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	10^999999+593499	1000000	Peter Kaiser	02/2013
6	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
7	(18^481147+1)/19	603970	Paul Bourdelais	07/2011
8	(2^1882787-2^941394+1)/5	566775	Borys Jaworski	11/2012
9	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
10	3^1059503-2^1059503	505512	Mike Oakes	04/2012
11	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
12	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
13	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
14	(10^424861-7)/3	424861	Leonid Durman	01/2012
15	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
16	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
17	F(1968721)	411439	Henri Lifchitz	11/2009
18	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
19	(10^380976-7)/3	380976	Leonid Durman	01/2012
20	F(1803059)	376817	Henri Lifchitz	06/2009
21	2^1191375+8543	358640	Phil Moore	06/2008
22	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
23	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
24	F(1636007)	341905	Henri Lifchitz	03/2009
25	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
26	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
27	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
28	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
29	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
30	10^300476+3	300477	Ed Trice	10/2012
31	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
32	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
33	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
34	2^983620+60451	296100	Phil Moore	03/2008
35	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
36	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
37	3^591827-2^591827	282374	Mike Oakes	08/2009
38	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
39	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
40	(7*10^271757-61)/9	271757	Erik Branger	03/2012
41	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
42	F(1285607)	268676	Henri Lifchitz	11/2008
43	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
44	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
45	(7*10^260198-61)/9	260198	Erik Branger	11/2011
46	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
47	11^246668-90	256879	Enzo Doria	12/2012
48	11^246167-90	256357	Enzo Doria	12/2012
49	11^243796-90	253888	Enzo Doria	12/2012
50	11^242579-60	252620	Enzo Doria	10/2012
51	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
52	11^227092-90	236492	Enzo Doria	11/2012
53	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
54	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
55	10^232599-3	232599	Markus Tervooren	10/2010
56	3^485977-2^485977	231870	Mike Oakes	09/2009
57	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
58	(18^180181-1)/17	226176	Andy Steward	04/2007
59	2^750740-3	225996	Paul Bourdelais	03/2012
60	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
61	11^213654-180	222498	Enzo Doria	01/2013
62	10^221631-9	221631	Alexander Gramolin	02/2011
63	L(1051849)	219824	Renaud Lifchitz	03/2009
64	11^210961-240	219694	Enzo Doria	01/2013
65	F(1049897)	219416	Henri Lifchitz	10/2008
66	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
67	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
68	227^89797+2	211565	Lelio R Paula	08/2012
69	2^702194-3	211382	Paul Bourdelais	03/2012
70	11^202357-1140	210734	Enzo Doria	12/2012
71	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
72	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
73	2^685578+3	206380	Paul Bourdelais	04/2012
74	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
75	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
76	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
77	2^678561+678561	204268	Henri Lifchitz	05/2006
78	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
79	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
80	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
81	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
82	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
83	11^187185-90	194934	Enzo Doria	09/2012
84	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
85	F(931517)	194676	Henri Lifchitz	09/2008
86	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
87	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
88	L(901657)	188436	Renaud Lifchitz	11/2008
89	11^179143-4170	186559	Enzo Doria	12/2012
90	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
91	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
92	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
93	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
94	11^176176-240	183469	Enzo Doria	11/2012
95	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
96	11^174145-360	181354	Enzo Doria	10/2012
97	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
98	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
99	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
100	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
101	10^175608+2971	175609	Mike Oakes	05/2010
102	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
103	11^164009-270	170798	Enzo Doria	10/2012
104	2^566496+7	170533	Donovan Johnson	07/2006
105	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
106	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
107	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
108	11^159756-2424	166369	Mike Oakes	06/2010
109	2^551542+19249	166031	Payam Samidoost	08/2002
110	11^158160-60	164707	Enzo Doria	07/2012
111	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
112	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
113	2^538104+1531	161986	Lelio R Paula	01/2013
114	3^336353-2^336353	160482	Mike Oakes	10/2007
115	11^152420-210	158730	Enzo Doria	09/2012
116	2^525690-9221	158249	Lelio R Paula	01/2013
117	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
118	53^90679-52^90679	156356	Robert Price	01/2013
119	2^517698+4429	155843	Lelio R Paula	01/2013
120	EPrime(155025)	155025	Eric W. Weisstein	10/2010
121	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
122	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
123	2^505431-505431	152150	Henri Lifchitz	04/2005
124	2^504054-2231	151736	Yves Minet	10/2011
125	2^502576-4019	151291	Yves Minet	10/2011
126	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
127	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
128	2^500899-500899	150786	Henri Lifchitz	04/2005
129	2^499534-221	150375	Yves Minet	06/2012
130	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
131	47^89113-46^89113	149006	Robert Price	10/2012
132	8*10^148860-3	148861	Ray Chandler	04/2011
133	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
134	2^491391-7807	147924	Lelio R Paula	01/2013
135	2^483302-3221	145489	Lelio R Paula	12/2012
136	53^84239-52^84239	145252	Robert Price	01/2013
137	2^481801-481801	145037	Henri Lifchitz	03/2005
138	29^99167+2	145022	Ray Chandler	08/2011
139	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
140	L(692147)	144651	Henri Lifchitz	10/2008
141	2^479844+3	144448	Donovan Johnson	06/2006
142	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
143	2^474053+2897	142705	Lelio R Paula	08/2012
144	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
145	2^470173-16465	141537	Enzo Doria	04/2013
146	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
147	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
148	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
149	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
150	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
151	2^459768+1531	138404	Lelio R Paula	06/2012
152	555555*2^458524+1513	138036	Darren Bedwell	08/2009
153	2^458465+2^32+1	138012	T. D. Noe	06/2007
154	2^457822+105	137819	Donovan Johnson	06/2006
155	11^132315-360	137792	Enzo Doria	09/2012
156	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
157	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
158	(37^87421-1)/36	137093	Robert Price	03/2012
159	2^454675-1777	136871	Yves Minet	10/2011
160	L(651821)	136223	Henri Lifchitz	09/2008
161	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
162	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
163	2^446494-16485	134409	Enzo Doria	04/2013
164	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
165	62^74521-61^74521	133571	Robert Price	05/2013
166	L(637751)	133283	Henri Lifchitz	09/2008
167	2^441063+383	132774	Lelio R Paula	06/2012
168	47^79201-46^79201	132432	Robert Price	10/2012
169	L(631181)	131910	Henri Lifchitz	09/2008
170	35^85243-34^85243	131621	Robert Price	05/2012
171	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
172	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
173	L(616787)	128901	Henri Lifchitz	09/2008
174	11^123594-240	128710	Enzo Doria	09/2012
175	11^122629-720	127705	Enzo Doria	11/2012
176	11^121910-840	126957	Enzo Doria	12/2012
177	331^50339-10004	126846	Enzo Doria	07/2012
178	F(604711)	126377	Henri Lifchitz	02/2005
179	2^419637+29	126324	Henri Lifchitz	02/2006
180	2^418829+167	126081	Lelio R Paula	01/2012
181	(23^91943-1)/22	125201	Robert Price	01/2012
182	43125^27010-106	125185	Enzo Doria	08/2012
183	2^415144-3683	124971	Yves Minet	10/2011
184	2^414032-5	124637	Henri Lifchitz	07/2006
185	2^412868-120599	124286	Paul Bourdelais	02/2012
186	F(593689)	124074	Henri Lifchitz	01/2005
187	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
188	F(590041)	123311	Henri Lifchitz	01/2005
189	11^117642-300	122512	Enzo Doria	10/2012
190	(30^82883-1)/29	122427	Robert Price	12/2011
191	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
192	3^256199-2^256199	122238	Mike Oakes	06/2005
193	2^404501-631	121767	Yves Minet	07/2012
194	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
195	11^116555-720	121380	Enzo Doria	11/2012
196	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
197	2^400424-216413	120540	Enzo Doria	04/2013
198	2^399918-95	120388	Lelio R Paula	04/2013
199	2^398877+105	120074	Donovan Johnson	01/2006
200	2^398710+57	120024	Lelio R Paula	04/2013
201	L(574219)	120005	Renaud Lifchitz	03/2004
202	2^398571+60413	119982	Yves Minet	03/2011
203	8*10^119930-3	119931	Ray Chandler	04/2011
204	11^114738-150	119488	Enzo Doria	10/2012
205	2^396790-21	119446	Lelio R Paula	04/2013
206	2^394034-3	118617	M. Frind & P. Underwood	09/2002
207	2^393180+73	118359	Lelio R Paula	04/2013
208	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
209	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
210	2^391933+5897	117984	Yves Minet	02/2011
211	2^391324+90901	117801	Yves Minet	02/2011
212	2^390779-30337	117637	Paul Bourdelais	02/2012
213	11^112916-780	117590	Enzo Doria	12/2012
214	31^78759-30	117459	Theodore Burton	02/2007
215	2^389998+37	117402	Lelio R Paula	03/2013
216	2^389478+43	117245	Lelio R Paula	03/2013
217	2^388888-1529	117067	Yves Minet	01/2013
218	2^388469-43	116941	Lelio R Paula	03/2013
219	2^388180+93	116854	Donovan Johnson	07/2008
220	(30^78857-1)/29	116480	Robert Price	12/2011
221	2^385969-823	116189	Yves Minet	05/2012
222	2^385564+781	116067	Lelio R Paula	01/2012
223	2^384953-111943	115883	Paul Bourdelais	02/2012
224	2^384834+93	115847	Donovan Johnson	07/2008
225	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
226	2^384312+81091	115690	Yves Minet	02/2010
227	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
228	2^383560-455	115464	Yves Minet	03/2012
229	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
230	2^382198+9	115054	Lelio R Paula	03/2013
231	2^381806-4481	114936	Yves Minet	07/2011
232	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
233	2^380700+91	114603	Lelio R Paula	03/2013
234	10^114575+3^114576	114576	Mike Oakes	09/2010
235	2*10^113941+9	113942	Dmitry Domanov	11/2010
236	2^378272-16565	113872	Enzo Doria	04/2013
237	2^378198+67	113849	Lelio R Paula	03/2013
238	6^146274-18893	113824	Enzo Doria	03/2013
239	2^378078+75	113813	Lelio R Paula	03/2013
240	2^377940+63	113772	Lelio R Paula	03/2013
241	2^377799+52223	113729	Yves Minet	08/2010
242	11^109190-270	113710	Enzo Doria	12/2012
243	2^377222+93679	113556	Yves Minet	02/2011
244	35^73477-34^73477	113454	Robert Price	05/2012
245	2^376790+27	113426	Lelio R Paula	03/2013
246	2^376731+21	113408	Lelio R Paula	03/2013
247	2^375537+4847	113048	Yves Minet	02/2011
248	2^375350-3221	112992	Yves Minet	07/2011
249	(29^77237-1)/28	112950	Robert Price	04/2012
250	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000

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PRP Records

Probable Primes Top 10000

(97912 PRPs in the top)