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) !!!

Submit your PRPs

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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	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
2	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
3	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
4	2^983620+60451	296100	Phil Moore	03/2008
5	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
6	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
7	Phi(180181,18)	226176	Andy Steward	04/2007
8	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
9	2^678561+678561	204268	Henri Lifchitz	05/2006
10	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
11	2^566496+7	170533	Donovan Johnson	07/2006
12	2^551542+19249	166031	Payam Samidoost	08/2002
13	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
14	3^336353-2^336353	160482	Mike Oakes	10/2007
15	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
16	2^505431-505431	152150	Henri Lifchitz	04/2005
17	2^500899-500899	150786	Henri Lifchitz	04/2005
18	2^481801-481801	145037	Henri Lifchitz	03/2005
19	2^479844+3	144448	Donovan Johnson	06/2006
20	2^458465+2^32+1	138012	T. D. Noe	06/2007
21	2^457822+105	137819	Donovan Johnson	06/2006
22	F(604711)	126377	Henri Lifchitz	02/2005
23	2^419637+29	126324	Henri Lifchitz	02/2006
24	2^414032-5	124637	Henri Lifchitz	07/2006
25	F(593689)	124074	Henri Lifchitz	01/2005
26	F(590041)	123311	Henri Lifchitz	01/2005
27	3^256199-2^256199	122238	Mike Oakes	06/2005
28	2^398877+105	120074	Donovan Johnson	01/2006
29	L(574219)	120005	Renaud Lifchitz	03/2004
30	2^394034-3	118617	M. Frind & P. Underwood	09/2002
31	31^78759-30	117459	Theodore Burton	02/2007
32	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
33	L(532277)	111240	Renaud Lifchitz	03/2004
34	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
35	(2^365689+2^182845+1)/5	110083	Jean Penné	11/2006
36	2^364982-5	109871	Henri Lifchitz	04/2006
37	2^363120+3	109311	Donovan Johnson	04/2006
38	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
39	2^354946-3	106850	M. Frind & P. Underwood	08/2002
40	43^63177-42	103198	Theodore Burton	02/2007
41	2^341134+2533	102692	Henri Lifchitz	09/2005
42	2^340688-29	102558	Henri Lifchitz	05/2005
43	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
44	(2^333227-2^166614+1)/5	100311	Jean Penné	11/2006
45	17^81417-16	100180	Theodore Burton	11/2005
46	25206!+p(4114)	100001	Henri Lifchitz	09/2005
47	25206!-p(5447)	100001	Henri Lifchitz	10/2005
48	25206!-p(12402)	100001	Henri Lifchitz	04/2006
49	25206!-p(16290)	100001	Henri Lifchitz	09/2006
50	25206!-p(19647)	100001	Henri Lifchitz	02/2007
51	2^332194+11473	100001	Henri Lifchitz	03/2007
52	10^100000+342909	100001	Milton L. Brown	12/2007
53	10^99999+309403	100000	Daniel Heuer	01/2004
54	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
55	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
56	2^316140-5	95168	Henri Lifchitz	02/2006
57	2^311471+311469	93763	Renaud Lifchitz	01/2003
58	(2^311027-2^155514+1)/5	93628	Jean Penné	11/2006
59	3^195430-2	93244	Theodore Burton	02/2007
60	41^57783-40	93192	Theodore Burton	02/2007
61	2^308809+37967	92961	Phil Moore	03/2008
62	L(443609)	92709	Renaud Lifchitz	11/2003
63	2^307407-307407^2	92539	Henri Lifchitz	05/2005
64	2^307125-49789	92454	Henri Lifchitz	08/2005
65	(2^305867-2^152934+1)/5	92075	Jean Penné	11/2006
66	2^304015+64133	91518	David Broadhurst	06/2002
67	2^303224+2533	91280	Henri Lifchitz	05/2005
68	2^302949+81	91197	Henri Lifchitz	02/2007
69	2^302505+81	91064	Henri Lifchitz	02/2007
70	2^301683-301683^2	90816	Henri Lifchitz	05/2005
71	F(433781)	90655	Henri Lifchitz	09/2003
72	10^89999+82939	90000	Dirk Augustin	04/2007
73	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
74	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
75	2^296016+81	89110	Henri Lifchitz	02/2007
76	31^59713-30	89054	Theodore Burton	02/2007
77	19^69025-18	88266	Theodore Burton	01/2006
78	2^292929+43877	88181	Donovan Johnson	04/2005
79	91382^9+9^91382	87201	Andrey Kulsha	11/2004
80	(10^86453-1)/9	86453	Lew Baxter	10/2000
81	2^284133-3	85533	M. Frind & P. Underwood	07/2002
82	19834^19834+8947	85235	Henri Lifchitz	11/2004
83	2^280852+97681	84545	Yves Minet	08/2004
84	F(397379)	83047	Henri Lifchitz	08/2003
85	2^275259+81	82862	Henri Lifchitz	01/2007
86	3^173191-2^173191	82634	Mike Oakes	02/2004
87	11^79133-10	82409	Theodore Burton	11/2005
88	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
89	L(387433)	80969	Renaud Lifchitz	11/2003
90	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
91	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
92	47^47667-46	79704	Theodore Burton	02/2007
93	19^61980-18	79258	Theodore Burton	12/2005
94	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
95	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
96	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
97	14*10^78362+1089	78364	Jens K. Andersen	11/2007
98	7^92511-6	78181	Theodore Burton	11/2005
99	Pi-Prime(78073)	78073	Eric W. Weisstein	07/2006
100	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
101	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
102	7^90291-6	76305	Theodore Burton	11/2005
103	14*10^75798+1089	75800	Jens K. Andersen	11/2007
104	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
105	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
106	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
107	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
108	2^247165-3	74405	M. Frind & P. Underwood	07/2002
109	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
110	2^246618+427	74240	Henri Lifchitz	02/2005
111	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
112	9998*2^245696+3	73966	Donovan Johnson	10/2004
113	7^86689-6^86689	73261	Predrag Minovic	09/2004
114	6^93812+5	73000	Wojciech Florek	03/2006
115	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
116	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
117	2^241004-3	72550	M. Frind & P. Underwood	07/2002
118	L(344293)	71953	Renaud Lifchitz	09/2003
119	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
120	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
121	2^235326+3	70841	Donovan Johnson	02/2006
122	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
123	(2^235099-2^117550+1)/5	70772	Jean Penné	11/2006
124	19471^16428-2	70467	Faysal YAtim	09/2005
125	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
126	10^70000+80487	70001	Milton L. Brown	05/2006
127	10^69999+134857	70000	Patrick De Geest	02/2007
128	2^228944+81	68920	Henri Lifchitz	01/2007
129	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
130	2^228271-228271	68717	Henri Lifchitz	11/2004
131	2^225536-29	67894	Henri Lifchitz	05/2005
132	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
133	2^224815-49789	67677	Henri Lifchitz	04/2005
134	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
135	2^222943+29	67113	Henri Lifchitz	08/2005
136	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
137	(2^221891-2^110946+1)/5	66796	Jean Penné	11/2006
138	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
139	2^219304+454245	66018	Henri Lifchitz	03/2007
140	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
141	2^218200+427	65685	Henri Lifchitz	01/2005
142	2^217190+94395	65381	Henri Lifchitz	02/2005
143	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
144	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
145	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
146	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
147	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
148	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
149	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
150	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
151	5^91493-4^91493	63951	Predrag Minovic	04/2004
152	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
153	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
154	2^210061+21	63235	Donovan Johnson	06/2006
155	V(301486)	63007	Henri Lifchitz	05/2003
156	2^208779+81	62849	Henri Lifchitz	01/2007
157	2^208292+81	62703	Henri Lifchitz	10/2005
158	2^207865+29	62574	Henri Lifchitz	08/2005
159	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
160	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
161	2^206574+613	62185	Jason Earls	04/2008
162	2^206506+427	62165	Henri Lifchitz	01/2005
163	2^205962+3	62001	Donovan Johnson	02/2006
164	2^205933-205933^2	61993	Henri Lifchitz	05/2005
165	14*10^61937+1089	61939	Jens K. Andersen	11/2007
166	((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768	61684	Phil Carmody	09/2004
167	2^204129+204129	61449	Henri Lifchitz	04/2002
168	2^203689-31	61317	Thomas Masser	10/2005
169	5^87606+4	61234	Wojciech Florek	11/2005
170	22355*2^203009-3	61117	Donovan Johnson	03/2004
171	10^60959-60959	60959	Henri Lifchitz	08/2002
172	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
173	2^201609-49789	60691	Henri Lifchitz	03/2005
174	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
175	2^199672+2533	60108	Henri Lifchitz	09/2004
176	10^60000+204331	60001	Milton L. Brown	04/2006
177	10^60000+87129	60001	Milton L. Brown	04/2006
178	10^59999+65197	60000	Patrick De Geest	04/2005
179	2^197872+81	59566	Henri Lifchitz	10/2005
180	15^50385-14	59258	Wojciech Florek	06/2006
181	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
182	1111*2^196610-555	59189	Henri Lifchitz	04/2005
183	7^69371-6^69371	58626	Predrag Minovic	08/2004
184	2^193965+5	58390	Henri Lifchitz	12/2002
185	3^122219-2^122219	58314	Mike Oakes	09/2003
186	L(277273)/11090921	57940	Donovan Johnson	11/2005
187	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
188	2^192023-192023^2	57805	Henri Lifchitz	05/2005
189	2^190945+29	57481	Henri Lifchitz	06/2005
190	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
191	2^189181+94395	56950	Henri Lifchitz	01/2005
192	2^189110-3	56928	M. Frind & P. Underwood	11/2002
193	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
194	2^187382+613	56408	Jason Earls	04/2008
195	2^187230+427	56362	Henri Lifchitz	01/2005
196	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
197	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
198	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
199	(2^184232+1)/257	55457	Donovan Johnson	03/2005
200	58046^9+9^58046	55390	Andrey Kulsha	02/2004
201	2^183632-5	55279	Henri Lifchitz	08/2005
202	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
203	2^182451-182451	54924	Henri Lifchitz	10/2004
204	2^182444+81	54922	Henri Lifchitz	10/2005
205	2^181913+29	54762	Henri Lifchitz	06/2005
206	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
207	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
208	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
209	2^180014+613	54190	Jason Earls	04/2008
210	2^180001+41877	54186	Jim Fougeron	08/2002
211	2^180000+130153	54186	Jim Fougeron	09/2002
212	2^179790+33	54123	Donovan Johnson	02/2006
213	2^179120+2533	53921	Henri Lifchitz	09/2004
214	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
215	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
216	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
217	(10^53718-7)/3	53718	Makoto Kamada	10/2004
218	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
219	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
220	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
221	2^176177+60947	53035	David Broadhurst	05/2002
222	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
223	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
224	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
225	(2^173867-1)/52536637502689	52326	Donovan Johnson	06/2005
226	41^32295-40	52085	Theodore Burton	02/2007
227	7*2^172403-3	51900	Henri Lifchitz	06/2003
228	(80051^10567+1)/80052	51809	Faysal YAtim	07/2007
229	2^171663+1155*171663	51676	Henri Lifchitz	01/2005
230	U(250849)	51425	Michael Porter	08/2007
231	9^53857-8^53857	51393	Jean-Louis Charton	11/2004
232	2^170296+2533	51265	Henri Lifchitz	07/2004
233	18225^622+622^18225	50917	Anatoly F. Selevich	11/2006
234	19312^429+429^19312	50839	Anatoly F. Selevich	12/2006
235	2^168811+15015*168811	50818	Henri Lifchitz	02/2005
236	10^50711+7	50712	Jason Earls	12/2007
237	117216#-p(117216)	50700	Henri Lifchitz	03/2007
238	(310027^9161+1)/310028	50302	Faysal YAtim	04/2008
239	13537!-2^13537+1	50052	Joe McLean	06/2006
240	2^166100+199015	50002	Lelio R Paula	05/2008
241	10^50000+65859	50001	Milton L. Brown	02/2006
242	10^49999+91701	50000	Patrick De Geest	03/2005
243	1111*2^166022-555	49981	Henri Lifchitz	02/2005
244	13517!-13517#+1	49970	Décio Gazzoni Filho	03/2005
245	(3^104243+1)/4	49736	Kamil Duszenko	05/2004
246	12166^12166+565	49700	Henri Lifchitz	11/2004
247	2^165025+165029	49678	Henri Lifchitz	04/2005
248	(110051^9851+1)/110052	49660	Faysal YAtim	09/2007
249	114667#-p(114667)	49591	Henri Lifchitz	03/2007
250	Pell-LucasQ(129127)/2	49427	Eric W. Weisstein	05/2006

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PRP Records

Probable Primes Top 10000

(22049 PRPs in the top)