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	(2^4031399+1)/3	1213572	Tony Reix / Diepeveen-Underwood -Reix	02/2010
4	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
5	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
6	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
7	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
8	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
9	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
10	F(1968721)	411439	Henri Lifchitz	11/2009
11	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
12	F(1803059)	376817	Henri Lifchitz	06/2009
13	2^1191375+8543	358640	Phil Moore	06/2008
14	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
15	F(1636007)	341905	Henri Lifchitz	03/2009
16	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
17	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
18	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
19	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
20	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
21	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
22	2^983620+60451	296100	Phil Moore	03/2008
23	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
24	3^591827-2^591827	282374	Mike Oakes	08/2009
25	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
26	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
27	F(1285607)	268676	Henri Lifchitz	11/2008
28	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
29	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
30	3^485977-2^485977	231870	Mike Oakes	09/2009
31	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
32	(18^180181-1)/17	226176	Andy Steward	04/2007
33	L(1051849)	219824	Renaud Lifchitz	03/2009
34	F(1049897)	219416	Henri Lifchitz	10/2008
35	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
36	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
37	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
38	2^678561+678561	204268	Henri Lifchitz	05/2006
39	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
40	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
41	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
42	F(931517)	194676	Henri Lifchitz	09/2008
43	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
44	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
45	L(901657)	188436	Renaud Lifchitz	11/2008
46	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
47	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
48	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
49	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
50	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
51	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
52	10^175608+2971	175609	Mike Oakes	05/2010
53	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
54	2^566496+7	170533	Donovan Johnson	07/2006
55	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
56	11^159756-2424	166369	Mike Oakes	06/2010
57	2^551542+19249	166031	Payam Samidoost	08/2002
58	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
59	3^336353-2^336353	160482	Mike Oakes	10/2007
60	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
61	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
62	2^505431-505431	152150	Henri Lifchitz	04/2005
63	2^500899-500899	150786	Henri Lifchitz	04/2005
64	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
65	2^481801-481801	145037	Henri Lifchitz	03/2005
66	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
67	L(692147)	144651	Henri Lifchitz	10/2008
68	2^479844+3	144448	Donovan Johnson	06/2006
69	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
70	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
71	555555*2^458524+1513	138036	Darren Bedwell	08/2009
72	2^458465+2^32+1	138012	T. D. Noe	06/2007
73	2^457822+105	137819	Donovan Johnson	06/2006
74	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
75	L(651821)	136223	Henri Lifchitz	09/2008
76	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
77	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
78	L(637751)	133283	Henri Lifchitz	09/2008
79	L(631181)	131910	Henri Lifchitz	09/2008
80	L(616787)	128901	Henri Lifchitz	09/2008
81	F(604711)	126377	Henri Lifchitz	02/2005
82	2^419637+29	126324	Henri Lifchitz	02/2006
83	2^414032-5	124637	Henri Lifchitz	07/2006
84	F(593689)	124074	Henri Lifchitz	01/2005
85	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
86	F(590041)	123311	Henri Lifchitz	01/2005
87	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
88	3^256199-2^256199	122238	Mike Oakes	06/2005
89	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
90	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
91	2^398877+105	120074	Donovan Johnson	01/2006
92	L(574219)	120005	Renaud Lifchitz	03/2004
93	2^394034-3	118617	M. Frind & P. Underwood	09/2002
94	31^78759-30	117459	Theodore Burton	02/2007
95	2^388180+93	116854	Donovan Johnson	07/2008
96	2^384834+93	115847	Donovan Johnson	07/2008
97	2^384312+81091	115690	Yves Minet	02/2010
98	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
99	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
100	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
101	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
102	L(532277)	111240	Renaud Lifchitz	03/2004
103	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
104	(2^365689+2^182845+1)/5	110083	Jean Penné	11/2006
105	2^364982-5	109871	Henri Lifchitz	04/2006
106	2^363120+3	109311	Donovan Johnson	04/2006
107	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
108	2^360497+53807	108521	Yves Minet	07/2010
109	2^357885+12857	107735	Yves Minet	07/2010
110	2^354946-3	106850	M. Frind & P. Underwood	08/2002
111	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
112	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
113	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
114	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
115	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
116	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
117	43^63177-42	103198	Theodore Burton	02/2007
118	2^341134+2533	102692	Henri Lifchitz	09/2005
119	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
120	2^340688-29	102558	Henri Lifchitz	05/2005
121	2^339889+29327	102317	Yves Minet	06/2010
122	2^338796+93	101988	Donovan Johnson	06/2008
123	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
124	2^336958+79	101435	Lelio R Paula	10/2009
125	2^336942+169	101430	Lelio R Paula	10/2009
126	2^335858+153	101104	Lelio R Paula	10/2009
127	2^335586+169	101022	Lelio R Paula	10/2009
128	2^334524+145	100702	Lelio R Paula	07/2009
129	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
130	(2^333227-2^166614+1)/5	100311	Jean Penné	11/2006
131	17^81417-16	100180	Theodore Burton	11/2005
132	25206!+p(4114)	100001	Henri Lifchitz	09/2005
133	25206!-p(5447)	100001	Henri Lifchitz	10/2005
134	25206!-p(12402)	100001	Henri Lifchitz	04/2006
135	25206!-p(16290)	100001	Henri Lifchitz	09/2006
136	25206!-p(19647)	100001	Henri Lifchitz	02/2007
137	2^332194+11473	100001	Henri Lifchitz	03/2007
138	10^100000+342909	100001	Milton L. Brown	12/2007
140	10^99999+309403	100000	Daniel Heuer	01/2004
139	10^100000-260199	100000	Patrick De Geest	01/2010
141	10^99999-59511	99999	Patrick De Geest	07/2009
142	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
143	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
144	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
145	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
146	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
147	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
148	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
149	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
150	2^317024+93	95434	Donovan Johnson	06/2008
151	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
152	2^316140-5	95168	Henri Lifchitz	02/2006
153	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
154	2^311471+311469	93763	Renaud Lifchitz	01/2003
155	(2^311027-2^155514+1)/5	93628	Jean Penné	11/2006
156	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
157	3^195430-2	93244	Theodore Burton	02/2007
158	41^57783-40	93192	Theodore Burton	02/2007
159	2^308809+37967	92961	Phil Moore	03/2008
160	L(443609)	92709	Renaud Lifchitz	11/2003
161	2^307407-307407^2	92539	Henri Lifchitz	05/2005
162	2^307125-49789	92454	Henri Lifchitz	08/2005
163	(2^305867-2^152934+1)/5	92075	Jean Penné	11/2006
164	2^305676+93	92018	Donovan Johnson	06/2008
165	(7*10^91856-61)/9	91856	Erik Branger	12/2009
166	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
167	2^304015+64133	91518	David Broadhurst	06/2002
168	2^303224+2533	91280	Henri Lifchitz	05/2005
169	7*10^91215+3	91216	Erik Branger	11/2009
170	2^302949+81	91197	Henri Lifchitz	02/2007
171	2^302505+81	91064	Henri Lifchitz	02/2007
172	2^301683-301683^2	90816	Henri Lifchitz	05/2005
173	F(433781)	90655	Henri Lifchitz	09/2003
174	10^90000+8869	90001	Patrick De Geest	12/2009
176	10^89999+82939	90000	Dirk Augustin	04/2007
175	10^90000-140343	90000	Patrick De Geest	12/2009
177	10^89999-194891	89999	Patrick De Geest	11/2009
178	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
179	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
180	2^296016+81	89110	Henri Lifchitz	02/2007
181	31^59713-30	89054	Theodore Burton	02/2007
182	19^69025-18	88266	Theodore Burton	01/2006
183	2^292929+43877	88181	Donovan Johnson	04/2005
184	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
185	10^87720-3	87720	Markus Tervooren	07/2010
186	91382^9+9^91382	87201	Andrey Kulsha	11/2004
187	(10^86453-1)/9	86453	Lew Baxter	10/2000
188	2^284133-3	85533	M. Frind & P. Underwood	07/2002
189	19834^19834+8947	85235	Henri Lifchitz	11/2004
190	((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
191	2^280852+97681	84545	Yves Minet	08/2004
192	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
193	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
194	2^276587-937	83261	Yves Minet	10/2009
195	F(397379)	83047	Henri Lifchitz	08/2003
196	3*10^82880-7^82880	82881	Mike Oakes	02/2010
197	2^275259+81	82862	Henri Lifchitz	01/2007
198	3^173191-2^173191	82634	Mike Oakes	02/2004
199	11^79133-10	82409	Theodore Burton	11/2005
200	2^273126+36937	82220	Yves Minet	06/2010
201	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
202	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
203	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
204	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
205	2^269490-3623	81125	Yves Minet	10/2009
206	L(387433)	80969	Renaud Lifchitz	11/2003
207	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
208	2^268079-1927	80700	Yves Minet	10/2009
209	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
210	10^80000+85731	80001	Patrick De Geest	10/2009
211	10^80000-7169	80000	Patrick De Geest	09/2009
212	10^79999+22399	80000	Patrick De Geest	09/2009
213	10^79999-74873	79999	Patrick De Geest	09/2009
214	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
215	47^47667-46	79704	Theodore Burton	02/2007
216	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
217	10^79362+3^79363	79363	Mike Oakes	06/2010
218	19^61980-18	79258	Theodore Burton	12/2005
219	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
220	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
221	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
222	2^261856+98765331	78827	Jason Earls	01/2009
223	2^261507-2287	78722	Yves Minet	04/2009
224	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
225	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
226	14*10^78362+1089	78364	Jens K. Andersen	11/2007
227	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
228	7^92511-6	78181	Theodore Burton	11/2005
229	7^92410-9266	78096	Mike Oakes	02/2010
230	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
231	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
232	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
233	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
234	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
235	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
236	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
237	Phi(76537,10)/66127969	76529	Maksym Voznyy	01/2010
238	7^90291-6	76305	Theodore Burton	11/2005
239	14*10^75798+1089	75800	Jens K. Andersen	11/2007
240	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
241	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
242	7^88713+2*3^88713	74972	Mike Oakes	07/2010
243	2*F(358297)-1	74880	Henri Lifchitz	12/2009
244	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
245	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
246	2^247165-3	74405	M. Frind & P. Underwood	07/2002
247	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
248	2^246618+427	74240	Henri Lifchitz	02/2005
249	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
250	9998*2^245696+3	73966	Donovan Johnson	10/2004

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PRP Records

Probable Primes Top 10000

(51605 PRPs in the top)