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	(3^8530117-1)/2	4069900	Ryan Propper	11/2023
5	2^13380298-27	4027872	Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist	03/2021
6	(2^13372531+1)/3	4025533	Ryan Propper	09/2013
7	(2^13347311+1)/3	4017941	Ryan Propper	09/2013
8	(2^12720787-1)/1119429257/175573124547437977/8480999878421106991	3829294	Anonymous	10/2022
9	(3^7973131-1)/2	3804150	Ryan Propper	11/2023
10	(2^12588091-1)/32075464348897282169539424801	3789365	Eden Avidan / Naegi Makoto	05/2023
11	(2^12503723-2^6251862+1)/5	3763995	Ryan Propper + Sergey Batalov	07/2020
12	(5^5154509-1)/4	3602847	Ryan Propper	02/2024
13	(5^4939471-1)/4	3452542	Ryan Propper	01/2024
14	(3^7034611+1)/4	3356362	Paul Bourdelais	12/2024
15	(2^10443557-1)/37289325994807	3143811	GIMPS-fre_games	07/2020
16	2^9092392+40291	2737083	Engracio Esmenda / Five or Bust	02/2011
17	(6^3360347-1)/5	2614858	Ryan Propper	10/2023
18	(2^8247949-1)/10623358313/23839855293703/179607668296296461174489	2482834	Anonymous	06/2024
19	(17^1990523-1)/16	2449236	Paul Bourdelais	08/2020
20	(35963^524288+1)/2	2388581	Ryan Propper	08/2022
21	500186^54465+54465^500186	2368940	Ryan Propper	08/2024
22	(11^2264611+1)/12	2358349	Paul Bourdelais	07/2021
23	(5^3300593-1)/4	2307015	Anonymous	02/2022
24	(3^4694803+2^4694803)/5	2239990	Ryan Propper	12/2023
25	(2^7313983-1)/305492080276193	2201714	Oliver Kruse	03/2018
26	(3^4571447+2^4571447)/5	2181134	Ryan Propper	12/2023
27	(15^1848811+1)/16	2174370	Paul Bourdelais	07/2024
28	F(10367321)	2166642	Ryan Propper	08/2024
29	(15^1841911+1)/16	2166255	Paul Bourdelais	07/2024
30	4532794^3+3^4532794	2162693	Ryan Propper	10/2023
31	F(10317107)	2156148	Ryan Propper	07/2024
32	(2^7080247-1)/156822217506727/11283326312536321/9632940548330339593	2131318	Gord Palameta	10/2017
33	360834^356345+356345^360834	2003304	Ryan Propper	02/2024
34	360339^356572+356572^360339	2000656	Ryan Propper	05/2024
35	(11^1868983-1)/10	1946345	Paul Bourdelais	06/2021
36	(36^1145393+1)/37	1782577	Paul Bourdelais	11/2023
37	(14^1522841+1)/15	1745370	Paul Bourdelais	02/2025
38	1343238^19+19^1343238	1717671	Ryan Propper	05/2023
39	(3^3598867-1)/2	1717096	Ryan Propper	12/2021
40	(13^1503503-1)/12	1674817	Paul Bourdelais	04/2020
41	Mills(3,30,6,80,12,450,894,3636,70756,97220,66768,300840,1623568,8436308)	1665461	Ryan Propper + Sergey Batalov	05/2024
42	F(7789819)	1627976	Ryan Propper	07/2024
43	(10^1600787+1)/11	1600786	Paul Bourdelais	05/2020
44	(18^1270141-1)/17	1594372	Paul Bourdelais	12/2021
45	(14^1385203+1)/15	1587619	Paul Bourdelais	02/2022
46	(2^5243339-2^2621670+1)/5	1578402	Ryan Propper + Sergey Batalov	06/2020
47	(2^5240707-1)/75392810903	1577600	Tony Prest / Never Odd Or Even	07/2016
48	2^5146295+41693	1549190	Engracio Esmenda / Five or Bust	11/2009
49	(2^4834891-1)/1701881633/70659688575577	1455425	Gord Palameta	01/2017
50	300102^59935+59935^300102	1433792	Ryan Propper	05/2023
51	(187503^262144+1)/2	1382288	Ryan Propper	08/2022
52	2^4583176+2131	1379674	Ben Maloney / Five or Bust	09/2009
53	F(6530879)	1364873	Ryan Propper	08/2022
54	(2^4533073+2^2266537+1)/5	1364591	Serge Batalov	03/2014
55	(13^1199467+1)/14	1336138	Paul Bourdelais	12/2015
56	(5^1888279-1)/4	1319850	Paul Bourdelais	04/2018
57	(5^1856147+1)/6	1297391	Paul Bourdelais	02/2019
58	(3^2704981-1)/2	1290604	Ryan Propper	12/2021
59	(20^984349-1)/19	1280667	Paul Bourdelais	09/2021
60	(3^2674381+1)/4	1276004	Paul Bourdelais	03/2024
61	1139148^13+13^1139148	1268947	Ryan Propper	07/2023
62	(2^4194304+1026473)/3	1262611	Tony Prest / Never Odd Or Even	07/2017
63	(2^4187251-1)/72234342371519	1260475	Tony Prest / Never Odd Or Even	05/2016
64	(14^1091401+1)/15	1250885	Paul Bourdelais	03/2014
65	(16^1025393+1)/17	1234695	Paul Bourdelais	08/2014
66	11^1181716+1181716	1230631	Kellen Shenton	07/2023
67	(2^4031399+1)/3	1213572	Tony Reix / Diepeveen-Underwood -Reix	02/2010
68	(3^2533963+1)/4	1209008	Paul Bourdelais	03/2020
69	2^3950407-991	1189192	Stefano Morozzi	04/2025
70	2^3900281+411	1174102	Stefano Morozzi	01/2025
71	L(5466311)	1142392	Ryan Propper	08/2022
72	(24^821497+1)/25	1133838	Paul Bourdelais	01/2025
73	(34^735439+1)/35	1126308	Paul Bourdelais	10/2023
74	(67*10^1116676+23)/9	1116677	Ryan Propper + Sergey Batalov	01/2023
75	2^3701725-139	1114331	Stefano Morozzi	09/2024
76	2^3701370-777	1114224	Stefano Morozzi	09/2024
77	2^3690839-1868407	1111054	Enzo Doria	03/2021
78	2^3678448+384541	1107324	Enzo Doria	03/2022
79	2^3668660+1888801	1104377	Enzo Doria	03/2020
80	(106*23^800873-7)/11	1090573	Curtis Bright	05/2015
81	(7^1264699-1)/6	1068794	Paul Bourdelais	01/2014
82	(6^1365019-1)/5	1062191	Paul Bourdelais	12/2019
83	2^3511529-15	1057076	Stefano Morozzi	06/2023
84	(3^2215303-1)/2	1056968	Paul Bourdelais	02/2019
85	2^3480081-9	1047609	Stefano Morozzi	05/2023
86	10^1043372+7	1043373	Alfred Reich	12/2021
87	(2^3464473-1)/604874508299177	1042896	Anand Nair	10/2014
88	202628^128217+128217^202628	1035013	Ryan Propper	12/2023
89	202688^125163+125163^202688	1033198	Ryan Propper	12/2023
90	201868^129567+129567^201868	1032050	Ryan Propper	11/2023
91	202168^126585+126585^202168	1031539	Ryan Propper	11/2023
92	202336^124213+124213^202336	1030734	Ryan Propper	11/2023
93	201754^125605+125605^201754	1028746	Ryan Propper	10/2023
94	(6^1313371+1)/7	1022001	Paul Bourdelais	01/2019
95	200307^126128+126128^200307	1021729	Ryan Propper	10/2023
96	193143^193143+214^214	1020931	Ryan Propper + Sergey Batalov	05/2024
97	200026^126791+126791^200026	1020751	Ryan Propper	09/2023
98	200068^125561+125561^200068	1020118	Ryan Propper	09/2023
99	192223^192223+166^166	1015669	Ryan Propper + Sergey Batalov	05/2024
100	(2^3352132+9)/5	1009092	Tony Prest / Never Odd Or Even	06/2018
101	(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221	1009003	Tony Prest / Never Odd Or Even	08/2019
102	(2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837	1008886	Tony Prest / Never Odd Or Even	08/2019
103	(2^3351346+113)/3/548533/39539021/94650838127	1008831	Tony Prest / Never Odd Or Even	11/2022
104	(2^3350899+115)/3/3/11/409	1008717	Tony Prest / Never Odd Or Even	04/2020
105	(2^3350068+183)/953/15761231	1008461	Tony Prest / Never Odd Or Even	03/2020
106	(2^3349565+57)/23/263/77893	1008311	Tony Prest / Never Odd Or Even	03/2020
107	(2^3349080+137)/3/79/8060419099	1008162	Tony Prest / Never Odd Or Even	07/2020
108	(2^3349027+183)/23/1277/11638321/5044848527	1008137	Tony Prest / Never Odd Or Even	09/2022
109	(2^3348456+23)/3/41	1007984	Tony Prest / Never Odd Or Even	01/2019
110	(2^3348338+213)/7	1007950	Tony Prest / Never Odd Or Even	10/2018
111	(2^3348184+123)/12491/322944263	1007892	Tony Prest / Never Odd Or Even	01/2021
112	(2^3348131+207)/5/11/41/43/12661193081/86868416749	1007862	Tony Prest / Never Odd Or Even	05/2021
113	(2^3348111+245)/9721/215412555797/19870494524087	1007854	Tony Prest / Never Odd Or Even	05/2021
114	(2^3347690+143)/3/7/167/585877	1007746	Tony Prest / Never Odd Or Even	06/2020
115	(2^3347613+103)/3/5/194809	1007726	Tony Prest / Never Odd Or Even	02/2020
116	(2^3347274+143)/3/3/3/234786457/3484003557569	1007608	Tony Prest / Never Odd Or Even	07/2022
117	(2^3346590+185)/3/31/83/2201765933/326210984543	1007400	Tony Prest / Never Odd Or Even	04/2021
118	(2^3346468+257)/3/7/13/71/10847	1007379	Tony Prest / Never Odd Or Even	05/2020
119	L(4819961)	1007313	Ryan Propper	07/2022
120	(2^3346066+139)/168803/7120527205063	1007249	Tony Prest / Never Odd Or Even	05/2023
121	(2^3345946+187)/7/3122957	1007223	Tony Prest / Never Odd Or Even	03/2019
122	2^3345603+63	1007127	Tony Prest / Never Odd Or Even	05/2018
123	(2^3345474+255)/19/29/2557	1007082	Tony Prest / Never Odd Or Even	12/2019
124	(2^3345364+43)/53/79/109/2389/10889/16838309	1007035	Tony Prest / Never Odd Or Even	07/2022
125	(2^3345080+247)/31/3967	1006965	Tony Prest / Never Odd Or Even	03/2019
126	(2^3343888+209)/3/3/5/31/179	1006606	Tony Prest / Never Odd Or Even	11/2019
127	(2^3343774+115)/12239	1006573	Tony Prest / Never Odd Or Even	10/2018
128	(2^3343633+105)/137	1006532	Tony Prest / Never Odd Or Even	10/2018
129	(2^3343714+149)/3/11/17/6047/23869/3993469/171388950721	1006530	Tony Prest / Never Odd Or Even	01/2021
130	(2^3343629+183)/5/35107/2154259/28212829709	1006511	Tony Prest / Never Odd Or Even	05/2022
131	(2^3343142+13)/587/212195573363/3775970066719	1006360	Tony Prest / Never Odd Or Even	05/2018
132	(2^3342880+215)/3/7/157/239/821	1006299	Tony Prest / Never Odd Or Even	04/2020
133	(2^3342804+51)/13/13/43/2069/149173	1006272	Tony Prest / Never Odd Or Even	01/2023
134	(2^3342732+41)/3/7/28513800139379	1006248	Tony Prest / Never Odd Or Even	03/2023
135	(2^3342588+95)/3/619/13174671553/22761066847	1006196	Tony Prest / Never Odd Or Even	08/2018
136	194968^136197+136197^194968	1000999	Hans Havermann	12/2023
137	191319^170462+170462^191319	1000910	Hans Havermann	07/2023
138	197180^119151+119151^197180	1000905	Hans Havermann	08/2023
139	198328^110673+110673^198328	1000375	Gabor Levai	12/2024
140	202818^85523+85523^202818	1000316	Gabor Levai	08/2023
141	(2^3322799+505)/3	1000262	Stefano Morozzi	08/2022
142	2^3322627-525	1000211	Stefano Morozzi	07/2024
143	265341^5882+5882^265341	1000210	Gabor Levai	04/2024
144	218767^37314+37314^218767	1000175	Gabor Levai	03/2023
145	2^3322077+659	1000045	Stefano Morozzi	04/2022
146	211185^54364+54364^211185	1000027	Gabor Levai	05/2022
153	10^999999+593499	1000000	Peter Kaiser	02/2013
147	10^999999+308267*10^292000+1	1000000	Sergey Batalov	09/2021
148	138159533888769035882147()973433052122012098003208^4096+1	1000000	Anonymous	11/2021
149	138159533888769035882147()973433052122012098115876^4096+1	1000000	Anonymous	11/2021
150	190880568043619196745858()064791100275825910782112^2048+1	1000000	Anonymous	05/2023
151	190880568043619196745858()064791100275825910980374^2048+1	1000000	Anonymous	05/2023
152	(sqrtnint(10^999999,1024)+407852)^1024+1	1000000	Anonymous	06/2024
154	10^999999-172473	999999	Patrick De Geest	12/2016
155	10^999999-1087604*10^287000-1	999999	Ryan Propper + Sergey Batalov	09/2021
156	10^999999-1022306*10^287000-1	999999	Ryan Propper + Sergey Batalov	09/2021
157	(7^1178033+1)/8	995553	Paul Bourdelais	01/2019
158	10^995256+7	995257	Alfred Reich	11/2021
159	F(4740217)	990647	Ryan Propper	07/2022
160	(3^2052329+2^2052329)/5	979210	Ryan Propper	12/2023
161	2^3223639+74333	970413	Enzo Doria	10/2021
162	2^3118435+73793	938743	Enzo Doria	01/2021
163	2^3037438+1885789	914360	Enzo Doria	05/2019
164	2^3032354+74209	912830	Enzo Doria	01/2020
165	2^3018556+31	908676	Robert Price	09/2019
166	(3^1896463+1)/4	904843	Paul Bourdelais	01/2020
167	Tau(181^72558)	900969	Nik Lygeros / Olivier Rozier / LR team	07/2018
168	2^2976221+2041857	895932	Makoto Morimoto	09/2014
169	1839730^3+3^1839730	877775	Ryan Propper	06/2023
170	(35^568453-1)/34	877729	Paul Bourdelais	10/2021
171	L(4161629)	869730	Ryan Propper	07/2022
172	(2^2860553+1)/(3152889120412311630352659013691)	861084	Gord Palameta	03/2019
173	2^2843446+1885789	855963	Enzo Doria	05/2019
174	3^1753088+2	836436	Paul Bourdelais	03/2022
175	(12^769543-1)/11	830476	Paul Bourdelais	12/2014
176	2^2740174+1884385	824875	Enzo Doria	01/2019
177	Tau(229^63498)	824146	Nik Lygeros / Olivier Rozier / LR team	07/2020
178	(168326^157609-1)/(168326^397-1)	821614	Ryan Propper	11/2023
179	(9^860029+1)/10	820676	Paul Bourdelais	09/2020
180	2^2723045+60227	819719	Enzo Doria	01/2020
181	2^2711746+74179	816317	Enzo Doria	11/2019
182	(2^2687383+1)/(3*440088720954577)	808968	Gord Palameta	03/2019
183	684614^15+15^684614	805169	Ryan Propper	05/2023
184	(31^535571-1)/30	798729	Alexander Zhirkov	08/2019
185	(9^835391-7^835391)/2	797166	Jon Grantham	07/2023
186	(64*10^779465-1)/81	779465	Serge Batalov	09/2014
187	(8^854149-3^854149)/5	771373	Jon Grantham	08/2023
188	(64*10^762811-1)/9	762812	Serge Batalov	09/2014
189	2^2515946+60529	757376	Enzo Doria	10/2018
190	(15^639833-1)/14	752501	Paul Bourdelais	04/2019
191	2^2442546+74209	735280	Enzo Doria	03/2020
192	2^2421175-25	728847	Boyan Hu	03/2025
193	(110212^143641-1)/(110212^379-1)	722361	Ryan Propper	11/2023
194	(79^379703+1)/80	720533	Paul Bourdelais	10/2023
195	(10^718580+269)/9	718580	Serge Batalov	12/2014
196	89^367176+367176	715770	Kellen Shenton	03/2025
197	(7^846913-2^846913)/5	715724	Jon Grantham	08/2023
198	(99^357779+1)/100	713995	Paul Bourdelais	02/2022
199	558232^19+19^558232	713842	Ryan Propper	05/2023
200	(26^501409+1)/27	709479	Paul Bourdelais	10/2023
201	(81^370421+1)/82	706942	Paul Bourdelais	12/2021
202	(2^2327417-1)/23915387348002001	700606	Anand Nair	08/2014
203	F(3340367)	698096	Henri Lifchitz	03/2018
204	(2^2305781-2^1152891+1)/5	694109	Serge Batalov	01/2014
205	135078^135078-13^13	693030	Henri Lifchitz	11/2024
206	(7^817519-3^817519)/4	690884	Jon Grantham	08/2023
207	2^2291342+73519	689763	Enzo Doria	12/2018
208	(10^685224+89)/9	685224	Serge Batalov	12/2014
209	(65^375017-1)/64	679872	Paul Bourdelais	10/2023
210	F(3244369)	678033	Henri Lifchitz	09/2017
211	2^2249255+28433	677094	Ben Maloney / Five or Bust	01/2009
212	(10^675470+269)/9	675470	Serge Batalov	12/2014
213	(2*10^672745-17)/3	672745	Rytis Slatkevicius	09/2024
214	Tau(151^56086)	672156	Nik Lygeros / Olivier Rozier / LR team	10/2017
215	(9^703393+1)/10	671207	Paul Bourdelais	08/2015
216	(121^320483+1)/122	667496	Paul Bourdelais	08/2019
217	(10^666903-7)/3	666903	Rytis Slatkevicius	01/2023
218	2^2213586+71389	666356	Enzo Doria	04/2018
219	(9614^167281-1)/(9614^409-1)	664636	Ryan Propper	11/2023
220	2^2205444+3	663905	Paul Bourdelais	08/2020
221	(41*13^592198+27)/4	659677	Eric Chen	11/2023
222	2^2191232+105	659627	Stefano Morozzi	10/2021
223	2^2187054+1886719	658369	Enzo Doria	11/2018
224	(6^840316-11)/5	653893	Paul Bourdelais	06/2020
225	2^2160082+39973	650250	Stefano Morozzi	07/2024
226	2^2160074+41857	650248	Stefano Morozzi	06/2024
227	2^2160054+24817	650242	Stefano Morozzi	06/2024
228	2^2160018+24099	650231	Stefano Morozzi	09/2024
229	(15^551927+1)/16	649116	Paul Bourdelais	07/2013
230	2^2153756+72181	648346	Enzo Doria	04/2018
231	(3^1353449-3^676725+1)/7	645759	Serge Batalov	03/2014
232	Tau(983^38932)	640784	Nik Lygeros / Olivier Rozier	02/2016
233	2^2119239+684443	637955	Enzo Doria	11/2018
234	2^2117699+89	637491	Stefano Morozzi	10/2021
235	(5*10^636570+31)/9	636570	Rytis Slatkevicius	02/2023
236	2^2114495+20753	636527	Enzo Doria	08/2023
237	2^2107382+105	634386	Stefano Morozzi	10/2021
238	(51*21^479149-1243)/4	633542	Curtis Bright	11/2015
239	2^2099459+71663	632001	Enzo Doria	07/2018
240	(10^631715+53)/9	631715	Rytis Slatkevicius	01/2023
241	Tau(881^38992)	631568	Nik Lygeros / Olivier Rozier	01/2016
242	2^2097791+60563	631499	Enzo Doria	04/2018
243	2^2086750-3	628175	Paul Bourdelais	05/2020
244	2^2083766+73519	627277	Enzo Doria	01/2019
245	(16105^146689-1)/(16105^383-1)	615504	Ryan Propper	11/2023
246	(20^472709-1)/19	615008	Paul Bourdelais	01/2015
247	PIPrime(613373)	613373	Adrian Bondrescu	05/2016
248	124452^80465+80465^124452	610513	Ryan Propper	10/2023
249	11^586020-2	610277	Paul Bourdelais	11/2021
250	(19^476929+1)/20	609874	Paul Bourdelais	03/2015

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PRP Records

Probable Primes Top 10000

(301352 PRPs in the top)