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	2^13380298-27	4027872	Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist	03/2021
2	(2^13372531+1)/3	4025533	Ryan Propper	09/2013
3	(2^13347311+1)/3	4017941	Ryan Propper	09/2013
4	(2^12503723-2^6251862+1)/5	3763995	Ryan Propper + Sergey Batalov	07/2020
5	(2^10443557-1)/37289325994807	3143811	GIMPS-fre_games	07/2020
6	2^9092392+40291	2737083	Engracio Esmenda / Five or Bust	02/2011
7	(17^1990523-1)/16	2449236	Paul Bourdelais	08/2020
8	(2^7313983-1)/305492080276193	2201714	Oliver Kruse	03/2018
9	(2^7080247-1)/156822217506727/11283326312536321/9632940548330339593	2131318	Gord Palameta	10/2017
10	(13^1503503-1)/12	1674817	Paul Bourdelais	04/2020
11	(10^1600787+1)/11	1600786	Paul Bourdelais	05/2020
12	(2^5243339-2^2621670+1)/5	1578402	Ryan Propper + Sergey Batalov	06/2020
13	(2^5240707-1)/75392810903	1577600	Tony Prest / Never Odd Or Even	07/2016
14	2^5146295+41693	1549190	Engracio Esmenda / Five or Bust	11/2009
15	(2^4834891-1)/1701881633/70659688575577	1455425	Gord Palameta	01/2017
16	2^4583176+2131	1379674	Ben Maloney / Five or Bust	09/2009
17	(2^4533073+2^2266537+1)/5	1364591	Serge Batalov	03/2014
18	(13^1199467+1)/14	1336138	Paul Bourdelais	12/2015
19	(5^1888279-1)/4	1319850	Paul Bourdelais	04/2018
20	(5^1856147+1)/6	1297391	Paul Bourdelais	02/2019
21	(2^4194304+1026473)/3	1262611	Tony Prest / Never Odd Or Even	07/2017
22	(2^4187251-1)/72234342371519	1260475	Tony Prest / Never Odd Or Even	05/2016
23	(14^1091401+1)/15	1250885	Paul Bourdelais	03/2014
24	(16^1025393+1)/17	1234695	Paul Bourdelais	08/2014
25	(2^4031399+1)/3	1213572	Tony Reix / Diepeveen-Underwood -Reix	02/2010
26	(3^2533963+1)/4	1209008	Paul Bourdelais	03/2020
27	2^3668660+1888801	1104377	Enzo Doria	03/2020
28	(106*23^800873-7)/11	1090573	Curtis Bright	05/2015
29	(7^1264699-1)/6	1068794	Paul Bourdelais	01/2014
30	(6^1365019-1)/5	1062191	Paul Bourdelais	12/2019
31	(3^2215303-1)/2	1056968	Paul Bourdelais	02/2019
32	(2^3464473-1)/604874508299177	1042896	Anand Nair	10/2014
33	(6^1313371+1)/7	1022001	Paul Bourdelais	01/2019
34	(2^3352132+9)/5	1009092	Tony Prest / Never Odd Or Even	06/2018
35	(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221	1009003	Tony Prest / Never Odd Or Even	08/2019
36	(2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837	1008886	Tony Prest / Never Odd Or Even	08/2019
37	(2^3350899+115)/3/3/11/409	1008717	Tony Prest / Never Odd Or Even	04/2020
38	(2^3350068+183)/953/15761231	1008461	Tony Prest / Never Odd Or Even	03/2020
39	(2^3349565+57)/23/263/77893	1008311	Tony Prest / Never Odd Or Even	03/2020
40	(2^3349080+137)/3/79/8060419099	1008162	Tony Prest / Never Odd Or Even	07/2020
41	(2^3348456+23)/3/41	1007984	Tony Prest / Never Odd Or Even	01/2019
42	(2^3348338+213)/7	1007950	Tony Prest / Never Odd Or Even	10/2018
43	(2^3348184+123)/12491/322944263	1007892	Tony Prest / Never Odd Or Even	01/2021
44	(2^3347690+143)/3/7/167/585877	1007746	Tony Prest / Never Odd Or Even	06/2020
45	(2^3347613+103)/3/5/194809	1007726	Tony Prest / Never Odd Or Even	02/2020
46	(2^3346468+257)/3/7/13/71/10847	1007379	Tony Prest / Never Odd Or Even	05/2020
47	(2^3345946+187)/7/3122957	1007223	Tony Prest / Never Odd Or Even	03/2019
48	2^3345603+63	1007127	Tony Prest / Never Odd Or Even	05/2018
49	(2^3345474+255)/19/29/2557	1007082	Tony Prest / Never Odd Or Even	12/2019
50	(2^3345080+247)/31/3967	1006965	Tony Prest / Never Odd Or Even	03/2019
51	(2^3343888+209)/3/3/5/31/179	1006606	Tony Prest / Never Odd Or Even	11/2019
52	(2^3343774+115)/12239	1006573	Tony Prest / Never Odd Or Even	10/2018
53	(2^3343633+105)/137	1006532	Tony Prest / Never Odd Or Even	10/2018
54	(2^3343714+149)/3/11/17/6047/23869/3993469/171388950721	1006530	Tony Prest / Never Odd Or Even	01/2021
55	(2^3343142+13)/587/212195573363/3775970066719	1006360	Tony Prest / Never Odd Or Even	05/2018
56	(2^3342880+215)/3/7/157/239/821	1006299	Tony Prest / Never Odd Or Even	04/2020
57	(2^3342588+95)/3/619/13174671553/22761066847	1006196	Tony Prest / Never Odd Or Even	08/2018
58	10^999999+593499	1000000	Peter Kaiser	02/2013
59	10^999999-172473	999999	Patrick De Geest	12/2016
60	(7^1178033+1)/8	995553	Paul Bourdelais	01/2019
61	2^3118435+73793	938743	Enzo Doria	01/2021
62	2^3037438+1885789	914360	Enzo Doria	05/2019
63	2^3032354+74209	912830	Enzo Doria	01/2020
64	2^3018556+31	908676	Robert Price	09/2019
65	(3^1896463+1)/4	904843	Paul Bourdelais	01/2020
66	Tau(181^72558)	900969	Nik Lygeros / Olivier Rozier / LR team	07/2018
67	2^2976221+2041857	895932	Makoto Morimoto	09/2014
68	(2^2860553+1)/(3152889120412311630352659013691)	861084	Gord Palameta	03/2019
69	2^2843446+1885789	855963	Enzo Doria	05/2019
70	(12^769543-1)/11	830476	Paul Bourdelais	12/2014
71	2^2740174+1884385	824875	Enzo Doria	01/2019
72	Tau(229^63498)	824146	Nik Lygeros / Olivier Rozier / LR team	07/2020
73	(9^860029+1)/10	820676	Paul Bourdelais	09/2020
74	2^2723045+60227	819719	Enzo Doria	01/2020
75	2^2711746+74179	816317	Enzo Doria	11/2019
76	(2^2687383+1)/(3*440088720954577)	808968	Gord Palameta	03/2019
77	(31^535571-1)/30	798729	Alexander Zhirkov	08/2019
78	(64*10^779465-1)/81	779465	Serge Batalov	09/2014
79	(64*10^762811-1)/9	762812	Serge Batalov	09/2014
80	2^2515946+60529	757376	Enzo Doria	10/2018
81	(15^639833-1)/14	752501	Paul Bourdelais	04/2019
82	2^2442546+74209	735280	Enzo Doria	03/2020
83	(10^718580+269)/9	718580	Serge Batalov	12/2014
84	(2^2327417-1)/23915387348002001	700606	Anand Nair	08/2014
85	F(3340367)	698096	Henri Lifchitz	03/2018
86	(2^2305781-2^1152891+1)/5	694109	Serge Batalov	01/2014
87	2^2291342+73519	689763	Enzo Doria	12/2018
88	(10^685224+89)/9	685224	Serge Batalov	12/2014
89	F(3244369)	678033	Henri Lifchitz	09/2017
90	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
91	(10^675470+269)/9	675470	Serge Batalov	12/2014
92	Tau(151^56086)	672156	Nik Lygeros / Olivier Rozier / LR team	10/2017
93	(9^703393+1)/10	671207	Paul Bourdelais	08/2015
94	(121^320483+1)/122	667496	Paul Bourdelais	08/2019
95	2^2213586+71389	666356	Enzo Doria	04/2018
96	2^2205444+3	663905	Paul Bourdelais	08/2020
97	2^2187054+1886719	658369	Enzo Doria	11/2018
98	(6^840316-11)/5	653893	Paul Bourdelais	06/2020
99	(15^551927+1)/16	649116	Paul Bourdelais	07/2013
100	2^2153756+72181	648346	Enzo Doria	04/2018
101	(3^1353449-3^676725+1)/7	645759	Serge Batalov	03/2014
102	Tau(983^38932)	640784	Nik Lygeros / Olivier Rozier	02/2016
103	2^2119239+684443	637955	Enzo Doria	11/2018
104	(51*21^479149-1243)/4	633542	Curtis Bright	11/2015
105	2^2099459+71663	632001	Enzo Doria	07/2018
106	Tau(881^38992)	631568	Nik Lygeros / Olivier Rozier	01/2016
107	2^2097791+60563	631499	Enzo Doria	04/2018
108	2^2086750-3	628175	Paul Bourdelais	05/2020
109	2^2083766+73519	627277	Enzo Doria	01/2019
110	(20^472709-1)/19	615008	Paul Bourdelais	01/2015
111	PIPrime(613373)	613373	Adrian Bondrescu	05/2016
112	(19^476929+1)/20	609874	Paul Bourdelais	03/2015
113	2^2019811+1867211	608024	Enzo Doria	04/2018
114	F(2904353)	606974	Henri Lifchitz	07/2014
115	2^2014720+71893	606492	Enzo Doria	04/2018
116	(18^481147+1)/19	603970	Paul Bourdelais	07/2011
117	(15^505117-1)/14	594063	Paul Bourdelais	01/2015
118	(152^270217-1)/(152-1)	589570	Michael Stocker	06/2015
119	2^1950002+1867369	587010	Enzo Doria	02/2018
120	2^1940812+3	584243	Paul Bourdelais	06/2020
121	(3^1205459+1)/4	575150	Paul Bourdelais	08/2015
122	2^1882800+384541	566780	Enzo Doria	12/2017
123	(2^1882787-2^941394+1)/5	566775	Borys Jaworski	11/2012
124	2^1882474+71389	566682	Enzo Doria	04/2018
125	(6^727496-11)/5	566102	Paul Bourdelais	08/2019
126	2^1875552+3	564598	Paul Bourdelais	04/2020
127	3^1180181-2	563090	Jorge Coveiro	05/2020
128	2^1852265+1890425	557588	Enzo Doria	11/2017
129	5^797390-2	557352	Paul Bourdelais	03/2021
130	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
131	Tau(773^34960)	555339	Nik Lygeros / Olivier Rozier	09/2015
132	((((((((((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
133	(2^1790743-1)/(1468409271583589849773835546416767873*20752172271489035681)	539014	Dario Alpern	06/2015
134	10^538640-3	538640	Paul Bourdelais	01/2021
135	2^1787167+71963	537991	Enzo Doria	12/2018
136	(12^495953+1)/13	535223	Paul Bourdelais	11/2018
137	2^1773644+72511	533921	Enzo Doria	10/2018
138	(11559^131072+1)/2	532535	Serge Batalov	04/2018
139	2^1762004-3	530417	Paul Bourdelais	04/2020
140	(21^394579+1)/22	521719	Paul Bourdelais	10/2018
141	2^1730246+384439	520856	Enzo Doria	09/2017
142	(18^414269-1)/17	520020	Paul Bourdelais	12/2014
143	20^396120-3	515365	Paul Bourdelais	01/2021
144	(20^393257+1)/21	511638	Paul Bourdelais	12/2014
145	10^509546+3	509547	Paul Bourdelais	01/2021
146	(14^441697-1)/13	506241	Paul Bourdelais	12/2014
147	3^1059503-2^1059503	505512	Mike Oakes	04/2012
148	2^1670703+60293	502932	Enzo Doria	11/2017
149	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
150	2^1661176+336631	500064	Tony Prest / Never Odd Or Even	09/2019
151	2^1660973+368139	500003	Tony Prest / Never Odd Or Even	08/2020
152	2^1660964-382425	500000	Tony Prest / Never Odd Or Even	05/2020
153	(87^257689-1)/86	499791	Paul Bourdelais	01/2021
154	(64*10^499210+53)/9	499211	Serge Batalov	03/2015
155	Tau(631^32370)	498503	Nik Lygeros / Olivier Rozier	05/2015
156	29^339887-28^339887	497051	Jean-Louis Charton	05/2019
157	(2^1629469-1)/644908484660139264379223	490496	Gord Palameta	11/2017
158	2^1617579+1889543	486940	Enzo Doria	09/2017
159	L(2316773)	484177	Serge Batalov	06/2017
160	10^480684-3	480684	Paul Bourdelais	01/2021
161	2^1595483+184133	480289	Enzo Doria	07/2017
162	2^1594947+3	480127	Paul Bourdelais	07/2019
163	(94^241993-1)/93	477482	Paul Bourdelais	09/2020
164	2^1585195+1888373	477192	Enzo Doria	08/2017
165	(33^313553+1)/34	476134	Paul Bourdelais	02/2021
166	3^994536+16	474515	Robert Price	10/2020
167	2^1575391+71483	474240	Enzo Doria	04/2018
168	(2^1572882+5)/3	473485	Serge Batalov	08/2015
169	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
170	3^989124+16	471933	Robert Price	10/2020
171	2^1567006+1888099	471716	Enzo Doria	05/2017
172	2^1563067+1889813	470531	Enzo Doria	08/2017
173	2^1549797+60197	466536	Enzo Doria	02/2018
174	2^1549030+1887619	466305	Enzo Doria	05/2017
175	416^177481-415^177481	464840	Jean-Louis Charton	12/2016
176	(78^245183-1)/77	463908	Paul Bourdelais	02/2021
177	2^1522569+71657	458339	Enzo Doria	04/2018
178	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
179	6^584279-5	454658	Paul Bourdelais	02/2021
180	2^1506029+1890167	453360	Enzo Doria	02/2018
181	(34^294277+1)/35	450678	Paul Bourdelais	06/2018
182	2^1495434+1890439	450171	Enzo Doria	12/2017
183	2^1493170+784129	449489	Enzo Doria	08/2017
184	2^1489873+1888277	448497	Enzo Doria	06/2017
185	2^1484671+1888463	446931	Enzo Doria	06/2017
186	2^1482867+1886783	446388	Enzo Doria	04/2017
187	2^1482148+284011	446172	Enzo Doria	04/2017
188	2^1479356+1888291	445331	Enzo Doria	06/2017
189	14^384558+3	440753	Paul Bourdelais	01/2021
190	2^1461244+784531	439879	Enzo Doria	10/2017
191	(80^228419+1)/81	434701	Paul Bourdelais	02/2021
192	2^1443089+60227	434414	Enzo Doria	10/2017
193	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
194	2^1434400+3	431798	Paul Bourdelais	06/2019
195	2^1432308+1888801	431168	Enzo Doria	10/2017
196	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
197	2^1425483+1886813	429114	Enzo Doria	04/2017
198	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
199	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
200	(10^427912+89)/9	427912	Serge Batalov	12/2014
201	2^1421089+1890167	427791	Enzo Doria	09/2017
202	20^326600+3	424917	Paul Bourdelais	01/2021
203	(10^424861-7)/3	424861	Leonid Durman	01/2012
204	2^1404213+184217	422711	Enzo Doria	09/2017
205	2^1401872+1884385	422006	Enzo Doria	04/2017
206	2^1401257+6077	421821	Enzo Doria	09/2017
207	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
208	2^1398269+131595	420921	Makoto Morimoto	10/2013
209	2^1397071+684443	420561	Enzo Doria	07/2017
210	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
211	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
212	2^1386321+60299	417325	Enzo Doria	02/2018
213	2^1386320+184531	417324	Enzo Doria	09/2017
214	2^1382074+1883587	416046	Enzo Doria	01/2017
215	2^1379907+1885223	415394	Enzo Doria	03/2017
216	2^1375574+1886719	414090	Enzo Doria	04/2017
217	2^1373111+1884833	413348	Enzo Doria	02/2017
218	2^1368632+1889731	412000	Enzo Doria	10/2017
219	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
220	F(1968721)	411439	Henri Lifchitz	11/2009
221	2^1366066+683749	411227	Enzo Doria	02/2017
222	2^1355790+1888939	408134	Enzo Doria	07/2017
223	2^1355635+1884203	408087	Enzo Doria	01/2017
224	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
225	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
226	2^1347744-3	405712	Paul Bourdelais	07/2019
227	10^400000+1415223	400001	Patrick De Geest	10/2020
228	10^400000-339233	400000	Patrick De Geest	10/2020
229	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
230	2^1319770+1884949	397291	Enzo Doria	06/2017
231	2^1313062+1888849	395272	Enzo Doria	08/2017
232	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
233	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
234	2^1311618+783529	394837	Enzo Doria	01/2017
235	2^1308000+1883521	393748	Enzo Doria	02/2017
236	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
237	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
238	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
239	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
240	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
241	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
242	2^1303102+1866409	392273	Enzo Doria	09/2017
243	2^1302818+283429	392188	Enzo Doria	01/2017
244	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
245	2^1299181+1886867	391093	Enzo Doria	04/2017
246	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
247	2^1298304+1882891	390829	Enzo Doria	01/2017
248	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
249	15^328574+328574^15	386434	Serge Batalov	05/2014
250	2^1280078+1885099	385342	Enzo Doria	08/2017

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Probable Primes Top 10000

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