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	2^348003-20377	104760	Enzo Doria	06/2013
4253	2^347994-741	104757	Lelio R Paula	12/2016
4252	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
4254	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
4255	25137^14702+14702^25137	104756	Hans Havermann	09/2020
4256	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
4257	2^347910-109937	104732	Enzo Doria	04/2014
4258	(88*10^104709-637)/9	104710	Robert Price	11/2020
4259	5^149794+28	104702	Lelio R Paula	11/2016
4260	105^51800-2	104698	Lelio R Paula	10/2017
4261	(16^86939+3^86939)/19	104684	Robert Price	06/2013
4262	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
4263	2^347731-18609	104678	Enzo Doria	05/2013
4264	4*6^134519+7	104677	Lelio R Paula	11/2014
4265	25321^13588+13588^25321	104656	Hans Havermann	09/2020
4266	2^347612-18545	104642	Enzo Doria	05/2013
4268	6^134465+95	104635	Lelio R Paula	11/2016
4267	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
4269	(166*10^104633-7)/3	104635	Robert Price	11/2020
4270	2^347517-17301	104614	Enzo Doria	05/2013
4271	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
4272	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
4273	3^219222-310	104596	Lelio R Paula	11/2016
4274	25993^10554+10554^25993	104581	Hans Havermann	09/2020
4275	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
4276	2^347372-17853	104570	Enzo Doria	05/2013
4277	2^347314+99	104552	Lelio R Paula	09/2011
4278	2^347300-22233	104548	Enzo Doria	06/2013
4279	2^347287-19845	104544	Enzo Doria	06/2013
4280	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
4281	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
4282	7*2^347239-3	104531	Lelio R Paula	09/2014
4283	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
4284	5*3^219047+8	104513	Lelio R Paula	09/2014
4285	2^347148-109073	104502	Enzo Doria	04/2014
4286	2^347129-20145	104497	Enzo Doria	06/2013
4287	4*10^104461-57	104462	Robert Price	10/2018
4288	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
4289	2^346923-19585	104435	Enzo Doria	05/2013
4290	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
4291	2^346854+346854^2+1	104414	Robert Price	06/2014
4292	2^346834+11715	104408	Lelio R Paula	04/2015
4293	24276^19961+19961^24276	104392	Hans Havermann	09/2020
4294	79^55009+78	104387	Norbert Schneider	02/2015
4295	3^218744+58	104368	Lelio R Paula	11/2016
4296	9*10^104361+89	104362	Robert Price	11/2019
4297	25048^14665+14665^25048	104358	Hans Havermann	09/2020
4298	2^346649+65	104352	Lelio R Paula	09/2011
4299	2^346638-17265	104349	Enzo Doria	05/2013
4300	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
4301	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
4302	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
4303	26092^9967+9967^26092	104331	Hans Havermann	09/2020
4304	5*10^104326+77	104327	Robert Price	12/2018
4305	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
4306	2^346527-111817	104316	Enzo Doria	05/2014
4307	6^134055+101	104316	Lelio R Paula	11/2016
4308	92105!4+8	104312	Robert Price	09/2019
4309	6^134013+163	104283	Lelio R Paula	11/2016
4310	18^83049-89	104250	Lelio R Paula	01/2017
4311	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
4312	2^346213+484049	104221	Enzo Doria	04/2017
4313	18^83021-91	104214	Lelio R Paula	01/2017
4315	10^104212+128779	104213	Patrick De Geest	05/2016
4316	10^104212+237447	104213	Patrick De Geest	05/2016
4317	10^104212+242139	104213	Patrick De Geest	05/2016
4318	10^104212+269199	104213	Patrick De Geest	05/2016
4314	24254^19803+19803^24254	104213	Hans Havermann	09/2020
4319	(10^104212-71)/1	104212	Serge Batalov	12/2014
4320	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
4321	2^346078+7695	104180	Lelio R Paula	12/2016
4322	2^346055-19537	104173	Enzo Doria	05/2013
4323	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
4324	2^346037-20125	104168	Enzo Doria	06/2013
4325	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
4326	6^133854-17993	104159	Enzo Doria	03/2013
4327	2^345990+1874239	104154	Enzo Doria	06/2016
4328	2^345988-20373	104153	Enzo Doria	06/2013
4329	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
4330	(26*10^104132-503)/9	104133	Robert Price	07/2018
4331	3*5^148968+8	104125	Lelio R Paula	11/2014
4332	(7*10^104113+53)/3	104114	Robert Price	05/2018
4333	p(21253)#/2+8	104113	Robert Price	01/2017
4334	33582^1259+1259^33582	104106	Hans Havermann	09/2020
4335	32958^1441+1441^32958	104104	Hans Havermann	09/2020
4336	29127^3748+3748^29127	104095	Hans Havermann	09/2020
4337	322^41507+41507^322	104094	Norbert Schneider	12/2014
4338	6^133768-17423	104092	Enzo Doria	03/2013
4339	2^345786-19557	104092	Enzo Doria	05/2013
4340	171^46606-2	104072	Lelio R Paula	10/2017
4341	(29*10^104071+91)/3	104072	Robert Price	04/2020
4342	2^345704-149	104068	Lelio R Paula	09/2011
4343	25821^10712+10712^25821	104056	Hans Havermann	09/2020
4344	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
4345	6^133704-17273	104042	Enzo Doria	02/2013
4346	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
4347	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
4348	2^345547+11	104021	Lelio R Paula	09/2011
4349	(19*10^104014-49)/3	104015	Robert Price	05/2019
4350	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
4351	2^345504+723	104008	Lelio R Paula	09/2011
4352	2^345498-20037	104006	Enzo Doria	06/2013
4354	18^82854-37	104005	Lelio R Paula	01/2017
4353	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
4355	2^345486-109065	104002	Enzo Doria	04/2014
4356	2^345487-1851507	104002	Enzo Doria	08/2015
4358	2^345476+777	103999	Lelio R Paula	09/2011
4357	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
4359	4*10^103981-83	103982	Robert Price	10/2018
4360	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
4361	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
4362	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
4363	(19*10^103907+77)/3	103908	Robert Price	05/2019
4364	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
4365	2^345106-112181	103888	Enzo Doria	06/2014
4366	2^345079+99	103880	Lelio R Paula	09/2011
4367	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
4368	11^99736-1500	103865	Enzo Doria	12/2012
4369	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
4370	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
4371	23927^21814+21814^23927	103813	Hans Havermann	09/2020
4372	2^344842-20157	103808	Enzo Doria	06/2013
4373	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
4374	2^344802-20765	103796	Enzo Doria	06/2013
4375	2^344794-3821	103794	Yves Minet	05/2011
4376	2^344782-109103	103790	Enzo Doria	04/2014
4377	3^217521-112292	103784	Enzo Doria	06/2014
4378	2^344759-3505	103783	Lelio R Paula	11/2016
4379	2^344735-147	103776	Lelio R Paula	09/2011
4380	L(496533)-p(496533)	103770	Robert Price	02/2018
4381	2*10^103749-69	103750	Robert Price	03/2018
4382	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
4383	2^344607-108891	103738	Enzo Doria	03/2014
4384	(148*10^103718-1)/3	103720	Robert Price	03/2020
4385	2^344541-19561	103718	Enzo Doria	05/2013
4386	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
4387	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
4388	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
4389	2^344444-455	103688	Yves Minet	03/2012
4390	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
4391	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
4393	2^344317-109933	103650	Enzo Doria	04/2014
4392	26055^9508+9508^26055	103650	Hans Havermann	09/2020
4394	2^344309-1852033	103648	Enzo Doria	08/2015
4395	25729^10672+10672^25729	103643	Hans Havermann	09/2020
4396	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
4397	3*10^103637+61	103638	Robert Price	09/2020
4398	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
4399	2^344213-21253	103619	Enzo Doria	06/2013
4400	2^344196-465	103614	Lelio R Paula	11/2016
4401	2^344187-20001	103611	Enzo Doria	06/2013
4402	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
4403	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
4404	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
4405	2^344085-20365	103580	Enzo Doria	06/2013
4406	5^148169+54	103566	Lelio R Paula	11/2016
4407	2^344017-108795	103560	Enzo Doria	03/2014
4408	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
4409	2^343971-5077	103546	Lelio R Paula	09/2011
4410	(7*10^103531+71)/3	103532	Robert Price	05/2018
4411	2^343899+141	103524	Lelio R Paula	08/2011
4412	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
4413	6^133029-67	103517	Lelio R Paula	11/2016
4414	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
4415	66*10^103507+7	103509	Robert Price	07/2020
4416	26297^8614+8614^26297	103485	Hans Havermann	09/2020
4417	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
4418	26499^8036+8036^26499	103480	Hans Havermann	09/2020
4419	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
4420	5^148014-24	103458	Lelio R Paula	11/2016
4421	28316^4503+4503^28316	103453	Hans Havermann	09/2020
4422	(22*10^103450+53)/3	103451	Robert Price	07/2019
4423	2^343604+9931	103436	Yves Minet	01/2011
4424	2^343601-21189	103435	Enzo Doria	06/2013
4425	2^343508-115229	103407	Enzo Doria	06/2015
4426	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
4427	3^216685-113056	103386	Enzo Doria	07/2014
4428	24829^14580+14580^24829	103382	Hans Havermann	08/2020
4429	91355!4+1024	103381	Robert Price	09/2019
4430	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
4431	11^99262-20	103371	Lelio R Paula	12/2016
4432	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
4433	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
4434	2^343356-2791889	103361	Enzo Doria	03/2016
4435	(25*10^103360-241)/9	103361	Robert Price	05/2018
4436	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
4437	24826^14511+14511^24826	103319	Hans Havermann	09/2020
4438	2^343182-171	103309	Lelio R Paula	08/2011
4439	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
4440	2^343079-1835611	103278	Enzo Doria	05/2015
4441	2^343063-1147	103273	Yves Minet	06/2013
4442	24741^14930+14930^24741	103271	Hans Havermann	09/2020
4443	(16*10^103255-73)/3	103256	Robert Price	07/2020
4444	9*6^132689+7	103254	Lelio R Paula	11/2014
4445	2^342979-18085	103247	Enzo Doria	05/2013
4446	(16*10^103244-31)/3	103245	Robert Price	03/2019
4447	2^342966-16995	103244	Lelio R Paula	11/2016
4448	23797^21774+21774^23797	103230	Hans Havermann	09/2020
4449	25388^11637+11637^25388	103224	Hans Havermann	09/2020
4450	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
4451	(16*10^103214-31)/3	103215	Robert Price	03/2019
4453	(37*10^103211+611)/9	103212	Robert Price	11/2018
4452	(238*10^103210-1)/3	103212	Robert Price	04/2020
4454	5^147650+16	103203	Lelio R Paula	11/2016
4455	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
4456	2^342817+2707067	103199	Enzo Doria	03/2016
4457	43^63177-42	103198	Theodore Burton	02/2007
4458	2^342805-21025	103195	Enzo Doria	06/2013
4459	24129^18890+18890^24129	103182	Hans Havermann	09/2020
4460	2^342714+12285	103168	Lelio R Paula	11/2016
4461	18^82178-4481	103156	Enzo Doria	03/2013
4462	2^342665-17349	103153	Enzo Doria	05/2013
4463	30408^2467+2467^30408	103150	Hans Havermann	09/2020
4464	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
4465	2^342612+175	103137	Lelio R Paula	08/2011
4466	5*2^342585-3	103130	Lelio R Paula	09/2014
4467	(16*10^103127+77)/3	103128	Robert Price	03/2019
4468	2^342503-19209	103104	Enzo Doria	05/2013
4469	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
4470	2^342476+51	103096	Lelio R Paula	08/2011
4471	2^342460-18885	103091	Enzo Doria	05/2013
4472	(194*10^103074-17)/3	103076	Robert Price	09/2020
4473	7^121968+82	103075	Lelio R Paula	10/2016
4474	2^342392-108863	103071	Enzo Doria	03/2014
4475	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
4476	3^216014+28	103065	Lelio R Paula	11/2016
4477	2^342353-108879	103059	Enzo Doria	03/2014
4478	10^103055+276081	103056	Patrick De Geest	12/2016
4479	10^103055-53	103055	Lelio R Paula	11/2016
4480	(58*10^103046+419)/9	103047	Robert Price	05/2019
4481	7^121933+4	103046	Lelio R Paula	11/2014
4482	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
4483	19^80560-68	103017	Lelio R Paula	10/2016
4484	2^342209+76607	103016	Enzo Doria	05/2016
4486	328^40945+40945^328	103013	Norbert Schneider	12/2014
4485	12^95454-91	103013	Lelio R Paula	10/2016
4487	25833^9716+9716^25833	103009	Hans Havermann	01/2019
4488	65^56809-64^56809	102990	Robert Price	08/2013
4489	5^147338-6	102985	Lelio R Paula	11/2014
4490	2^342084-112739	102978	Enzo Doria	06/2014
4491	9*6^132330+7	102974	Lelio R Paula	11/2014
4492	2^342034-16737	102963	Enzo Doria	05/2013
4493	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
4494	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
4495	2^341991-17421	102950	Enzo Doria	05/2013
4496	2^341969-112225	102943	Enzo Doria	06/2014
4497	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
4498	2^341859+1869413	102910	Enzo Doria	05/2016
4499	10^102909+61	102910	Lelio R Paula	11/2016
4500	10^102909-67049	102909	Patrick De Geest	12/2016

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