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	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
4252	2^303344-2786969	91316	Enzo Doria	03/2016
4253	6^117346+65	91313	Lelio R Paula	05/2016
4254	2^303321+855	91309	Lelio R Paula	02/2016
4255	12^84606+47	91306	Lelio R Paula	06/2016
4256	2^303288+1874311	91299	Enzo Doria	06/2016
4257	197^39788-2	91293	Lelio R Paula	10/2017
4258	11^87663-1710	91292	Enzo Doria	12/2012
4259	2^303224+2533	91280	Henri Lifchitz	05/2005
4260	6^117302+143	91279	Lelio R Paula	05/2016
4261	3^191306-112880	91277	Enzo Doria	07/2014
4262	2^303207+12915	91275	Lelio R Paula	02/2016
4263	2^303191-111259	91270	Enzo Doria	05/2014
4264	10^91230+9^(91230+1)	91231	Robert Price	08/2016
4265	10^91230+7921	91231	Patrick De Geest	11/2016
4266	10^91230-911141	91230	Patrick De Geest	11/2016
4267	6^117232-17423	91225	Enzo Doria	02/2013
4268	7*10^91215+3	91216	Erik Branger	11/2009
4269	97*10^91205-3	91207	Robert Price	01/2017
4270	2^302979-161181	91206	Enzo Doria	04/2013
4271	2^302949+81	91197	Henri Lifchitz	02/2007
4272	4*6^117192-5	91194	Lelio R Paula	10/2014
4273	2^302918+99	91188	Lelio R Paula	11/2012
4274	2^302797+1869587	91151	Enzo Doria	05/2016
4275	265^37614+37614^265	91148	Norbert Schneider	01/2015
4276	7^107852+82	91146	Lelio R Paula	04/2016
4277	(38*10^91144-11)/9	91145	Robert Price	05/2015
4278	(55*10^91142+377)/9	91143	Robert Price	10/2017
4279	249^38030+38030^249	91128	Norbert Schneider	01/2015
4280	6^117094-211049	91117	Mike Oakes	05/2011
4281	2^302602-1867181	91093	Enzo Doria	03/2016
4282	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
4283	15^77445-16	91083	Lelio R Paula	07/2016
4284	2^302505+81	91064	Henri Lifchitz	02/2007
4285	2^302496-112349	91061	Enzo Doria	06/2014
4286	17^73999-72	91052	Lelio R Paula	07/2016
4287	(16*10^91032+41)/3	91033	Robert Price	10/2017
4288	2^302332+577294575	91012	Lelio R Paula	08/2016
4289	2^302274+74209	90994	Enzo Doria	04/2016
4290	(311^36497-1)/310	90976	Eric Chen	09/2017
4291	(3^190668+2)/89	90970	Lelio R Paula	04/2013
4292	2^302188+90195	90968	Lelio R Paula	02/2016
4293	(53*10^90965-71)/9	90966	Robert Price	09/2015
4294	2^302113+74105	90946	Enzo Doria	04/2016
4295	2^302102-6555	90942	Lelio R Paula	02/2016
4297	156(10^(422731)-1)/101-1	90925	Robert Price	05/2014
4296	3^190568+38	90925	Lelio R Paula	04/2016
4298	2^302009-16449	90914	Enzo Doria	04/2013
4299	(17*2^301951-1)/165	90896	Lelio R Paula	02/2014
4300	3^190497+74	90891	Lelio R Paula	04/2016
4301	(24737*2^301896+1)/399	90882	Lelio R Paula	06/2014
4302	18^72397+89	90878	Lelio R Paula	06/2016
4303	6^116769-47	90864	Lelio R Paula	05/2016
4304	2^301712-465	90825	Lelio R Paula	02/2016
4305	2^301693-69	90819	Lelio R Paula	11/2012
4306	2^301683-301683^2	90816	Henri Lifchitz	05/2005
4307	11^87187-1710	90796	Enzo Doria	12/2012
4308	5*10^90793+21	90794	Robert Price	01/2017
4309	(22*10^90792-13)/9	90793	Robert Price	03/2015
4310	2^301591-1615	90788	Lelio R Paula	02/2016
4311	(52^52901+1)/53	90777	Paul Bourdelais	08/2017
4312	2^301546-109037	90775	Enzo Doria	04/2014
4313	14^79195-3	90768	Lelio R Paula	06/2016
4314	2^301517-1861693	90766	Enzo Doria	11/2015
4315	2^301460-173	90749	Lelio R Paula	11/2012
4316	(85*10^90745-103)/9	90746	Robert Price	10/2017
4317	2^301312-89	90704	Lelio R Paula	11/2012
4318	2^301285-129	90696	Lelio R Paula	11/2012
4319	2^301282-109991	90695	Enzo Doria	04/2014
4320	2^301228-1854269	90679	Enzo Doria	09/2015
4321	(151*10^90669-1)/3	90671	Robert Price	04/2017
4322	(32*10^90669+13)/9	90670	Robert Price	04/2015
4323	3*5^129698+8	90656	Lelio R Paula	10/2014
4324	F(433781)	90655	Henri Lifchitz	09/2003
4325	19^70891+82	90653	Lelio R Paula	06/2016
4326	(29*2^301124-1)/13	90648	Lelio R Paula	02/2014
4327	7*3^189953-8	90632	Lelio R Paula	08/2014
4328	11^87022-1800	90625	Enzo Doria	12/2012
4329	(2^301042+47)/12036969	90616	Lelio R Paula	06/2013
4330	2^301004-2786939	90612	Enzo Doria	03/2016
4331	2^300980-27	90605	Lelio R Paula	11/2012
4332	2*10^90597-7	90598	Dmitry Domanov	11/2010
4333	197^39485+2	90597	Lelio R Paula	06/2013
4334	7^107198+48	90593	Lelio R Paula	04/2016
4335	(86*10^90588+121)/9	90589	Robert Price	03/2017
4336	2^300923+53	90587	Lelio R Paula	11/2012
4337	2^300874+7	90573	Lelio R Paula	10/2012
4338	5^129568-56	90565	Lelio R Paula	04/2016
4339	2^300847-112831	90564	Enzo Doria	06/2014
4340	2^300718+255255	90526	Lelio R Paula	02/2016
4341	2^300637+95	90501	Lelio R Paula	11/2012
4342	7^107087-24	90500	Lelio R Paula	04/2016
4343	(10^90499+3^90499)/13	90498	Robert Price	01/2013
4344	13^81241+90	90498	Lelio R Paula	06/2016
4345	6^116273-85	90478	Lelio R Paula	05/2016
4346	6^116256-17573	90465	Enzo Doria	02/2013
4347	2^300502+54615	90461	Lelio R Paula	02/2016
4348	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
4349	(3^189545-8)/5	90436	Lelio R Paula	01/2013
4350	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
4351	4*5^129332+3	90400	Lelio R Paula	10/2014
4352	2^300249-16245	90384	Enzo Doria	04/2013
4353	(7*10^90371-313)/9	90371	Robert Price	11/2016
4354	2*6^116118+7	90358	Lelio R Paula	10/2014
4355	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
4356	4*10^90334-21	90335	Robert Price	04/2016
4357	2^300019-110335	90315	Enzo Doria	05/2014
4358	2^299949-1005	90294	Lelio R Paula	11/2013
4359	10^90279-1551	90279	Patrick De Geest	09/2018
4360	2^299868-109613	90270	Enzo Doria	04/2014
4361	10^90259-9443	90259	Patrick De Geest	09/2018
4362	10^90252-8103	90252	Patrick De Geest	09/2018
4363	5*2^299799-3	90250	Lelio R Paula	08/2014
4364	13^81008-2	90239	Lelio R Paula	09/2013
4365	64^49957-63^49957	90232	Robert Price	07/2013
4366	10^90227+56281	90228	Patrick De Geest	06/2016
4369	2^299725+315	90227	Lelio R Paula	11/2013
4367	10^90227-1000000001	90227	Robert Price	05/2016
4368	10^90227-68763	90227	Patrick De Geest	06/2016
4370	5^129082+48	90225	Lelio R Paula	03/2016
4371	2^299699+195	90219	Lelio R Paula	10/2012
4372	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
4373	10^90209+8971	90210	Patrick De Geest	09/2018
4374	10^90208-2247	90208	Patrick De Geest	09/2018
4375	116^43693-115	90203	Norbert Schneider	08/2018
4376	10^90202+3553	90203	Patrick De Geest	09/2018
4377	3^189053+280	90202	Lelio R Paula	04/2016
4378	2^299639-187	90201	Lelio R Paula	10/2012
4379	10^90199-2891	90199	Patrick De Geest	09/2018
4380	2^299631+183	90198	Lelio R Paula	10/2012
4381	10^90196-9683	90196	Patrick De Geest	09/2018
4382	10^90193-9809	90193	Patrick De Geest	09/2018
4383	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
4384	2^299567+113	90179	Lelio R Paula	10/2012
4385	2^299550+189	90174	Lelio R Paula	10/2012
4386	10^90170-6749	90170	Patrick De Geest	09/2018
4387	(2^299535+3)/29	90168	Lelio R Paula	01/2013
4388	10^90160-5613	90160	Patrick De Geest	09/2018
4389	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
4390	3^188938+8680	90147	Lelio R Paula	04/2016
4391	10^90146-2027	90146	Patrick De Geest	09/2018
4393	6^115840-55	90142	Lelio R Paula	05/2016
4392	(5*10^90142-473)/9	90142	Robert Price	12/2017
4394	8*7^106659+5	90139	Lelio R Paula	10/2014
4395	2^299406-16653	90131	Enzo Doria	05/2013
4397	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
4396	10^90128-8387	90128	Patrick De Geest	09/2018
4398	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
4399	6^115819-53	90125	Lelio R Paula	05/2016
4400	10^90123+6313	90124	Patrick De Geest	09/2018
4401	6^115816-16853	90123	Enzo Doria	02/2013
4402	6^115813-23	90121	Lelio R Paula	05/2016
4403	(22*10^90110+161)/3	90111	Robert Price	02/2017
4404	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
4405	10^90105-767	90105	Patrick De Geest	09/2018
4406	10^90104-7703	90104	Patrick De Geest	09/2018
4407	10^90103+9159	90104	Patrick De Geest	09/2018
4408	10^90101-3207	90101	Patrick De Geest	09/2018
4409	(29*10^90096-17)/3	90097	Erik Branger	09/2014
4410	10^90089-3573	90089	Patrick De Geest	09/2018
4411	2^299247+1870529	90083	Enzo Doria	05/2016
4412	10^90079+1609	90080	Patrick De Geest	09/2018
4413	2^299229-2797783	90077	Enzo Doria	04/2016
4414	2^299220-16317	90075	Enzo Doria	04/2013
4415	11^86491-1350	90072	Enzo Doria	12/2012
4416	10^90071-1233	90071	Patrick De Geest	09/2018
4417	10^90069-7841	90069	Patrick De Geest	09/2018
4418	(31*10^90064-1)/3	90066	Robert Price	03/2017
4419	10^90060-839	90060	Patrick De Geest	09/2018
4420	10^90052+2361	90053	Patrick De Geest	09/2018
4421	10^90047+619	90048	Patrick De Geest	09/2018
4422	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
4423	2^299112+73951	90042	Enzo Doria	04/2016
4424	8^99702+7^(99702-1)	90040	Robert Price	02/2016
4425	10^90038-9687	90038	Patrick De Geest	09/2018
4426	5*10^90033+3	90034	Dmitry Domanov	11/2010
4427	10^90030-1461	90030	Patrick De Geest	09/2018
4428	243^37738+37738^243	90029	Norbert Schneider	01/2015
4429	10^90025-8703	90025	Patrick De Geest	09/2018
4430	2^299048-113297	90023	Enzo Doria	07/2014
4431	10^90015+849	90016	Patrick De Geest	09/2018
4432	10^90010+6811	90011	Patrick De Geest	09/2018
4433	10^90008+847	90009	Patrick De Geest	09/2018
4434	3^188648+92	90008	Lelio R Paula	12/2015
4435	5*2^298991+7	90006	Lelio R Paula	08/2014
4436	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
4437	10^90000+8869	90001	Patrick De Geest	12/2009
4439	10^89999+82939	90000	Dirk Augustin	04/2007
4438	10^90000-140343	90000	Patrick De Geest	12/2009
4440	10^89999-194891	89999	Patrick De Geest	11/2009
4441	19^70365-78	89980	Lelio R Paula	12/2015
4442	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
4443	2^298852-64875	89964	Lelio R Paula	11/2013
4444	18^71659+37	89952	Lelio R Paula	12/2015
4445	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
4446	17^73067+20	89906	Lelio R Paula	11/2015
4447	2^298637-99	89899	Lelio R Paula	10/2012
4448	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
4449	9*10^89858+19	89859	Robert Price	05/2016
4450	2^298501+1870067	89858	Enzo Doria	05/2016
4451	11^86280-98	89852	Lelio R Paula	11/2015
4452	2^298473-110059	89850	Enzo Doria	04/2014
4453	19^70263-32	89850	Lelio R Paula	12/2015
4454	(299*10^89836-17)/3	89838	Robert Price	01/2017
4455	3^188286+14	89836	Robert Price	09/2013
4456	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
4457	2^298367+58905	89818	Lelio R Paula	11/2013
4458	2^298319-109657	89803	Enzo Doria	04/2014
4459	8*10^89800+81	89801	Robert Price	05/2017
4460	18^71505-91	89759	Lelio R Paula	12/2015
4461	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
4462	2^298079-109531	89731	Enzo Doria	04/2014
4463	117^43380+116	89718	Norbert Schneider	08/2018
4464	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
4465	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
4466	2^298003-66945	89708	Lelio R Paula	11/2013
4467	(23*10^89705-83)/3	89706	Robert Price	09/2017
4468	17^72900-54	89700	Lelio R Paula	11/2015
4469	3*2^297956+5	89695	Lelio R Paula	08/2014
4470	20^68938-11	89691	Lelio R Paula	01/2016
4471	89*10^89687-7	89689	Robert Price	03/2017
4472	2^297923+77783	89684	Enzo Doria	05/2016
4473	11^86107-24576000	89672	Enzo Doria	02/2013
4474	2^297878-111911	89671	Enzo Doria	05/2014
4475	7^106084+40	89652	Lelio R Paula	10/2015
4476	(86*10^89640-311)/9	89641	Robert Price	10/2017
4477	3*10^89608-59	89609	Robert Price	10/2017
4478	3^187780-11038	89594	Enzo Doria	05/2014
4479	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
4480	5^128141-36	89567	Lelio R Paula	10/2015
4481	4*7^105951+9	89540	Lelio R Paula	10/2014
4482	(7*10^89539-439)/9	89539	Robert Price	09/2017
4483	2^297397+177257	89526	Enzo Doria	05/2016
4484	2^297346-16241	89511	Enzo Doria	04/2013
4485	(5*10^89510+79)/3	89511	Robert Price	11/2017
4487	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
4486	2^297328-869688105	89505	Lelio R Paula	07/2016
4488	2^297325-459043	89504	Enzo Doria	05/2015
4489	2^297310-112391	89500	Enzo Doria	06/2014
4490	2^297296-112157	89496	Enzo Doria	06/2014
4491	57^50966-2	89490	Lelio R Paula	08/2013
4492	(266*10^89482+1)/3	89484	Robert Price	02/2016
4493	(14*10^89480-101)/3	89481	Robert Price	04/2017
4494	2^297122+99	89443	Lelio R Paula	10/2012
4495	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
4496	(25*10^89413+161)/3	89414	Robert Price	01/2017
4497	2^296990+1870699	89403	Enzo Doria	05/2016
4498	2^296972-1017	89398	Lelio R Paula	11/2013
4499	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
4500	(85*10^89375-31)/9	89376	Robert Price	11/2015

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Probable Primes Top 10000

(224926 PRPs in the top)