Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize theses numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 10000)	Who ?	When ?
1	2^5146295+41693	1549190	Engracio Esmenda / Five or Bust	11/2009
2	2^4583176+2131	1379674	Ben Maloney / Five or Bust	09/2009
3	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
4	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
5	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
6	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
7	F(1968721)	411439	Henri Lifchitz	11/2009
8	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
9	F(1803059)	376817	Henri Lifchitz	06/2009
10	2^1191375+8543	358640	Phil Moore	06/2008
11	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
12	F(1636007)	341905	Henri Lifchitz	03/2009
13	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
14	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
15	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
16	2^983620+60451	296100	Phil Moore	03/2008
17	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
18	3^591827-2^591827	282374	Mike Oakes	08/2009
19	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
20	F(1285607)	268676	Henri Lifchitz	11/2008
21	3^485977-2^485977	231870	Mike Oakes	09/2009
22	Phi(180181,18)	226176	Andy Steward	04/2007
23	L(1051849)	219824	Renaud Lifchitz	03/2009
24	F(1049897)	219416	Henri Lifchitz	10/2008
25	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
26	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
27	2^678561+678561	204268	Henri Lifchitz	05/2006
28	F(931517)	194676	Henri Lifchitz	09/2008
29	L(901657)	188436	Renaud Lifchitz	11/2008
30	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
31	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
32	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
33	2^566496+7	170533	Donovan Johnson	07/2006
34	2^551542+19249	166031	Payam Samidoost	08/2002
35	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
36	3^336353-2^336353	160482	Mike Oakes	10/2007
37	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
38	2^505431-505431	152150	Henri Lifchitz	04/2005
39	2^500899-500899	150786	Henri Lifchitz	04/2005
40	2^481801-481801	145037	Henri Lifchitz	03/2005
41	L(692147)	144651	Henri Lifchitz	10/2008
42	2^479844+3	144448	Donovan Johnson	06/2006
43	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
44	555555*2^458524+1513	138036	Darren Bedwell	08/2009
45	2^458465+2^32+1	138012	T. D. Noe	06/2007
46	2^457822+105	137819	Donovan Johnson	06/2006
47	L(651821)	136223	Henri Lifchitz	09/2008
48	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
49	L(637751)	133283	Henri Lifchitz	09/2008
50	L(631181)	131910	Henri Lifchitz	09/2008
51	L(616787)	128901	Henri Lifchitz	09/2008
52	F(604711)	126377	Henri Lifchitz	02/2005
53	2^419637+29	126324	Henri Lifchitz	02/2006
54	2^414032-5	124637	Henri Lifchitz	07/2006
55	F(593689)	124074	Henri Lifchitz	01/2005
56	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
57	F(590041)	123311	Henri Lifchitz	01/2005
58	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
59	3^256199-2^256199	122238	Mike Oakes	06/2005
60	2^398877+105	120074	Donovan Johnson	01/2006
61	L(574219)	120005	Renaud Lifchitz	03/2004
62	2^394034-3	118617	M. Frind & P. Underwood	09/2002
63	31^78759-30	117459	Theodore Burton	02/2007
64	2^388180+93	116854	Donovan Johnson	07/2008
65	2^384834+93	115847	Donovan Johnson	07/2008
66	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
67	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
68	L(532277)	111240	Renaud Lifchitz	03/2004
69	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
70	(2^365689+2^182845+1)/5	110083	Jean Penné	11/2006
71	2^364982-5	109871	Henri Lifchitz	04/2006
72	2^363120+3	109311	Donovan Johnson	04/2006
73	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
74	2^354946-3	106850	M. Frind & P. Underwood	08/2002
75	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
76	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
77	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
78	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
79	43^63177-42	103198	Theodore Burton	02/2007
80	2^341134+2533	102692	Henri Lifchitz	09/2005
81	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
82	2^340688-29	102558	Henri Lifchitz	05/2005
83	2^338796+93	101988	Donovan Johnson	06/2008
84	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
85	2^336958+79	101435	Lelio R Paula	10/2009
86	2^336942+169	101430	Lelio R Paula	10/2009
87	2^335858+153	101104	Lelio R Paula	10/2009
88	2^335586+169	101022	Lelio R Paula	10/2009
89	2^334524+145	100702	Lelio R Paula	07/2009
90	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
91	(2^333227-2^166614+1)/5	100311	Jean Penné	11/2006
92	17^81417-16	100180	Theodore Burton	11/2005
93	25206!+p(4114)	100001	Henri Lifchitz	09/2005
94	25206!-p(5447)	100001	Henri Lifchitz	10/2005
95	25206!-p(12402)	100001	Henri Lifchitz	04/2006
96	25206!-p(16290)	100001	Henri Lifchitz	09/2006
97	25206!-p(19647)	100001	Henri Lifchitz	02/2007
98	2^332194+11473	100001	Henri Lifchitz	03/2007
99	10^100000+342909	100001	Milton L. Brown	12/2007
101	10^99999+309403	100000	Daniel Heuer	01/2004
100	10^100000-260199	100000	Patrick De Geest	01/2010
102	10^99999-59511	99999	Patrick De Geest	07/2009
103	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
104	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
105	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
106	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
107	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
108	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
109	2^317024+93	95434	Donovan Johnson	06/2008
110	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
111	2^316140-5	95168	Henri Lifchitz	02/2006
112	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
113	2^311471+311469	93763	Renaud Lifchitz	01/2003
114	(2^311027-2^155514+1)/5	93628	Jean Penné	11/2006
115	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
116	3^195430-2	93244	Theodore Burton	02/2007
117	41^57783-40	93192	Theodore Burton	02/2007
118	2^308809+37967	92961	Phil Moore	03/2008
119	L(443609)	92709	Renaud Lifchitz	11/2003
120	2^307407-307407^2	92539	Henri Lifchitz	05/2005
121	2^307125-49789	92454	Henri Lifchitz	08/2005
122	(2^305867-2^152934+1)/5	92075	Jean Penné	11/2006
123	2^305676+93	92018	Donovan Johnson	06/2008
124	(7*10^91856-61)/9	91856	Erik Branger	12/2009
125	2^304015+64133	91518	David Broadhurst	06/2002
126	2^303224+2533	91280	Henri Lifchitz	05/2005
127	7*10^91215+3	91216	Erik Branger	11/2009
128	2^302949+81	91197	Henri Lifchitz	02/2007
129	2^302505+81	91064	Henri Lifchitz	02/2007
130	2^301683-301683^2	90816	Henri Lifchitz	05/2005
131	F(433781)	90655	Henri Lifchitz	09/2003
132	10^90000+8869	90001	Patrick De Geest	12/2009
134	10^89999+82939	90000	Dirk Augustin	04/2007
133	10^90000-140343	90000	Patrick De Geest	12/2009
135	10^89999-194891	89999	Patrick De Geest	11/2009
136	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
137	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
138	2^296016+81	89110	Henri Lifchitz	02/2007
139	31^59713-30	89054	Theodore Burton	02/2007
140	19^69025-18	88266	Theodore Burton	01/2006
141	2^292929+43877	88181	Donovan Johnson	04/2005
142	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
143	91382^9+9^91382	87201	Andrey Kulsha	11/2004
144	(10^86453-1)/9	86453	Lew Baxter	10/2000
145	2^284133-3	85533	M. Frind & P. Underwood	07/2002
146	19834^19834+8947	85235	Henri Lifchitz	11/2004
147	((1+sqrt(3)+sqrt(2))^79357-1)((1+sqrt(3)-sqrt(2))^79357-1)((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(3	84849	Mike Oakes	04/2009
148	2^280852+97681	84545	Yves Minet	08/2004
149	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
150	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
151	2^276587-937	83261	Yves Minet	10/2009
152	F(397379)	83047	Henri Lifchitz	08/2003
153	2^275259+81	82862	Henri Lifchitz	01/2007
154	3^173191-2^173191	82634	Mike Oakes	02/2004
155	11^79133-10	82409	Theodore Burton	11/2005
156	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
157	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
158	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
159	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
160	2^269490-3623	81125	Yves Minet	10/2009
161	L(387433)	80969	Renaud Lifchitz	11/2003
162	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
163	2^268079-1927	80700	Yves Minet	10/2009
164	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
165	10^80000+85731	80001	Patrick De Geest	10/2009
166	10^80000-7169	80000	Patrick De Geest	09/2009
167	10^79999+22399	80000	Patrick De Geest	09/2009
168	10^79999-74873	79999	Patrick De Geest	09/2009
169	47^47667-46	79704	Theodore Burton	02/2007
170	19^61980-18	79258	Theodore Burton	12/2005
171	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
172	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
173	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
174	2^261856+98765331	78827	Jason Earls	01/2009
175	2^261507-2287	78722	Yves Minet	04/2009
176	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
177	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
178	14*10^78362+1089	78364	Jens K. Andersen	11/2007
179	7^92511-6	78181	Theodore Burton	11/2005
180	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
181	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
182	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
183	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
184	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
185	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
186	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
187	Phi(76537,10)/66127969	76529	Maksym Voznyy	01/2010
188	7^90291-6	76305	Theodore Burton	11/2005
189	14*10^75798+1089	75800	Jens K. Andersen	11/2007
190	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
191	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
192	2*F(358297)-1	74880	Henri Lifchitz	12/2009
193	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
194	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
195	2^247165-3	74405	M. Frind & P. Underwood	07/2002
196	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
197	2^246618+427	74240	Henri Lifchitz	02/2005
198	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
199	9998*2^245696+3	73966	Donovan Johnson	10/2004
200	2^244618-2297	73638	Yves Minet	10/2009
201	7^86689-6^86689	73261	Predrag Minovic	09/2004
202	6^93812+5	73000	Wojciech Florek	03/2006
203	2^242150+17659	72895	Lelio R Paula	11/2009
204	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
205	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
206	2^241004-3	72550	M. Frind & P. Underwood	07/2002
207	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
208	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
209	L(344293)	71953	Renaud Lifchitz	09/2003
210	2^238568+98765331	71817	Jason Earls	01/2009
211	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
212	2^238144+98765331	71689	Jason Earls	01/2009
213	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
214	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
215	2^237407-9787	71467	Lelio R Paula	11/2009
216	2^236911-1147	71318	Yves Minet	10/2009
217	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
218	2^235326+3	70841	Donovan Johnson	02/2006
219	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
220	(2^235099-2^117550+1)/5	70772	Jean Penné	11/2006
221	2^234133-3163	70482	Yves Minet	04/2009
222	19471^16428-2	70467	Faysal YAtim	09/2005
223	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
224	10^70000+80487	70001	Milton L. Brown	05/2006
225	10^69999+134857	70000	Patrick De Geest	02/2007
226	10^70000-9273	70000	Patrick De Geest	08/2009
227	10^69999-88251	69999	Patrick De Geest	08/2009
228	2^228944+81	68920	Henri Lifchitz	01/2007
229	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
230	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
231	2^228271-228271	68717	Henri Lifchitz	11/2004
232	2*F(328450)-1	68642	Henri Lifchitz	12/2009
233	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
234	2^227115-7807	68369	Lelio R Paula	10/2009
235	2^225536-29	67894	Henri Lifchitz	05/2005
236	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
237	2^224815-49789	67677	Henri Lifchitz	04/2005
238	((1+sqrt(7)+sqrt(6))^45863-1)((1+sqrt(7)-sqrt(6))^45863-1)((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(7	67653	Mike Oakes	05/2009
239	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
240	2^222943+29	67113	Henri Lifchitz	08/2005
241	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
242	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
243	(2^221891-2^110946+1)/5	66796	Jean Penné	11/2006
244	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
245	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
246	2^219812-3149	66171	Yves Minet	10/2009
247	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
248	2^219304+454245	66018	Henri Lifchitz	03/2007
249	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
250	2*F(314335)-1	65693	Henri Lifchitz	12/2009

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Probable Primes Top 10000

(46339 PRPs in the top)