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

See the Top discoverers
See the Latest PRPs
Search by form


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	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
2	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
3	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
4	F(1803059)	376817	Henri Lifchitz	06/2009
5	2^1191375+8543	358640	Phil Moore	06/2008
6	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
7	F(1636007)	341905	Henri Lifchitz	03/2009
8	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
9	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
10	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
11	2^983620+60451	296100	Phil Moore	03/2008
12	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
13	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
14	F(1285607)	268676	Henri Lifchitz	11/2008
15	Phi(180181,18)	226176	Andy Steward	04/2007
16	L(1051849)	219824	Renaud Lifchitz	03/2009
17	F(1049897)	219416	Henri Lifchitz	10/2008
18	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
19	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
20	2^678561+678561	204268	Henri Lifchitz	05/2006
21	F(931517)	194676	Henri Lifchitz	09/2008
22	L(901657)	188436	Renaud Lifchitz	11/2008
23	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
24	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
25	2^566496+7	170533	Donovan Johnson	07/2006
26	2^551542+19249	166031	Payam Samidoost	08/2002
27	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
28	3^336353-2^336353	160482	Mike Oakes	10/2007
29	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
30	2^505431-505431	152150	Henri Lifchitz	04/2005
31	2^500899-500899	150786	Henri Lifchitz	04/2005
32	2^481801-481801	145037	Henri Lifchitz	03/2005
33	L(692147)	144651	Henri Lifchitz	10/2008
34	2^479844+3	144448	Donovan Johnson	06/2006
35	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
36	2^458465+2^32+1	138012	T. D. Noe	06/2007
37	2^457822+105	137819	Donovan Johnson	06/2006
38	L(651821)	136223	Henri Lifchitz	09/2008
39	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
40	L(637751)	133283	Henri Lifchitz	09/2008
41	L(631181)	131910	Henri Lifchitz	09/2008
42	L(616787)	128901	Henri Lifchitz	09/2008
43	F(604711)	126377	Henri Lifchitz	02/2005
44	2^419637+29	126324	Henri Lifchitz	02/2006
45	2^414032-5	124637	Henri Lifchitz	07/2006
46	F(593689)	124074	Henri Lifchitz	01/2005
47	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
48	F(590041)	123311	Henri Lifchitz	01/2005
49	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
50	3^256199-2^256199	122238	Mike Oakes	06/2005
51	2^398877+105	120074	Donovan Johnson	01/2006
52	L(574219)	120005	Renaud Lifchitz	03/2004
53	2^394034-3	118617	M. Frind & P. Underwood	09/2002
54	31^78759-30	117459	Theodore Burton	02/2007
55	2^388180+93	116854	Donovan Johnson	07/2008
56	2^384834+93	115847	Donovan Johnson	07/2008
57	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
58	L(532277)	111240	Renaud Lifchitz	03/2004
59	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
60	(2^365689+2^182845+1)/5	110083	Jean Penné	11/2006
61	2^364982-5	109871	Henri Lifchitz	04/2006
62	2^363120+3	109311	Donovan Johnson	04/2006
63	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
64	2^354946-3	106850	M. Frind & P. Underwood	08/2002
65	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
66	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
67	43^63177-42	103198	Theodore Burton	02/2007
68	2^341134+2533	102692	Henri Lifchitz	09/2005
69	2^340688-29	102558	Henri Lifchitz	05/2005
70	2^338796+93	101988	Donovan Johnson	06/2008
71	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
72	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
73	(2^333227-2^166614+1)/5	100311	Jean Penné	11/2006
74	17^81417-16	100180	Theodore Burton	11/2005
75	25206!+p(4114)	100001	Henri Lifchitz	09/2005
76	25206!-p(5447)	100001	Henri Lifchitz	10/2005
77	25206!-p(12402)	100001	Henri Lifchitz	04/2006
78	25206!-p(16290)	100001	Henri Lifchitz	09/2006
79	25206!-p(19647)	100001	Henri Lifchitz	02/2007
80	2^332194+11473	100001	Henri Lifchitz	03/2007
81	10^100000+342909	100001	Milton L. Brown	12/2007
82	10^99999+309403	100000	Daniel Heuer	01/2004
83	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
84	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
85	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
86	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
87	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
88	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
89	2^317024+93	95434	Donovan Johnson	06/2008
90	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
91	2^316140-5	95168	Henri Lifchitz	02/2006
92	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
93	2^311471+311469	93763	Renaud Lifchitz	01/2003
94	(2^311027-2^155514+1)/5	93628	Jean Penné	11/2006
95	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
96	3^195430-2	93244	Theodore Burton	02/2007
97	41^57783-40	93192	Theodore Burton	02/2007
98	2^308809+37967	92961	Phil Moore	03/2008
99	L(443609)	92709	Renaud Lifchitz	11/2003
100	2^307407-307407^2	92539	Henri Lifchitz	05/2005
101	2^307125-49789	92454	Henri Lifchitz	08/2005
102	(2^305867-2^152934+1)/5	92075	Jean Penné	11/2006
103	2^305676+93	92018	Donovan Johnson	06/2008
104	2^304015+64133	91518	David Broadhurst	06/2002
105	2^303224+2533	91280	Henri Lifchitz	05/2005
106	2^302949+81	91197	Henri Lifchitz	02/2007
107	2^302505+81	91064	Henri Lifchitz	02/2007
108	2^301683-301683^2	90816	Henri Lifchitz	05/2005
109	F(433781)	90655	Henri Lifchitz	09/2003
110	10^89999+82939	90000	Dirk Augustin	04/2007
111	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
112	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
113	2^296016+81	89110	Henri Lifchitz	02/2007
114	31^59713-30	89054	Theodore Burton	02/2007
115	19^69025-18	88266	Theodore Burton	01/2006
116	2^292929+43877	88181	Donovan Johnson	04/2005
117	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
118	91382^9+9^91382	87201	Andrey Kulsha	11/2004
119	(10^86453-1)/9	86453	Lew Baxter	10/2000
120	2^284133-3	85533	M. Frind & P. Underwood	07/2002
121	19834^19834+8947	85235	Henri Lifchitz	11/2004
122	((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
123	2^280852+97681	84545	Yves Minet	08/2004
124	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
125	F(397379)	83047	Henri Lifchitz	08/2003
126	2^275259+81	82862	Henri Lifchitz	01/2007
127	3^173191-2^173191	82634	Mike Oakes	02/2004
128	11^79133-10	82409	Theodore Burton	11/2005
129	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
130	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
131	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
132	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
133	L(387433)	80969	Renaud Lifchitz	11/2003
134	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
135	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
136	47^47667-46	79704	Theodore Burton	02/2007
137	19^61980-18	79258	Theodore Burton	12/2005
138	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
139	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
140	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
141	2^261856+98765331	78827	Jason Earls	01/2009
142	2^261507-2287	78722	Yves Minet	04/2009
143	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
144	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
145	14*10^78362+1089	78364	Jens K. Andersen	11/2007
146	7^92511-6	78181	Theodore Burton	11/2005
147	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
148	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
149	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
150	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
151	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
152	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
153	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
154	7^90291-6	76305	Theodore Burton	11/2005
155	14*10^75798+1089	75800	Jens K. Andersen	11/2007
156	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
157	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
158	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
159	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
160	2^247165-3	74405	M. Frind & P. Underwood	07/2002
161	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
162	2^246618+427	74240	Henri Lifchitz	02/2005
163	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
164	9998*2^245696+3	73966	Donovan Johnson	10/2004
165	7^86689-6^86689	73261	Predrag Minovic	09/2004
166	6^93812+5	73000	Wojciech Florek	03/2006
167	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
168	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
169	2^241004-3	72550	M. Frind & P. Underwood	07/2002
170	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
171	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
172	L(344293)	71953	Renaud Lifchitz	09/2003
173	2^238568+98765331	71817	Jason Earls	01/2009
174	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
175	2^238144+98765331	71689	Jason Earls	01/2009
176	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
177	((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
178	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
179	2^235326+3	70841	Donovan Johnson	02/2006
180	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
181	(2^235099-2^117550+1)/5	70772	Jean Penné	11/2006
182	2^234133-3163	70482	Yves Minet	04/2009
183	19471^16428-2	70467	Faysal YAtim	09/2005
184	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
185	10^70000+80487	70001	Milton L. Brown	05/2006
186	10^69999+134857	70000	Patrick De Geest	02/2007
187	2^228944+81	68920	Henri Lifchitz	01/2007
188	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
189	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
190	2^228271-228271	68717	Henri Lifchitz	11/2004
191	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
192	2^225536-29	67894	Henri Lifchitz	05/2005
193	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
194	2^224815-49789	67677	Henri Lifchitz	04/2005
195	((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
196	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
197	2^222943+29	67113	Henri Lifchitz	08/2005
198	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
199	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
200	(2^221891-2^110946+1)/5	66796	Jean Penné	11/2006
201	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
202	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
203	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
204	2^219304+454245	66018	Henri Lifchitz	03/2007
205	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
206	2^218200+427	65685	Henri Lifchitz	01/2005
207	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
208	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
209	2^217190+94395	65381	Henri Lifchitz	02/2005
210	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
211	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
212	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
213	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
214	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
215	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
216	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
217	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
218	5^91493-4^91493	63951	Predrag Minovic	04/2004
219	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
220	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
221	2^210464+98765331	63356	Jason Earls	12/2008
222	2^210061+21	63235	Donovan Johnson	06/2006
223	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
224	V(301486)	63007	Henri Lifchitz	05/2003
225	2^208779+81	62849	Henri Lifchitz	01/2007
226	2^208594+93	62794	Donovan Johnson	06/2008
227	2^208292+81	62703	Henri Lifchitz	10/2005
228	2^207865+29	62574	Henri Lifchitz	08/2005
229	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
230	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
231	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
232	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
233	2^206574+613	62185	Jason Earls	04/2008
234	2^206506+427	62165	Henri Lifchitz	01/2005
235	2^205962+3	62001	Donovan Johnson	02/2006
236	2^205933-205933^2	61993	Henri Lifchitz	05/2005
237	14*10^61937+1089	61939	Jens K. Andersen	11/2007
238	((((((((((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
239	2^204129+204129	61449	Henri Lifchitz	04/2002
240	2^203689-31	61317	Thomas Masser	10/2005
241	5^87606+4	61234	Wojciech Florek	11/2005
242	22355*2^203009-3	61117	Donovan Johnson	03/2004
243	10^60959+57	60960	Patrick De Geest	12/2008
245	10^60959-60959	60959	Henri Lifchitz	08/2002
244	10^60959-29177	60959	Patrick De Geest	08/2008
246	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
247	2^201609-49789	60691	Henri Lifchitz	03/2005
248	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
249	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
250	2^199872+93	60168	Donovan Johnson	06/2008

Find by discoverer :

PRP Records

Probable Primes Top 10000

(32572 PRPs in the top)