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 ?
4251	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
4252	2^318496-97305	95877	Lelio R Paula	03/2016
4253	2^318466+15015	95868	Lelio R Paula	03/2016
4254	6^123187-173129	95859	Mike Oakes	04/2011
4255	2^318423-487	95855	Yves Minet	03/2012
4256	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
4257	45369!2+1024	95787	Robert Price	02/2015
4258	3^200758-86	95786	Lelio R Paula	05/2016
4259	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
4260	3*10^95776-59	95777	Robert Price	10/2017
4261	193^41901-2	95768	Lelio R Paula	10/2017
4262	4*10^95752-71	95753	Robert Price	11/2017
4263	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
4264	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
4265	4*10^95672+91	95673	Robert Price	11/2017
4266	(11*10^95641-113)/3	95642	Robert Price	01/2017
4267	(13*10^95588+11)/3	95589	Robert Price	05/2015
4268	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
4269	3^200325+70	95580	Lelio R Paula	05/2016
4270	(25*10^95574-7)/9	95575	Robert Price	12/2014
4271	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
4272	2^317464+31	95567	Lelio R Paula	11/2012
4273	7^113073+82	95558	Lelio R Paula	04/2016
4274	2^317251+465	95503	Lelio R Paula	03/2016
4275	19^74684+58	95503	Lelio R Paula	06/2016
4276	(2^317250-7)/339	95500	Lelio R Paula	07/2013
4277	6^122718-79	95494	Lelio R Paula	05/2016
4278	2^317141-110491	95469	Enzo Doria	05/2014
4279	2^317094+76309	95455	Enzo Doria	05/2016
4280	2^317085+95	95453	Lelio R Paula	11/2012
4281	(17*10^95451-377)/9	95452	Robert Price	11/2017
4282	2^317057-109551	95444	Enzo Doria	04/2014
4283	3^200026+28	95437	Lelio R Paula	05/2016
4284	2^317024+93	95434	Donovan Johnson	06/2008
4285	2^316999+1605	95427	Lelio R Paula	03/2016
4286	2^316995-110427	95426	Enzo Doria	05/2014
4288	2^316937+177	95408	Lelio R Paula	11/2012
4287	4*10^95407+91	95408	Robert Price	11/2017
4289	2^316908+1915	95399	Lelio R Paula	03/2016
4290	2^316894+99	95395	Lelio R Paula	11/2012
4291	6^122547+11	95361	Lelio R Paula	05/2016
4292	2^316771+82875	95358	Lelio R Paula	03/2016
4294	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
4293	1*10^95326+57	95327	Robert Price	03/2011
4295	10^95326-393687	95326	Patrick De Geest	09/2013
4296	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
4297	2^316654-109481	95323	Enzo Doria	04/2014
4298	8*10^95316+51	95317	Robert Price	05/2017
4299	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
4300	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
4301	(71*10^95277-539)/9	95278	Robert Price	11/2017
4302	19^74503-56	95271	Lelio R Paula	06/2016
4303	11^91475-4380	95262	Enzo Doria	01/2013
4304	(62*10^95251-611)/9	95252	Robert Price	05/2017
4305	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
4306	(79*10^95214-43)/9	95215	Erik Branger	11/2013
4307	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
4308	5*2^316213+9	95191	Lelio R Paula	08/2014
4309	2^316205-1848163	95188	Enzo Doria	07/2015
4310	2^316185-2787913	95182	Enzo Doria	04/2016
4311	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
4312	2^316140-5	95168	Henri Lifchitz	02/2006
4313	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
4314	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
4315	2^316069+76817	95147	Enzo Doria	05/2016
4316	(199*10^95134-7)/3	95136	Robert Price	02/2017
4317	2^316027-97305	95134	Lelio R Paula	03/2016
4318	2^316006-2798051	95128	Enzo Doria	04/2016
4319	2^315921-2797603	95102	Enzo Doria	04/2016
4320	2*10^95095+63	95096	Robert Price	10/2017
4321	2^315857+1299	95083	Lelio R Paula	03/2016
4322	14^82955-43	95078	Lelio R Paula	06/2016
4323	(2*10^95072-17)/3	95072	Robert Price	08/2014
4324	2^315727+65	95044	Lelio R Paula	11/2012
4325	2^315725+1885757	95043	Enzo Doria	03/2017
4326	1*10^94983+21	94984	Robert Price	03/2011
4327	10^94983-717	94983	Patrick De Geest	08/2013
4328	17^77187-82	94975	Lelio R Paula	07/2016
4329	3*10^94964+37	94965	Robert Price	10/2017
4330	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
4331	2^315423-110329	94952	Enzo Doria	05/2014
4332	11^91169-7230	94943	Enzo Doria	02/2013
4333	7*10^94938+61	94939	Robert Price	02/2017
4334	2^315351+1025	94931	Lelio R Paula	03/2016
4335	2^315350-112253	94930	Enzo Doria	06/2014
4337	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
4336	2^315268+7	94906	Lelio R Paula	10/2012
4338	11^91133+62	94906	Lelio R Paula	05/2016
4339	30^64244+41	94897	Lelio R Paula	08/2012
4340	(151*10^94885-7)/9	94887	Robert Price	07/2017
4341	4^157583+22147	94875	Mike Oakes	01/2011
4342	2^315098+123	94854	Lelio R Paula	11/2012
4343	3^198791-34	94848	Robert Price	11/2013
4344	3*2^315067+7	94846	Lelio R Paula	08/2014
4345	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
4346	(16*10^94822+53)/3	94823	Robert Price	12/2016
4347	8*6^121849-7	94818	Lelio R Paula	10/2014
4348	(85*10^94802+473)/9	94803	Robert Price	03/2017
4349	2^314870-108761	94786	Enzo Doria	03/2014
4350	5*2^314841-3	94778	Lelio R Paula	08/2014
4351	6^121772+113	94758	Lelio R Paula	05/2016
4352	6^121756-16253	94745	Enzo Doria	02/2013
4353	2^314718-112793	94740	Enzo Doria	06/2014
4354	2^314697-1847293	94734	Enzo Doria	07/2015
4355	2^314548-249	94689	Yves Minet	02/2012
4356	5^135469+42	94689	Lelio R Paula	04/2016
4357	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
4358	(2*10^94604+547)/9	94604	Robert Price	10/2017
4359	3*2^314152+5	94570	Lelio R Paula	08/2014
4360	2*6^121530-5	94570	Lelio R Paula	10/2014
4361	7*10^94563+87	94564	Robert Price	11/2016
4362	2^314114-109677	94558	Enzo Doria	04/2014
4363	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
4364	2^314059+76583	94542	Enzo Doria	05/2016
4365	2^314041-4035	94536	Lelio R Paula	03/2016
4366	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
4367	11^90760-4710	94517	Enzo Doria	01/2013
4368	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
4369	94*10^94493-3	94495	Robert Price	11/2016
4370	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
4371	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
4372	7^111792-32	94476	Lelio R Paula	04/2016
4373	11^90680-5850	94434	Enzo Doria	01/2013
4374	2^313675-110125	94426	Enzo Doria	04/2014
4375	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
4376	2^313609-112225	94406	Enzo Doria	06/2014
4377	2^313584+72901	94399	Enzo Doria	04/2016
4378	2^313510-112865	94376	Enzo Doria	06/2014
4379	7*10^94373+87	94374	Robert Price	11/2016
4380	(9^98897+8^98897)/17	94371	Robert Price	12/2012
4381	2^313453-114703	94359	Enzo Doria	04/2015
4382	8*10^94357-51	94358	Robert Price	10/2017
4383	(379*10^94337-1)/9	94339	Robert Price	08/2017
4384	2^313344-313344+1	94326	Robert Price	10/2014
4385	20^72481-49	94300	Lelio R Paula	05/2016
4386	44725!2+128	94289	Robert Price	03/2015
4387	4*10^94286+9	94287	Robert Price	05/2015
4388	17^76621+24	94279	Lelio R Paula	07/2016
4389	2^313156-112859	94270	Enzo Doria	06/2014
4390	6^121130-59	94258	Lelio R Paula	05/2016
4391	3^197542+28	94252	Robert Price	11/2013
4392	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
4393	2^313045-5955	94236	Lelio R Paula	03/2016
4394	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
4395	2^312909-1865203	94195	Enzo Doria	03/2016
4396	2^312848-149	94177	Lelio R Paula	11/2012
4397	4^156403-77597	94164	Mike Oakes	04/2011
4398	18^75004-85	94151	Lelio R Paula	06/2016
4399	19^73622-48	94145	Lelio R Paula	06/2016
4400	(11^90397-3^90397)/8	94138	Robert Price	04/2011
4401	(3^197287+5)/16	94129	Lelio R Paula	04/2013
4402	12^87212-37	94118	Lelio R Paula	06/2016
4403	11^90376+76	94117	Lelio R Paula	05/2016
4404	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
4405	(10^94096+191)/3	94096	Robert Price	11/2017
4406	2^312562-112685	94091	Enzo Doria	06/2014
4407	137^44026-2	94072	Lelio R Paula	10/2017
4408	2^312404-869688105	94043	Lelio R Paula	09/2016
4409	2^312387+2793533	94038	Enzo Doria	03/2016
4411	10^94016+91	94017	Robert Price	04/2011
4410	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4413	10^94016-188963	94016	Patrick De Geest	08/2013
4412	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4414	6^120802+7661	94003	Mike Oakes	04/2011
4415	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4416	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4417	2^312201+51	93982	Lelio R Paula	11/2012
4418	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4419	3^196892+58	93942	Lelio R Paula	05/2016
4420	2^312060+18915	93940	Lelio R Paula	03/2016
4421	42^57867-41	93933	Norbert Schneider	08/2018
4422	2^311992-16209	93919	Enzo Doria	04/2013
4423	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4424	2^311965-39	93911	Lelio R Paula	11/2012
4425	2^311920-111689	93898	Enzo Doria	05/2014
4426	130^44414+129	93889	Norbert Schneider	01/2019
4427	7*10^93887-47	93888	Robert Price	02/2017
4428	12^86965-13	93851	Lelio R Paula	06/2016
4429	2^311705+16095	93833	Lelio R Paula	03/2016
4430	2^311665-81	93821	Lelio R Paula	11/2012
4431	730^32761+32761^730	93806	Norbert Schneider	09/2017
4432	11^90073+92	93802	Lelio R Paula	05/2016
4433	6*10^93792+41	93793	Robert Price	01/2017
4434	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4435	12^86900-77	93781	Lelio R Paula	06/2016
4436	2^311508-109769	93774	Enzo Doria	04/2014
4437	2^311486-1859621	93767	Enzo Doria	03/2016
4438	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4439	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4440	2^311471+311469	93763	Renaud Lifchitz	01/2003
4441	(88*10^93760-1)/3	93762	Robert Price	10/2017
4442	2^311426+79459	93749	Enzo Doria	06/2016
4443	2^311294+5775	93709	Lelio R Paula	03/2016
4444	2^311252-1017	93697	Lelio R Paula	03/2016
4445	2^311247-112041	93695	Enzo Doria	06/2014
4446	7*10^93692-83	93693	Robert Price	09/2017
4447	2^311205-109645	93683	Enzo Doria	04/2014
4448	5^134027-84	93681	Lelio R Paula	04/2016
4449	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4450	(2^311027-2^155514+1)/5	93628		11/2006
4451	3^196192-28	93608	Robert Price	12/2013
4452	216091#+261433	93606	Makoto Morimoto	12/2015
4453	5^133917+68	93604	Lelio R Paula	04/2016
4454	2^310924-1709	93598	Yves Minet	03/2013
4455	(266*10^93577-11)/3	93579	Robert Price	09/2016
4456	(16*10^93577+161)/3	93578	Robert Price	05/2016
4457	3^196113-56	93570	Lelio R Paula	04/2016
4458	2^310806-110345	93562	Enzo Doria	05/2014
4459	3^196093+86	93561	Lelio R Paula	04/2016
4460	2^310780-2327	93555	Yves Minet	10/2013
4461	30^63332+41	93550	Lelio R Paula	08/2012
4462	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4463	8*5^133807+7	93528	Lelio R Paula	10/2014
4464	2^310686+8193	93526	Lelio R Paula	03/2016
4465	2^310646+63	93514	Lelio R Paula	11/2012
4466	(77*10^93508+31)/9	93509	Robert Price	10/2015
4467	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4468	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4469	3^195958-112852	93496	Enzo Doria	07/2014
4470	2^310583+16385	93495	Lelio R Paula	03/2016
4471	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4472	9*7^110614+2	93481	Lelio R Paula	11/2014
4473	2^310469-8295	93461	Lelio R Paula	03/2016
4474	2^310459-1159	93458	Yves Minet	11/2012
4475	6^120075-95	93437	Lelio R Paula	05/2016
4476	148^43041-147	93411	Norbert Schneider	05/2019
4477	2^310289+98327	93407	Yves Minet	11/2010
4478	2^310217-113143	93385	Enzo Doria	07/2014
4479	7^110494-68	93379	Lelio R Paula	04/2016
4480	2^310184-113093	93375	Enzo Doria	07/2014
4481	2^310180-110417	93374	Enzo Doria	05/2014
4482	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4483	3^195669+68	93358	Lelio R Paula	04/2016
4484	10^93356+91	93357	Robert Price	04/2011
4485	10^93356-28313	93356	Patrick De Geest	08/2013
4486	(85*10^93346+23)/9	93347	Robert Price	11/2015
4487	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4488	3^195556+8680	93304	Lelio R Paula	04/2016
4489	2^309942-109991	93302	Enzo Doria	04/2014
4490	2^309926-1867301	93298	Enzo Doria	03/2016
4491	2^309924+85951	93297	Yves Minet	03/2011
4492	2^309896-4229	93288	Yves Minet	08/2018
4493	(86*10^93263-77)/9	93264	Robert Price	05/2016
4494	6^119836-125	93251	Lelio R Paula	05/2016
4495	(77*10^93249-257)/9	93250	Robert Price	10/2017
4496	3^195430-2	93244	Theodore Burton	02/2007
4497	(13*10^93236+47)/3	93237	Robert Price	01/2017
4498	(67*10^93226-7)/3	93228	Robert Price	10/2017
4499	(86*10^93217-221)/9	93218	Robert Price	06/2017
4500	2^309637-16329	93211	Enzo Doria	04/2013

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Probable Primes Top 10000

(253476 PRPs in the top)