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 (> 30000)	Who ?	When ?
4251	11^82426-1230	85838	Enzo Doria	11/2012
4252	2^285113-109881	85828	Enzo Doria	04/2014
4253	5^122746-92	85796	Lelio R Paula	10/2015
4254	2^285001-113461	85794	Enzo Doria	08/2014
4255	(11*10^85782-131)/3	85783	Robert Price	02/2017
4256	2^284913-110491	85768	Enzo Doria	05/2014
4257	6^110220+47	85768	Lelio R Paula	12/2015
4258	3*6^110202-5	85755	Lelio R Paula	10/2014
4259	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
4260	(3^179705+7)/250	85739	Lelio R Paula	12/2012
4261	2^284734-6555	85714	Lelio R Paula	09/2013
4262	(10^85712+53)/9	85712	Robert Price	01/2015
4263	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
4264	20^65855+83	85680	Lelio R Paula	01/2016
4265	6^110105+53	85679	Lelio R Paula	12/2015
4267	2^284567-7605	85664	Lelio R Paula	09/2013
4266	9*5^122555-2	85664	Lelio R Paula	10/2014
4268	5^122554-14	85662	Lelio R Paula	10/2015
4269	9*5^122543+4	85655	Lelio R Paula	10/2014
4270	3^179489-2^(179489-1)	85639	Robert Price	01/2016
4271	2^284429+177	85622	Lelio R Paula	08/2012
4272	2*3^179452+5	85621	Lelio R Paula	07/2014
4273	(19^66919+3^66919)/22	85572	Robert Price	07/2013
4274	66^47023-65	85561	Norbert Schneider	11/2014
4275	6^109943+13	85553	Lelio R Paula	12/2015
4276	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
4277	2^284133-3	85533	M. Frind & P. Underwood	07/2002
4278	2^284113+315	85527	Lelio R Paula	09/2013
4279	(16*10^85495-19)/3	85496	Robert Price	03/2016
4280	2^284004+177	85494	Lelio R Paula	08/2012
4281	(16*10^85473-91)/3	85474	Robert Price	06/2016
4282	3^179120+22	85462	Robert Price	12/2013
4283	2^283872-2792249	85454	Enzo Doria	03/2016
4284	(29*10^85438+259)/9	85439	Robert Price	04/2017
4285	2^283817+82875	85438	Lelio R Paula	09/2013
4286	(2^283815-5)/201	85435	Lelio R Paula	01/2013
4287	2^283796-125	85432	Lelio R Paula	08/2012
4288	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
4289	15^72592-28	85375	Lelio R Paula	11/2015
4290	2^283604-58695	85374	Lelio R Paula	09/2013
4291	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
4292	15^72572+92	85352	Lelio R Paula	11/2015
4293	2^283473-1615	85334	Lelio R Paula	09/2013
4294	2^283466-15	85332	Lelio R Paula	08/2012
4295	11^81916-7020	85307	Enzo Doria	02/2013
4296	6^109626-7	85306	Lelio R Paula	11/2014
4297	2^283374-110327	85305	Enzo Doria	05/2014
4298	33*10^85297+7	85299	Robert Price	07/2016
4299	18^67933+41	85275	Lelio R Paula	11/2015
4300	2^283271-109341	85274	Enzo Doria	04/2014
4301	(25*10^85249-73)/3	85250	Robert Price	09/2016
4302	2*5^121959+3	85246	Lelio R Paula	10/2014
4303	19834^19834+8947	85235	Henri Lifchitz	11/2004
4304	2^283140+1915	85234	Lelio R Paula	09/2013
4305	(16*10^85221-31)/3	85222	Robert Price	03/2016
4306	2^283083+1869383	85217	Enzo Doria	05/2016
4307	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
4308	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
4309	2^283026-109893	85200	Enzo Doria	04/2014
4310	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
4311	2^282860-109727	85150	Enzo Doria	04/2014
4312	2^282819+1869413	85138	Enzo Doria	05/2016
4313	3^178428+2	85132	Ray Chandler	07/2011
4314	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
4315	(16^70687+5^70687)/21	85115	Robert Price	07/2013
4316	(3^178352-2)/7	85095	Lelio R Paula	12/2012
4317	11^81699-2790	85081	Enzo Doria	12/2012
4318	2^282612-95	85075	Lelio R Paula	08/2012
4319	75^45366-2	85065	Lelio R Paula	08/2013
4320	2^282511+69	85045	Lelio R Paula	08/2012
4321	69^46249+2	85045	Lelio R Paula	06/2013
4322	3^178226+10	85036	Robert Price	10/2013
4323	(14*10^85010+73)/3	85011	Robert Price	04/2016
4324	9*2^282338-7	84994	Lelio R Paula	08/2014
4325	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
4326	2^282203+5	84952	Lelio R Paula	08/2012
4327	2^282184+13	84946	Lelio R Paula	08/2012
4328	11^81568-2400	84945	Enzo Doria	12/2012
4329	11^81562-2340	84939	Enzo Doria	12/2012
4330	(41*10^84927+31)/9	84928	Robert Price	05/2015
4331	(2*10^84904-17)/3	84904	Robert Price	08/2014
4332	(4^141017+23)/3	84901	Robert Price	02/2017
4333	6^109100-18653	84897	Enzo Doria	03/2013
4334	2^281973+1025	84883	Lelio R Paula	09/2013
4335	2^281951-109651	84876	Enzo Doria	04/2014
4336	11^81491-5430	84865	Enzo Doria	01/2013
4337	((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
4338	2^281825-1861483	84838	Enzo Doria	03/2016
4339	2^281809-97305	84833	Lelio R Paula	09/2013
4340	2^281780-114893	84825	Enzo Doria	05/2015
4341	3^177719+64	84794	Lelio R Paula	12/2015
4343	2^281675-199	84793	Lelio R Paula	08/2012
4342	2^281673-111223	84793	Enzo Doria	05/2014
4344	(4*10^84779+149)/9	84779	Robert Price	03/2017
4345	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
4346	11^81398-630	84768	Enzo Doria	11/2012
4347	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
4348	2^281500-455	84740	Yves Minet	03/2012
4349	10^84725+1145141919	84726	Marisa Kirisame	03/2015
4350	10^84725+142041	84726	Patrick De Geest	10/2015
4351	10^84725-138677	84725	Patrick De Geest	02/2016
4352	76^45044+75	84720	Norbert Schneider	02/2015
4353	54^48897-53	84709	Norbert Schneider	08/2014
4354	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
4355	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
4356	2^281337-111223	84691	Enzo Doria	05/2014
4357	2^281308+54615	84683	Lelio R Paula	09/2013
4358	7*5^121144-6	84677	Lelio R Paula	10/2014
4359	(2^281252+47)/3	84665	Lelio R Paula	01/2013
4360	11^81297-3150	84663	Enzo Doria	12/2012
4361	2^281208-303	84653	Yves Minet	02/2012
4362	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
4363	11^81247-84	84611	Lelio R Paula	10/2015
4364	17^68747-64	84590	Lelio R Paula	11/2015
4365	5^121018-15596	84588	Enzo Doria	02/2013
4366	6^108702+7	84587	Lelio R Paula	11/2014
4367	10^84582+100677	84583	Patrick De Geest	05/2016
4368	10^84582-8001	84582	Robert Price	03/2016
4369	3*5^121004-8	84579	Lelio R Paula	10/2014
4370	5^120996-84	84573	Lelio R Paula	10/2015
4371	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
4372	2^280852+97681	84545	Yves Minet	08/2004
4373	2^280848-1203	84544	Lelio R Paula	09/2013
4374	5^120946-24	84538	Lelio R Paula	10/2015
4375	2^280810-2111	84533	Yves Minet	08/2013
4376	11^81161-5160	84521	Enzo Doria	01/2013
4377	2^280737-93	84511	Lelio R Paula	08/2012
4378	2^280698+315	84499	Lelio R Paula	09/2013
4379	3^177099-340	84498	Lelio R Paula	12/2015
4380	(5*10^84469-107)/3	84470	Robert Price	01/2017
4381	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
4382	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
4383	14^73660-5	84424	Lelio R Paula	11/2015
4384	(19*10^84409-61)/3	84410	Robert Price	04/2017
4385	2^280388+117	84406	Lelio R Paula	08/2012
4386	2^280389-566533	84406	Paul Bourdelais	03/2013
4387	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
4388	2^280240-173	84361	Lelio R Paula	08/2012
4389	(184*10^84348-1)/3	84350	Robert Price	02/2017
4390	4*10^84346+93	84347	Robert Price	01/2017
4391	7*2^280156-5	84337	Lelio R Paula	08/2014
4392	8*7^99782-3	84327	Lelio R Paula	10/2014
4393	2^280116+133	84324	Lelio R Paula	08/2012
4394	2^280118+54615	84324	Lelio R Paula	09/2013
4395	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
4396	6^108354+47	84316	Lelio R Paula	12/2015
4397	10^84305+141963	84306	Patrick De Geest	07/2013
4398	10^84305-57	84305	Robert Price	05/2011
4399	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
4400	3^176648-112804	84283	Enzo Doria	06/2014
4401	6^108310+115	84282	Lelio R Paula	12/2015
4402	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
4403	6^108288-16643	84265	Enzo Doria	02/2013
4404	2^279917-58695	84264	Lelio R Paula	08/2013
4405	65^46477+36	84259	Lelio R Paula	01/2016
4406	2^279866-1907	84249	Yves Minet	05/2013
4407	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
4408	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
4410	18^67103-41	84233	Lelio R Paula	11/2015
4409	20^64743-43	84233	Lelio R Paula	01/2016
4411	143^39070+39070^143	84209	Serge Batalov	05/2014
4412	11^80857-5400	84204	Enzo Doria	01/2013
4413	(13*10^84179+161)/3	84180	Robert Price	04/2017
4414	2^279634-110405	84179	Enzo Doria	05/2014
4415	2^279582-1017	84163	Lelio R Paula	08/2013
4416	(22*10^84159-19)/3	84160	Robert Price	02/2017
4417	p(17513)#/2+512	84156	Robert Price	05/2017
4418	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
4419	11^80792-810	84137	Enzo Doria	11/2012
4420	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
4421	p(17507)#/2+32	84125	Robert Price	12/2016
4422	21485^8224+8224^21485	84116	Hans Havermann	04/2017
4423	3^176294-340	84114	Lelio R Paula	12/2015
4424	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
4425	2^279388-719	84105	Yves Minet	05/2012
4426	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
4427	2^279332-110447	84088	Enzo Doria	05/2014
4428	2^279320+7	84084	Lelio R Paula	06/2012
4429	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
4430	2^279218-111347	84053	Enzo Doria	05/2014
4431	35^54435+2	84052	Lelio R Paula	05/2013
4432	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
4433	20996^10059+10059^20996	84038	Hans Havermann	05/2017
4434	97*10^84033-3	84035	Robert Price	01/2017
4435	21234^9067+9067^21234	84033	Hans Havermann	05/2017
4436	2^279095-109717	84016	Enzo Doria	04/2014
4437	14^73282-99	83991	Lelio R Paula	11/2015
4438	21457^8200+8200^21457	83979	Hans Havermann	06/2017
4439	89*10^83976-7	83978	Robert Price	03/2017
4440	2^278955+173	83974	Lelio R Paula	06/2012
4441	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
4442	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
4443	5^120076-14846	83930	Enzo Doria	02/2013
4444	(85*10^83921-1)/3	83923	Robert Price	07/2017
4445	(2^278770-3)/23	83917	Lelio R Paula	12/2012
4446	(10^83916+449)/9	83916	Serge Batalov	12/2014
4447	2^278715+99	83902	Lelio R Paula	06/2012
4448	40235!2-2^40235	83899	Robert Price	09/2015
4449	2^278698-171	83897	Lelio R Paula	06/2012
4450	6^107802+25	83887	Lelio R Paula	12/2015
4451	8*10^83880+39	83881	Robert Price	01/2017
4452	(58*10^83878+23)/9	83879	Robert Price	09/2015
4453	7^99244-90	83871	Lelio R Paula	10/2015
4454	2^278554+4257	83854	Lelio R Paula	08/2013
4455	2^278504-109619	83839	Enzo Doria	04/2014
4456	2^278499+1870433	83837	Enzo Doria	05/2016
4457	105^41475+104	83829	Norbert Schneider	11/2016
4458	15^71276-68	83828	Lelio R Paula	11/2015
4459	2^278464-216413	83827	Enzo Doria	04/2013
4460	2^278400+40755	83807	Lelio R Paula	08/2013
4461	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
4462	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
4463	19551^19268+19268^19551	83773	Hans Havermann	05/2017
4464	20625^11522+11522^20625	83770	Hans Havermann	05/2017
4465	2^278235-49	83758	Lelio R Paula	06/2012
4466	23543^3610+3610^23543	83755	Hans Havermann	05/2017
4467	18^66711-91	83741	Lelio R Paula	11/2015
4468	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
4469	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
4470	4*7^99059-9	83716	Lelio R Paula	10/2014
4471	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
4472	2^278077+1867211	83710	Enzo Doria	03/2016
4473	2^278059-27	83705	Lelio R Paula	06/2012
4474	214^35917+35917^214	83702	Norbert Schneider	12/2014
4475	(23*10^83693+7)/3	83694	Robert Price	10/2015
4476	85^43375-2	83689	Lelio R Paula	09/2013
4477	5*3^175360+4	83669	Lelio R Paula	07/2014
4478	(23^61441-1)/22	83665	Robert Price	01/2012
4479	20091^14596+14596^20091	83664	Hans Havermann	03/2017
4480	2^277907-110629	83659	Enzo Doria	05/2014
4481	19522^19283+19283^19522	83656	Hans Havermann	04/2017
4482	8*5^119664-3	83643	Lelio R Paula	10/2014
4483	8*3^175299-7	83640	Lelio R Paula	07/2014
4484	3^175250+22	83616	Robert Price	12/2013
4485	11^80285+30	83609	Lelio R Paula	10/2015
4486	26870^1293+1293^26870	83609	Hans Havermann	03/2017
4487	2^277691+1874423	83594	Enzo Doria	06/2016
4488	13^75022-60	83571	Lelio R Paula	11/2015
4489	14^72905-51	83559	Lelio R Paula	11/2015
4490	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
4491	5^119532-12	83550	Lelio R Paula	10/2015
4492	6^107358-16253	83541	Enzo Doria	02/2013
4493	2^277478-460211	83530	Enzo Doria	06/2015
4494	(22*10^83525-7)/3	83526	Erik Branger	09/2014
4495	(30^56543+1)/31	83520	Robert Price	07/2013
4496	2^277417-460783	83511	Paul Bourdelais	04/2013
4497	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
4498	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
4499	21368^8085+8085^21368	83500	Hans Havermann	04/2017
4500	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012

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Probable Primes Top 10000

(177649 PRPs in the top)