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	2^9092392+40291	2737083	Engracio Esmenda / Five or Bust	02/2011
2	2^5146295+41693	1549190	Engracio Esmenda / Five or Bust	11/2009
3	2^4583176+2131	1379674	Ben Maloney / Five or Bust	09/2009
4	(2^4031399+1)/3	1213572	Tony Reix / Diepeveen-Underwood -Reix	02/2010
5	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
6	(18^481147+1)/19	603970	Paul Bourdelais	07/2011
7	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
8	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
9	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
10	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
11	(10^424861-7)/3	424861	Leonid Durman	01/2012
12	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
13	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
14	F(1968721)	411439	Henri Lifchitz	11/2009
15	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
16	(10^380976-7)/3	380976	Leonid Durman	01/2012
17	F(1803059)	376817	Henri Lifchitz	06/2009
18	2^1191375+8543	358640	Phil Moore	06/2008
19	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
20	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
21	F(1636007)	341905	Henri Lifchitz	03/2009
22	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
23	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
24	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
25	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
26	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
27	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
28	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
29	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
30	2^983620+60451	296100	Phil Moore	03/2008
31	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
32	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
33	3^591827-2^591827	282374	Mike Oakes	08/2009
34	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
35	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
36	F(1285607)	268676	Henri Lifchitz	11/2008
37	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
38	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
39	(7*10^260198-61)/9	260198	Erik Branger	11/2011
40	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
41	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
42	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
43	10^232599-3	232599	Markus Tervooren	10/2010
44	3^485977-2^485977	231870	Mike Oakes	09/2009
45	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
46	(18^180181-1)/17	226176	Andy Steward	04/2007
47	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
48	10^221631-9	221631	Alexander Gramolin	02/2011
49	L(1051849)	219824	Renaud Lifchitz	03/2009
50	F(1049897)	219416	Henri Lifchitz	10/2008
51	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
52	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
53	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
54	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
55	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
56	2^678561+678561	204268	Henri Lifchitz	05/2006
57	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
58	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
59	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
60	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
61	F(931517)	194676	Henri Lifchitz	09/2008
62	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
63	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
64	L(901657)	188436	Renaud Lifchitz	11/2008
65	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
66	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
67	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
68	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
69	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
70	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
71	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
72	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
73	10^175608+2971	175609	Mike Oakes	05/2010
74	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
75	2^566496+7	170533	Donovan Johnson	07/2006
76	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
77	11^159756-2424	166369	Mike Oakes	06/2010
78	2^551542+19249	166031	Payam Samidoost	08/2002
79	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
80	3^336353-2^336353	160482	Mike Oakes	10/2007
81	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
82	EPrime(155025)	155025	Eric W. Weisstein	10/2010
83	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
84	2^505431-505431	152150	Henri Lifchitz	04/2005
85	2^504054-2231	151736	Yves Minet	10/2011
86	2^502576-4019	151291	Yves Minet	10/2011
87	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
88	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
89	2^500899-500899	150786	Henri Lifchitz	04/2005
90	8*10^148860-3	148861	Ray Chandler	04/2011
91	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
92	2^481801-481801	145037	Henri Lifchitz	03/2005
93	29^99167+2	145022	Ray Chandler	08/2011
94	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
95	L(692147)	144651	Henri Lifchitz	10/2008
96	2^479844+3	144448	Donovan Johnson	06/2006
97	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
98	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
99	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
100	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
101	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
102	555555*2^458524+1513	138036	Darren Bedwell	08/2009
103	2^458465+2^32+1	138012	T. D. Noe	06/2007
104	2^457822+105	137819	Donovan Johnson	06/2006
105	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
106	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
107	2^454675-1777	136871	Yves Minet	10/2011
108	L(651821)	136223	Henri Lifchitz	09/2008
109	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
110	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
111	L(637751)	133283	Henri Lifchitz	09/2008
112	L(631181)	131910	Henri Lifchitz	09/2008
113	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
114	Phi(5,1181#)	128937	Mike Oakes	01/2011
115	L(616787)	128901	Henri Lifchitz	09/2008
116	F(604711)	126377	Henri Lifchitz	02/2005
117	2^419637+29	126324	Henri Lifchitz	02/2006
118	(23^91943-1)/22	125201	Robert Price	01/2012
119	2^415144-3683	124971	Yves Minet	10/2011
120	2^414032-5	124637	Henri Lifchitz	07/2006
121	F(593689)	124074	Henri Lifchitz	01/2005
122	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
123	F(590041)	123311	Henri Lifchitz	01/2005
124	(30^82883-1)/29	122427	Robert Price	12/2011
125	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
126	3^256199-2^256199	122238	Mike Oakes	06/2005
127	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
128	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
129	2^398877+105	120074	Donovan Johnson	01/2006
130	L(574219)	120005	Renaud Lifchitz	03/2004
131	2^398571+60413	119982	Yves Minet	03/2011
132	8*10^119930-3	119931	Ray Chandler	04/2011
133	2^394034-3	118617	M. Frind & P. Underwood	09/2002
134	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
135	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
136	2^391933+5897	117984	Yves Minet	02/2011
137	2^391324+90901	117801	Yves Minet	02/2011
138	31^78759-30	117459	Theodore Burton	02/2007
139	2^388180+93	116854	Donovan Johnson	07/2008
140	(30^78857-1)/29	116480	Robert Price	12/2011
141	2^384834+93	115847	Donovan Johnson	07/2008
142	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
143	2^384312+81091	115690	Yves Minet	02/2010
144	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
145	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
146	2^381806-4481	114936	Yves Minet	07/2011
147	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
148	10^114575+3^114576	114576	Mike Oakes	09/2010
149	2*10^113941+9	113942	Dmitry Domanov	11/2010
150	2^377799+52223	113729	Yves Minet	08/2010
151	2^377222+93679	113556	Yves Minet	02/2011
152	2^375537+4847	113048	Yves Minet	02/2011
153	2^375350-3221	112992	Yves Minet	07/2011
154	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
155	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
156	EPrime(112280)	112280	Eric W. Weisstein	10/2010
157	(7*10^111706-61)/9	111706	Erik Branger	01/2011
158	2^370643-37	111575	Yves Minet	01/2012
159	L(532277)	111240	Renaud Lifchitz	03/2004
160	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
161	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
162	(2^365689+2^182845+1)/5	110083	Jean Penné	11/2006
163	2^364982-5	109871	Henri Lifchitz	04/2006
164	4^182415-85061	109825	Mike Oakes	06/2011
165	2^364687-187	109782	Lelio R Paula	01/2012
166	2^364644+67	109769	Lelio R Paula	01/2012
167	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
168	2^364094-113	109604	Lelio R Paula	01/2012
169	2^364041-6883	109588	Lelio R Paula	09/2011
170	2^363556+55	109442	Lelio R Paula	01/2012
171	2^363120+3	109311	Donovan Johnson	04/2006
172	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
173	2^361567+51	108843	Lelio R Paula	01/2012
174	2^361497+767	108822	Lelio R Paula	01/2012
175	2^360918-35	108648	Lelio R Paula	01/2012
176	2^360497+53807	108521	Yves Minet	07/2010
177	2^360366+1459	108481	Lelio R Paula	09/2011
178	2^360042+723	108384	Lelio R Paula	01/2012
179	2^359730+753	108290	Lelio R Paula	12/2011
180	2^359454-177	108207	Lelio R Paula	12/2011
181	2^359352-179	108176	Lelio R Paula	12/2011
182	2^359137-81	108112	Lelio R Paula	12/2011
183	2^358538+55	107931	Lelio R Paula	12/2011
184	2^358194+175	107828	Lelio R Paula	12/2011
185	2^358030-171	107778	Lelio R Paula	12/2011
186	2^357885+12857	107735	Yves Minet	07/2010
187	(30^72871-1)/29	107638	Robert Price	12/2011
188	2^357081+107	107493	Lelio R Paula	12/2011
189	2^356654+85	107364	Lelio R Paula	11/2011
190	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
191	2^355915-117	107142	Lelio R Paula	11/2011
192	4^177830-8243	107065	Mike Oakes	02/2011
193	2^354946-3	106850	M. Frind & P. Underwood	08/2002
194	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
195	2^354585+95	106741	Lelio R Paula	10/2011
196	2^354553+189	106732	Lelio R Paula	10/2011
197	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
198	2^354220-57	106631	Lelio R Paula	10/2011
199	2^353992-57	106563	Lelio R Paula	10/2011
200	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
201	2^353387+65	106381	Lelio R Paula	10/2011
202	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
203	2^352883-187	106229	Lelio R Paula	10/2011
204	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
205	2^352814-131	106208	Lelio R Paula	10/2011
206	2^352030+715	105972	Lelio R Paula	10/2011
207	2^351831+23	105912	Lelio R Paula	10/2011
208	2^351213-73	105726	Lelio R Paula	10/2011
209	2^351192-4589	105720	Yves Minet	07/2011
210	2^351060-4559	105680	Yves Minet	07/2011
211	2^350851+135	105617	Lelio R Paula	10/2011
212	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
213	2^348437+35	104890	Lelio R Paula	09/2011
214	2^348348+135	104864	Lelio R Paula	09/2011
215	2^348095-171	104788	Lelio R Paula	09/2011
216	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
217	2^347314+99	104552	Lelio R Paula	09/2011
218	2^346649+65	104352	Lelio R Paula	09/2011
219	2^345704-149	104068	Lelio R Paula	09/2011
220	2^345547+11	104021	Lelio R Paula	09/2011
221	2^345504+723	104008	Lelio R Paula	09/2011
222	2^345476+777	103999	Lelio R Paula	09/2011
223	2^345079+99	103880	Lelio R Paula	09/2011
224	2^344794-3821	103794	Yves Minet	05/2011
225	2^344735-147	103776	Lelio R Paula	09/2011
226	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
227	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
228	2^343971-5077	103546	Lelio R Paula	09/2011
229	2^343899+141	103524	Lelio R Paula	08/2011
230	2^343604+9931	103436	Yves Minet	01/2011
231	2^343182-171	103309	Lelio R Paula	08/2011
232	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
233	43^63177-42	103198	Theodore Burton	02/2007
234	2^342612+175	103137	Lelio R Paula	08/2011
235	2^342476+51	103096	Lelio R Paula	08/2011
236	2^341466+4429	102792	Lelio R Paula	09/2011
237	2^341460-107	102790	Lelio R Paula	08/2011
238	2^341355+21	102759	Lelio R Paula	08/2011
239	2^341134+2533	102692	Henri Lifchitz	09/2005
240	2^341053+129	102668	Lelio R Paula	08/2011
241	2^341004-173	102653	Lelio R Paula	08/2011
242	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
243	2^340688-29	102558	Henri Lifchitz	05/2005
244	2^339889+29327	102317	Yves Minet	06/2010
245	5*3^214250+2	102224	Serge Batalov	10/2010
246	2^339407-177	102172	Lelio R Paula	08/2011
247	2^339355+65	102157	Lelio R Paula	07/2011
248	2^339168+21	102100	Lelio R Paula	07/2011
249	2^339156+163	102097	Lelio R Paula	08/2011
250	2^338796+93	101988	Donovan Johnson	06/2008

Find by discoverer :

PRP Records

Probable Primes Top 10000

(71217 PRPs in the top)