000-130000 Harvey [ ] 180000-230000 Harvey,
230000-260000 Griffin
297 16000-120000 Szmidt, 120000-130000 Harvey [ ] 180000-230000 Harvey,
230000-260000 Griffin
299 16000-110000 Szmidt, 110000-130000 Harvey [ ] 150000-155000 Harvey [ ]
165000-230000 Harvey, 230000-260000 Griffin
3*2^n-1 Search, 12121 Search, Dale Andrews, Gary Barnes, David Broadhurst, Ingo Buechel, Phil Carmody, Rüdiger Eckhard, Tony Galvan, Ingmar Goudt, Michael Graef, James Griffin, Steven Harvey, Kimmo Herranen, Patrick Keller, Wilfrid Keller, Tom Kuechler, Henri Lifchitz, Thomas Masser, Predrag Minovic, Hugo Pfoertner, Thomas Ritschel, Rick Shepherd, Stéphane Roth, Robert Smith, Jiong Sun, Janusz Szmidt, Andrew Walker, Bouk de Water.