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 these 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 (> 50000)	Who ?	When ?
1	(10^8177207-1)/9	8177207	Ryan Propper + Sergey Batalov	05/2021
2	(10^5794777-1)/9	5794777	Ryan Propper + Sergey Batalov	04/2021
3	(2^15135397+1)/3	4556209	Ryan Propper	06/2021
4	2^13380298-27	4027872	Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist	03/2021
5	(2^13372531+1)/3	4025533	Ryan Propper	09/2013
6	(2^13347311+1)/3	4017941	Ryan Propper	09/2013
7	(2^12720787-1)/1119429257/175573124547437977/8480999878421106991	3829294	Anonymous	10/2022
8	(2^12503723-2^6251862+1)/5	3763995	Ryan Propper + Sergey Batalov	07/2020
9	(2^10443557-1)/37289325994807	3143811	GIMPS-fre_games	07/2020
10	2^9092392+40291	2737083	Engracio Esmenda / Five or Bust	02/2011
11	(17^1990523-1)/16	2449236	Paul Bourdelais	08/2020
12	(35963^524288+1)/2	2388581	Ryan Propper	08/2022
13	(11^2264611+1)/12	2358349	Paul Bourdelais	07/2021
14	(5^3300593-1)/4	2307015	Anonymous	02/2022
15	(2^7313983-1)/305492080276193	2201714	Oliver Kruse	03/2018
16	(2^7080247-1)/156822217506727/11283326312536321/9632940548330339593	2131318	Gord Palameta	10/2017
17	(11^1868983-1)/10	1946345	Paul Bourdelais	06/2021
18	(3^3598867-1)/2	1717096	Ryan Propper	12/2021
19	(13^1503503-1)/12	1674817	Paul Bourdelais	04/2020
20	(10^1600787+1)/11	1600786	Paul Bourdelais	05/2020
21	(18^1270141-1)/17	1594372	Paul Bourdelais	12/2021
22	(14^1385203+1)/15	1587619	Paul Bourdelais	02/2022
23	(2^5243339-2^2621670+1)/5	1578402	Ryan Propper + Sergey Batalov	06/2020
24	(2^5240707-1)/75392810903	1577600	Tony Prest / Never Odd Or Even	07/2016
25	2^5146295+41693	1549190	Engracio Esmenda / Five or Bust	11/2009
26	(2^4834891-1)/1701881633/70659688575577	1455425	Gord Palameta	01/2017
27	(187503^262144+1)/2	1382288	Ryan Propper	08/2022
28	2^4583176+2131	1379674	Ben Maloney / Five or Bust	09/2009
29	F(6530879)	1364873	Ryan Propper	08/2022
30	(2^4533073+2^2266537+1)/5	1364591	Serge Batalov	03/2014
31	(13^1199467+1)/14	1336138	Paul Bourdelais	12/2015
32	(5^1888279-1)/4	1319850	Paul Bourdelais	04/2018
33	(5^1856147+1)/6	1297391	Paul Bourdelais	02/2019
34	(3^2704981-1)/2	1290604	Ryan Propper	12/2021
35	(20^984349-1)/19	1280667	Paul Bourdelais	09/2021
36	(2^4194304+1026473)/3	1262611	Tony Prest / Never Odd Or Even	07/2017
37	(2^4187251-1)/72234342371519	1260475	Tony Prest / Never Odd Or Even	05/2016
38	(14^1091401+1)/15	1250885	Paul Bourdelais	03/2014
39	(16^1025393+1)/17	1234695	Paul Bourdelais	08/2014
40	(2^4031399+1)/3	1213572	Tony Reix / Diepeveen-Underwood -Reix	02/2010
41	(3^2533963+1)/4	1209008	Paul Bourdelais	03/2020
42	L(5466311)	1142392	Ryan Propper	08/2022
43	2^3690839-1868407	1111054	Enzo Doria	03/2021
44	2^3678448+384541	1107324	Enzo Doria	03/2022
45	2^3668660+1888801	1104377	Enzo Doria	03/2020
46	(106*23^800873-7)/11	1090573	Curtis Bright	05/2015
47	(7^1264699-1)/6	1068794	Paul Bourdelais	01/2014
48	(6^1365019-1)/5	1062191	Paul Bourdelais	12/2019
49	(3^2215303-1)/2	1056968	Paul Bourdelais	02/2019
50	10^1043372+7	1043373	Alfred Reich	12/2021
51	(2^3464473-1)/604874508299177	1042896	Anand Nair	10/2014
52	(6^1313371+1)/7	1022001	Paul Bourdelais	01/2019
53	(2^3352132+9)/5	1009092	Tony Prest / Never Odd Or Even	06/2018
54	(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221	1009003	Tony Prest / Never Odd Or Even	08/2019
55	(2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837	1008886	Tony Prest / Never Odd Or Even	08/2019
56	(2^3351346+113)/3/548533/39539021/94650838127	1008831	Tony Prest / Never Odd Or Even	11/2022
57	(2^3350899+115)/3/3/11/409	1008717	Tony Prest / Never Odd Or Even	04/2020
58	(2^3350068+183)/953/15761231	1008461	Tony Prest / Never Odd Or Even	03/2020
59	(2^3349565+57)/23/263/77893	1008311	Tony Prest / Never Odd Or Even	03/2020
60	(2^3349080+137)/3/79/8060419099	1008162	Tony Prest / Never Odd Or Even	07/2020
61	(2^3349027+183)/23/1277/11638321/5044848527	1008137	Tony Prest / Never Odd Or Even	09/2022
62	(2^3348456+23)/3/41	1007984	Tony Prest / Never Odd Or Even	01/2019
63	(2^3348338+213)/7	1007950	Tony Prest / Never Odd Or Even	10/2018
64	(2^3348184+123)/12491/322944263	1007892	Tony Prest / Never Odd Or Even	01/2021
65	(2^3348131+207)/5/11/41/43/12661193081/86868416749	1007862	Tony Prest / Never Odd Or Even	05/2021
66	(2^3348111+245)/9721/215412555797/19870494524087	1007854	Tony Prest / Never Odd Or Even	05/2021
67	(2^3347690+143)/3/7/167/585877	1007746	Tony Prest / Never Odd Or Even	06/2020
68	(2^3347613+103)/3/5/194809	1007726	Tony Prest / Never Odd Or Even	02/2020
69	(2^3347274+143)/3/3/3/234786457/3484003557569	1007608	Tony Prest / Never Odd Or Even	07/2022
70	(2^3346590+185)/3/31/83/2201765933/326210984543	1007400	Tony Prest / Never Odd Or Even	04/2021
71	(2^3346468+257)/3/7/13/71/10847	1007379	Tony Prest / Never Odd Or Even	05/2020
72	L(4819961)	1007313	Ryan Propper	07/2022
73	(2^3345946+187)/7/3122957	1007223	Tony Prest / Never Odd Or Even	03/2019
74	2^3345603+63	1007127	Tony Prest / Never Odd Or Even	05/2018
75	(2^3345474+255)/19/29/2557	1007082	Tony Prest / Never Odd Or Even	12/2019
76	(2^3345364+43)/53/79/109/2389/10889/16838309	1007035	Tony Prest / Never Odd Or Even	07/2022
77	(2^3345080+247)/31/3967	1006965	Tony Prest / Never Odd Or Even	03/2019
78	(2^3343888+209)/3/3/5/31/179	1006606	Tony Prest / Never Odd Or Even	11/2019
79	(2^3343774+115)/12239	1006573	Tony Prest / Never Odd Or Even	10/2018
80	(2^3343633+105)/137	1006532	Tony Prest / Never Odd Or Even	10/2018
81	(2^3343714+149)/3/11/17/6047/23869/3993469/171388950721	1006530	Tony Prest / Never Odd Or Even	01/2021
82	(2^3343629+183)/5/35107/2154259/28212829709	1006511	Tony Prest / Never Odd Or Even	05/2022
83	(2^3343142+13)/587/212195573363/3775970066719	1006360	Tony Prest / Never Odd Or Even	05/2018
84	(2^3342880+215)/3/7/157/239/821	1006299	Tony Prest / Never Odd Or Even	04/2020
85	(2^3342588+95)/3/619/13174671553/22761066847	1006196	Tony Prest / Never Odd Or Even	08/2018
86	(2^3322799+505)/3	1000262	Stefano Morozzi	08/2022
87	2^3322077+659	1000045	Stefano Morozzi	04/2022
88	211185^54364+54364^211185	1000027	Gabor Levai	05/2022
92	10^999999+593499	1000000	Peter Kaiser	02/2013
89	10^999999+308267*10^292000+1	1000000	Sergey Batalov	09/2021
90	138159533888769035882147()973433052122012098003208^4096+1	1000000	Anonymous	11/2021
91	138159533888769035882147()973433052122012098115876^4096+1	1000000	Anonymous	11/2021
95	10^999999-172473	999999	Patrick De Geest	12/2016
93	10^999999-1087604*10^287000-1	999999	Ryan Propper + Sergey Batalov	09/2021
94	10^999999-1022306*10^287000-1	999999	Ryan Propper + Sergey Batalov	09/2021
96	(7^1178033+1)/8	995553	Paul Bourdelais	01/2019
97	10^995256+7	995257	Alfred Reich	11/2021
98	F(4740217)	990647	Ryan Propper	07/2022
99	2^3223639+74333	970413	Enzo Doria	10/2021
100	2^3118435+73793	938743	Enzo Doria	01/2021
101	2^3037438+1885789	914360	Enzo Doria	05/2019
102	2^3032354+74209	912830	Enzo Doria	01/2020
103	2^3018556+31	908676	Robert Price	09/2019
104	(3^1896463+1)/4	904843	Paul Bourdelais	01/2020
105	Tau(181^72558)	900969	Nik Lygeros / Olivier Rozier / LR team	07/2018
106	2^2976221+2041857	895932	Makoto Morimoto	09/2014
107	(35^568453-1)/34	877729	Paul Bourdelais	10/2021
108	L(4161629)	869730	Ryan Propper	07/2022
109	(2^2860553+1)/(3152889120412311630352659013691)	861084	Gord Palameta	03/2019
110	2^2843446+1885789	855963	Enzo Doria	05/2019
111	3^1753088+2	836436	Paul Bourdelais	03/2022
112	(12^769543-1)/11	830476	Paul Bourdelais	12/2014
113	2^2740174+1884385	824875	Enzo Doria	01/2019
114	Tau(229^63498)	824146	Nik Lygeros / Olivier Rozier / LR team	07/2020
115	(9^860029+1)/10	820676	Paul Bourdelais	09/2020
116	2^2723045+60227	819719	Enzo Doria	01/2020
117	2^2711746+74179	816317	Enzo Doria	11/2019
118	(2^2687383+1)/(3*440088720954577)	808968	Gord Palameta	03/2019
119	(31^535571-1)/30	798729	Alexander Zhirkov	08/2019
120	(64*10^779465-1)/81	779465	Serge Batalov	09/2014
121	(64*10^762811-1)/9	762812	Serge Batalov	09/2014
122	2^2515946+60529	757376	Enzo Doria	10/2018
123	(15^639833-1)/14	752501	Paul Bourdelais	04/2019
124	2^2442546+74209	735280	Enzo Doria	03/2020
125	(10^718580+269)/9	718580	Serge Batalov	12/2014
126	(99^357779+1)/100	713995	Paul Bourdelais	02/2022
127	(81^370421+1)/82	706942	Paul Bourdelais	12/2021
128	(2^2327417-1)/23915387348002001	700606	Anand Nair	08/2014
129	F(3340367)	698096	Henri Lifchitz	03/2018
130	(2^2305781-2^1152891+1)/5	694109	Serge Batalov	01/2014
131	2^2291342+73519	689763	Enzo Doria	12/2018
132	(10^685224+89)/9	685224	Serge Batalov	12/2014
133	F(3244369)	678033	Henri Lifchitz	09/2017
134	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
135	(10^675470+269)/9	675470	Serge Batalov	12/2014
136	Tau(151^56086)	672156	Nik Lygeros / Olivier Rozier / LR team	10/2017
137	(9^703393+1)/10	671207	Paul Bourdelais	08/2015
138	(121^320483+1)/122	667496	Paul Bourdelais	08/2019
139	2^2213586+71389	666356	Enzo Doria	04/2018
140	2^2205444+3	663905	Paul Bourdelais	08/2020
141	2^2191232+105	659627	Stefano Morozzi	10/2021
142	2^2187054+1886719	658369	Enzo Doria	11/2018
143	(6^840316-11)/5	653893	Paul Bourdelais	06/2020
144	(15^551927+1)/16	649116	Paul Bourdelais	07/2013
145	2^2153756+72181	648346	Enzo Doria	04/2018
146	(3^1353449-3^676725+1)/7	645759	Serge Batalov	03/2014
147	Tau(983^38932)	640784	Nik Lygeros / Olivier Rozier	02/2016
148	2^2119239+684443	637955	Enzo Doria	11/2018
149	2^2117699+89	637491	Stefano Morozzi	10/2021
150	2^2107382+105	634385	Stefano Morozzi	10/2021
151	(51*21^479149-1243)/4	633542	Curtis Bright	11/2015
152	2^2099459+71663	632001	Enzo Doria	07/2018
153	Tau(881^38992)	631568	Nik Lygeros / Olivier Rozier	01/2016
154	2^2097791+60563	631499	Enzo Doria	04/2018
155	2^2086750-3	628175	Paul Bourdelais	05/2020
156	2^2083766+73519	627277	Enzo Doria	01/2019
157	(20^472709-1)/19	615008	Paul Bourdelais	01/2015
158	PIPrime(613373)	613373	Adrian Bondrescu	05/2016
159	11^586020-2	610277	Paul Bourdelais	11/2021
160	(19^476929+1)/20	609874	Paul Bourdelais	03/2015
161	2^2019811+1867211	608024	Enzo Doria	04/2018
162	F(2904353)	606974	Henri Lifchitz	07/2014
163	2^2014720+71893	606492	Enzo Doria	04/2018
164	L(2894561)	604928	Ryan Propper	06/2022
165	(18^481147+1)/19	603970	Paul Bourdelais	07/2011
166	200^262144+119^262144	603202	Kellen Shenton	08/2022
167	(15^505117-1)/14	594063	Paul Bourdelais	01/2015
168	(152^270217-1)/(152-1)	589570	Michael Stocker	06/2015
169	Phi(177147,94259)	587458	Anonymous	09/2022
170	2^1950002+1867369	587010	Enzo Doria	02/2018
171	2^1940812+3	584243	Paul Bourdelais	06/2020
172	2^1923104+153	578912	Stefano Morozzi	07/2021
173	(3^1205459+1)/4	575150	Paul Bourdelais	08/2015
174	2^1882800+384541	566780	Enzo Doria	12/2017
175	(2^1882787-2^941394+1)/5	566775	Borys Jaworski	11/2012
176	2^1882474+71389	566682	Enzo Doria	04/2018
177	(6^727496-11)/5	566102	Paul Bourdelais	08/2019
178	2^1875552+3	564598	Paul Bourdelais	04/2020
179	3^1180181-2	563090	Jorge Coveiro	05/2020
180	2^1852265+1890425	557588	Enzo Doria	11/2017
181	5^797390-2	557352	Paul Bourdelais	03/2021
182	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
183	Tau(773^34960)	555339	Nik Lygeros / Olivier Rozier	09/2015
184	((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568	555154	Serge Batalov	08/2013
185	(42^337081-1)/41	547165	Paul Bourdelais	09/2021
186	(2^1790743-1)/(1468409271583589849773835546416767873*20752172271489035681)	539014	Dario Alpern	06/2015
187	10^538640-3	538640	Paul Bourdelais	01/2021
188	2^1787167+71963	537991	Enzo Doria	12/2018
189	(12^495953+1)/13	535223	Paul Bourdelais	11/2018
190	2^1773644+72511	533921	Enzo Doria	10/2018
191	(92^271639-1)/91	533440	Paul Bourdelais	02/2022
192	(11559^131072+1)/2	532535	Serge Batalov	04/2018
193	(85^275881-1)/84	532289	Paul Bourdelais	02/2022
194	2^1762004-3	530417	Paul Bourdelais	04/2020
195	(73^280697+1)/74	523028	Paul Bourdelais	02/2022
196	(21^394579+1)/22	521719	Paul Bourdelais	10/2018
197	2^1730246+384439	520856	Enzo Doria	09/2017
198	(55^299087+1)/56	520519	Paul Bourdelais	02/2022
199	(18^414269-1)/17	520020	Paul Bourdelais	12/2014
200	20^396120-3	515365	Paul Bourdelais	01/2021
201	(62^286483+1)/63	513488	Paul Bourdelais	02/2022
202	(20^393257+1)/21	511638	Paul Bourdelais	12/2014
203	10^509546+3	509547	Paul Bourdelais	01/2021
204	(72^273149-1)/71	507327	Paul Bourdelais	02/2022
205	107890^49423+49423^107890	506429	Miklos Levai	02/2022
206	(14^441697-1)/13	506241	Paul Bourdelais	12/2014
207	3^1059503-2^1059503	505512	Mike Oakes	04/2012
208	101542^92885+92885^101542	504465	Gabor Levai	04/2022
209	105098^61113+61113^105098	503014	Miklos Levai	09/2022
210	2^1670703+60293	502932	Enzo Doria	11/2017
211	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
212	101311^90816+90816^101311	502317	Gabor Levai	12/2021
213	101643^87368+87368^101643	502254	Gabor Levai	11/2022
214	101863^84922+84922^101863	502085	Gabor Levai	10/2022
215	100207^99856+99856^100207	500973	Gabor Levai	11/2021
216	101839^83028+83028^101839	500969	Gabor Levai	11/2022
217	100263^98600+98600^100263	500702	Gabor Levai	09/2021
218	101761^82168+82168^101761	500126	Gabor Levai	03/2022
219	2^1661176+336631	500064	Tony Prest / Never Odd Or Even	09/2019
220	101070^88579+88579^101070	500027	Gabor Levai	01/2022
221	(85^259159-1)/84	500025	Paul Bourdelais	11/2021
222	2^1660973+368139	500003	Tony Prest / Never Odd Or Even	08/2020
223	2^1660964-382425	500000	Tony Prest / Never Odd Or Even	05/2020
224	(87^257689-1)/86	499791	Paul Bourdelais	01/2021
225	(64*10^499210+53)/9	499211	Serge Batalov	03/2015
226	Tau(631^32370)	498503	Nik Lygeros / Olivier Rozier	05/2015
227	29^339887-28^339887	497051	Jean-Louis Charton	05/2019
228	(2^1629469-1)/644908484660139264379223	490496	Gord Palameta	11/2017
229	10^487291+7	487292	Alfred Reich	06/2021
230	2^1617579+1889543	486940	Enzo Doria	09/2017
231	L(2316773)	484177	Serge Batalov	06/2017
232	(57^275669-1)/56	484039	Paul Bourdelais	04/2021
233	2^1599120-5	481384	Stefano Morozzi	12/2022
234	10^480684-3	480684	Paul Bourdelais	01/2021
235	2^1595483+184133	480289	Enzo Doria	07/2017
236	2^1594947+3	480127	Paul Bourdelais	07/2019
237	(94^241993-1)/93	477482	Paul Bourdelais	09/2020
238	2^1585195+1888373	477192	Enzo Doria	08/2017
239	(33^313553+1)/34	476134	Paul Bourdelais	02/2021
240	3^994536+16	474515	Robert Price	10/2020
241	2^1575391+71483	474240	Enzo Doria	04/2018
242	(2^1572882+5)/3	473485	Serge Batalov	08/2015
243	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
244	3^989124+16	471933	Robert Price	10/2020
245	2^1567006+1888099	471716	Enzo Doria	05/2017
246	2^1563067+1889813	470531	Enzo Doria	08/2017
247	2^1549797+60197	466536	Enzo Doria	02/2018
248	2^1549030+1887619	466305	Enzo Doria	05/2017
249	416^177481-415^177481	464840	Jean-Louis Charton	12/2016
250	(78^245183-1)/77	463908	Paul Bourdelais	02/2021

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PRP Records

Probable Primes Top 10000

(291658 PRPs in the top)