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	11^91133+62	94906	Lelio R Paula	05/2016
4252	30^64244+41	94897	Lelio R Paula	08/2012
4253	(151*10^94885-7)/9	94887	Robert Price	07/2017
4254	4^157583+22147	94875	Mike Oakes	01/2011
4255	2^315098+123	94854	Lelio R Paula	11/2012
4256	3^198791-34	94848	Robert Price	11/2013
4257	3*2^315067+7	94846	Lelio R Paula	08/2014
4258	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
4259	(16*10^94822+53)/3	94823	Robert Price	12/2016
4260	8*6^121849-7	94818	Lelio R Paula	10/2014
4261	(85*10^94802+473)/9	94803	Robert Price	03/2017
4262	2^314870-108761	94786	Enzo Doria	03/2014
4263	5*2^314841-3	94778	Lelio R Paula	08/2014
4264	6^121772+113	94758	Lelio R Paula	05/2016
4265	6^121756-16253	94745	Enzo Doria	02/2013
4266	2^314718-112793	94740	Enzo Doria	06/2014
4267	2^314697-1847293	94734	Enzo Doria	07/2015
4268	2^314548-249	94689	Yves Minet	02/2012
4269	5^135469+42	94689	Lelio R Paula	04/2016
4270	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
4271	(2*10^94604+547)/9	94604	Robert Price	10/2017
4272	3*2^314152+5	94570	Lelio R Paula	08/2014
4273	2*6^121530-5	94570	Lelio R Paula	10/2014
4274	7*10^94563+87	94564	Robert Price	11/2016
4275	2^314114-109677	94558	Enzo Doria	04/2014
4276	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
4277	2^314059+76583	94542	Enzo Doria	05/2016
4278	2^314041-4035	94536	Lelio R Paula	03/2016
4279	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
4280	11^90760-4710	94517	Enzo Doria	01/2013
4281	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
4282	94*10^94493-3	94495	Robert Price	11/2016
4283	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
4284	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
4285	7^111792-32	94476	Lelio R Paula	04/2016
4286	11^90680-5850	94434	Enzo Doria	01/2013
4287	2^313675-110125	94426	Enzo Doria	04/2014
4288	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
4289	2^313609-112225	94406	Enzo Doria	06/2014
4290	2^313584+72901	94399	Enzo Doria	04/2016
4291	2^313510-112865	94376	Enzo Doria	06/2014
4292	7*10^94373+87	94374	Robert Price	11/2016
4293	(9^98897+8^98897)/17	94371	Robert Price	12/2012
4294	2^313453-114703	94359	Enzo Doria	04/2015
4295	8*10^94357-51	94358	Robert Price	10/2017
4296	(379*10^94337-1)/9	94339	Robert Price	08/2017
4297	2^313344-313344+1	94326	Robert Price	10/2014
4298	20^72481-49	94300	Lelio R Paula	05/2016
4299	44725!2+128	94289	Robert Price	03/2015
4300	4*10^94286+9	94287	Robert Price	05/2015
4301	17^76621+24	94279	Lelio R Paula	07/2016
4302	2^313156-112859	94270	Enzo Doria	06/2014
4303	6^121130-59	94258	Lelio R Paula	05/2016
4304	3^197542+28	94252	Robert Price	11/2013
4305	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
4306	2^313045-5955	94236	Lelio R Paula	03/2016
4307	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
4308	2^312909-1865203	94195	Enzo Doria	03/2016
4309	2^312848-149	94177	Lelio R Paula	11/2012
4310	4^156403-77597	94164	Mike Oakes	04/2011
4311	18^75004-85	94151	Lelio R Paula	06/2016
4312	19^73622-48	94145	Lelio R Paula	06/2016
4313	(11^90397-3^90397)/8	94138	Robert Price	04/2011
4314	(3^197287+5)/16	94129	Lelio R Paula	04/2013
4315	12^87212-37	94118	Lelio R Paula	06/2016
4316	11^90376+76	94117	Lelio R Paula	05/2016
4317	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
4318	(10^94096+191)/3	94096	Robert Price	11/2017
4319	2^312562-112685	94091	Enzo Doria	06/2014
4320	137^44026-2	94072	Lelio R Paula	10/2017
4321	2^312404-869688105	94043	Lelio R Paula	09/2016
4322	2^312387+2793533	94038	Enzo Doria	03/2016
4324	10^94016+91	94017	Robert Price	04/2011
4323	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4326	10^94016-188963	94016	Patrick De Geest	08/2013
4325	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4327	6^120802+7661	94003	Mike Oakes	04/2011
4328	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4329	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4330	2^312201+51	93982	Lelio R Paula	11/2012
4331	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4332	3^196892+58	93942	Lelio R Paula	05/2016
4333	2^312060+18915	93940	Lelio R Paula	03/2016
4334	42^57867-41	93933	Norbert Schneider	08/2018
4335	2^311992-16209	93919	Enzo Doria	04/2013
4336	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4337	2^311965-39	93911	Lelio R Paula	11/2012
4338	2^311920-111689	93898	Enzo Doria	05/2014
4339	130^44414+129	93889	Norbert Schneider	01/2019
4340	7*10^93887-47	93888	Robert Price	02/2017
4341	12^86965-13	93851	Lelio R Paula	06/2016
4342	2^311705+16095	93833	Lelio R Paula	03/2016
4343	2^311665-81	93821	Lelio R Paula	11/2012
4344	730^32761+32761^730	93806	Norbert Schneider	09/2017
4345	11^90073+92	93802	Lelio R Paula	05/2016
4346	6*10^93792+41	93793	Robert Price	01/2017
4347	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4348	12^86900-77	93781	Lelio R Paula	06/2016
4349	2^311508-109769	93774	Enzo Doria	04/2014
4350	2^311486-1859621	93767	Enzo Doria	03/2016
4351	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4352	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4353	2^311471+311469	93763	Renaud Lifchitz	01/2003
4354	(88*10^93760-1)/3	93762	Robert Price	10/2017
4355	2^311426+79459	93749	Enzo Doria	06/2016
4356	2^311294+5775	93709	Lelio R Paula	03/2016
4357	2^311252-1017	93697	Lelio R Paula	03/2016
4358	2^311247-112041	93695	Enzo Doria	06/2014
4359	7*10^93692-83	93693	Robert Price	09/2017
4360	2^311205-109645	93683	Enzo Doria	04/2014
4361	5^134027-84	93681	Lelio R Paula	04/2016
4362	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4363	(2^311027-2^155514+1)/5	93628		11/2006
4364	3^196192-28	93608	Robert Price	12/2013
4365	216091#+261433	93606	Makoto Morimoto	12/2015
4366	5^133917+68	93604	Lelio R Paula	04/2016
4367	2^310924-1709	93598	Yves Minet	03/2013
4368	(266*10^93577-11)/3	93579	Robert Price	09/2016
4369	(16*10^93577+161)/3	93578	Robert Price	05/2016
4370	3^196113-56	93570	Lelio R Paula	04/2016
4371	2^310806-110345	93562	Enzo Doria	05/2014
4372	3^196093+86	93561	Lelio R Paula	04/2016
4373	2^310780-2327	93555	Yves Minet	10/2013
4374	30^63332+41	93550	Lelio R Paula	08/2012
4375	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4376	8*5^133807+7	93528	Lelio R Paula	10/2014
4377	2^310686+8193	93526	Lelio R Paula	03/2016
4378	2^310646+63	93514	Lelio R Paula	11/2012
4379	(77*10^93508+31)/9	93509	Robert Price	10/2015
4380	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4381	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4382	3^195958-112852	93496	Enzo Doria	07/2014
4383	2^310583+16385	93495	Lelio R Paula	03/2016
4384	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4385	9*7^110614+2	93481	Lelio R Paula	11/2014
4386	2^310469-8295	93461	Lelio R Paula	03/2016
4387	2^310459-1159	93458	Yves Minet	11/2012
4388	6^120075-95	93437	Lelio R Paula	05/2016
4389	148^43041-147	93411	Norbert Schneider	05/2019
4390	2^310289+98327	93407	Yves Minet	11/2010
4391	2^310217-113143	93385	Enzo Doria	07/2014
4392	7^110494-68	93379	Lelio R Paula	04/2016
4393	2^310184-113093	93375	Enzo Doria	07/2014
4394	2^310180-110417	93374	Enzo Doria	05/2014
4395	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4396	3^195669+68	93358	Lelio R Paula	04/2016
4397	10^93356+91	93357	Robert Price	04/2011
4398	10^93356-28313	93356	Patrick De Geest	08/2013
4399	(85*10^93346+23)/9	93347	Robert Price	11/2015
4400	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4401	3^195556+8680	93304	Lelio R Paula	04/2016
4402	2^309942-109991	93302	Enzo Doria	04/2014
4403	2^309926-1867301	93298	Enzo Doria	03/2016
4404	2^309924+85951	93297	Yves Minet	03/2011
4405	2^309896-4229	93288	Yves Minet	08/2018
4406	(86*10^93263-77)/9	93264	Robert Price	05/2016
4407	6^119836-125	93251	Lelio R Paula	05/2016
4408	(77*10^93249-257)/9	93250	Robert Price	10/2017
4409	3^195430-2	93244	Theodore Burton	02/2007
4410	(13*10^93236+47)/3	93237	Robert Price	01/2017
4411	(67*10^93226-7)/3	93228	Robert Price	10/2017
4412	(86*10^93217-221)/9	93218	Robert Price	06/2017
4413	2^309637-16329	93211	Enzo Doria	04/2013
4414	(41*10^93207+49)/9	93208	Robert Price	04/2016
4415	14^81312-57	93194	Lelio R Paula	06/2016
4416	41^57783-40	93192	Theodore Burton	02/2007
4417	3*10^93179-97	93180	Robert Price	08/2017
4418	5*7^110252-4	93175	Lelio R Paula	11/2014
4419	2^309380-27	93133	Lelio R Paula	11/2012
4420	23*10^93116-7	93118	Robert Price	03/2016
4421	(29*10^93082+1)/3	93083	Robert Price	11/2015
4422	(58*10^93062-13)/9	93063	Robert Price	09/2015
4423	2^309131+1869383	93058	Enzo Doria	05/2016
4424	2^309066-93	93039	Lelio R Paula	11/2012
4425	2^309063-113269	93038	Enzo Doria	07/2014
4426	3^194965+16	93022	Robert Price	10/2013
4427	2^308979+1869143	93012	Enzo Doria	05/2016
4428	5^133064+54	93008	Lelio R Paula	04/2016
4429	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4430	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4431	(2*10^92976-17)/3	92976	Robert Price	08/2014
4432	2^308809+37967	92961	Phil Moore	03/2008
4433	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4434	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4435	2^308650+513	92913	Lelio R Paula	02/2016
4436	5*7^109936+6	92908	Lelio R Paula	10/2014
4437	2*10^92897+89	92898	Robert Price	07/2016
4438	12^86073-29	92889	Lelio R Paula	06/2016
4439	2^308566-117	92888	Lelio R Paula	11/2012
4440	(17*10^92869-11)/3	92870	Robert Price	07/2015
4441	2^308459+75431	92856	Enzo Doria	04/2016
4442	2^308426-1866377	92846	Enzo Doria	03/2016
4443	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4444	2^308349-112111	92823	Enzo Doria	06/2014
4445	9*10^92821+19	92822	Robert Price	05/2016
4446	2^308337-75	92819	Lelio R Paula	11/2012
4447	4*3^194508+7	92805	Lelio R Paula	08/2014
4448	22*25^66379-113	92796	Curtis Bright	05/2015
4449	11^89101-1080	92790	Enzo Doria	12/2012
4450	2^308236-1867859	92789	Enzo Doria	04/2016
4451	12^85963+25	92770	Lelio R Paula	06/2016
4452	7^109750-66	92750	Lelio R Paula	04/2016
4453	9*10^92742+11	92743	Robert Kinser	01/2017
4454	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4455	2^307997-110655	92717	Enzo Doria	05/2014
4456	L(443609)	92709	Renaud Lifchitz	11/2003
4457	10^92691+9	92692	Robert Price	03/2011
4458	10^92691-252291	92691	Patrick De Geest	08/2013
4459	2^307879-2521	92681	Yves Minet	07/2014
4460	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4461	14^80831+47	92643	Lelio R Paula	06/2016
4462	15^78744+92	92611	Lelio R Paula	07/2016
4463	65^51083-64	92610	Norbert Schneider	11/2014
4464	131^43737-130	92604	Norbert Schneider	02/2019
4465	6^118996-16943	92597	Enzo Doria	02/2013
4466	(16*10^92591+41)/3	92592	Robert Price	10/2017
4467	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4468	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4469	(26*10^92546-77)/3	92547	Robert Price	02/2017
4470	3^193954+340	92540	Lelio R Paula	04/2016
4471	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4472	(17*10^92513-11)/3	92514	Robert Price	07/2015
4473	2^307318-4211	92512	Yves Minet	06/2011
4474	2^307280+193	92501	Lelio R Paula	11/2012
4475	20^71075-33	92471	Lelio R Paula	05/2016
4476	2^307126-78795	92455	Lelio R Paula	02/2016
4477	2^307125-49789	92454	Henri Lifchitz	08/2005
4478	2^307099+23	92447	Lelio R Paula	11/2012
4479	129^43798+128	92440	Norbert Schneider	01/2019
4480	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
4481	7*10^92414-69	92415	Robert Price	01/2017
4482	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4483	2^306915+1873373	92391	Enzo Doria	06/2016
4484	2^306908+12915	92389	Lelio R Paula	02/2016
4485	19^72244-80	92383	Lelio R Paula	06/2016
4487	2^306849+75	92371	Lelio R Paula	11/2012
4486	(397*10^92369+53)/9	92371	Robert Price	11/2017
4488	2^306813-869688105	92360	Lelio R Paula	08/2016
4489	2^306672-109059	92318	Enzo Doria	04/2014
4490	6^118604-17063	92292	Enzo Doria	02/2013
4491	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4492	2^306467-1835611	92256	Enzo Doria	04/2015
4493	2^306433+76427	92246	Enzo Doria	05/2016
4495	2^306430-113313	92245	Enzo Doria	07/2014
4494	(23*10^92244-59)/9	92245	Robert Price	03/2017
4496	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4497	(25*10^92186+59)/3	92187	Robert Price	05/2016
4498	2^306213-286183	92180	Enzo Doria	06/2015
4499	10^92178+61	92179	Robert Price	04/2011
4500	10^92178-175509	92178	Patrick De Geest	07/2013

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Probable Primes Top 10000

(252932 PRPs in the top)