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	2^338559-1858777	101917	Enzo Doria	04/2016
4252	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
4253	24502^14419+14419^24502	101903	Hans Havermann	01/2019
4254	2^338497-17041	101898	Enzo Doria	05/2013
4255	2^338475+54615	101892	Lelio R Paula	10/2016
4256	2^338426-19797	101877	Enzo Doria	06/2013
4257	2^338368-20369	101859	Enzo Doria	06/2013
4258	2^338366+74179	101859	Enzo Doria	04/2016
4259	27088^5755+5755^27088	101853	Hans Havermann	01/2019
4260	2^338280-19745	101833	Enzo Doria	06/2013
4261	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
4262	6^130841+103	101815	Lelio R Paula	10/2016
4263	2^338122-20117	101785	Enzo Doria	06/2013
4264	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
4265	35^65917-7092	101781	Enzo Doria	03/2013
4266	2^338010-19833	101752	Enzo Doria	06/2013
4267	3^213215-76	101730	Lelio R Paula	09/2016
4268	23907^17998+17998^23907	101730	Hans Havermann	01/2019
4269	10^101728+154953	101729	Patrick De Geest	02/2020
4272	2^337930+63	101728	Lelio R Paula	07/2011
4270	10^101728-987654321	101728	Robert Price	12/2019
4271	10^101728-60741	101728	Patrick De Geest	02/2020
4273	2^337920+1869661	101725	Enzo Doria	05/2016
4274	24116^16509+16509^24116	101715	Hans Havermann	01/2019
4275	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
4276	2^337859-19645	101706	Enzo Doria	05/2013
4277	2^337754+1869169	101675	Enzo Doria	05/2016
4278	3*10^101657-37	101658	Robert Price	07/2018
4279	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
4280	11^97605-24	101646	Lelio R Paula	10/2016
4281	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
4282	8^112539-112539	101633	Robert Price	01/2014
4283	25694^9003+9003^25694	101605	Hans Havermann	12/2018
4284	2^337515-19869	101603	Enzo Doria	06/2013
4285	2^337473+719	101590	Lelio R Paula	08/2011
4286	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
4287	2^337452-108815	101584	Enzo Doria	03/2014
4288	2^337453+1185	101584	Lelio R Paula	09/2016
4289	2^337410-113561	101571	Enzo Doria	08/2014
4290	2^337387+855	101564	Lelio R Paula	09/2016
4291	2^337367-17295	101558	Lelio R Paula	09/2016
4292	2^337342-109035	101551	Enzo Doria	04/2014
4293	23703^19238+19238^23703	101548	Hans Havermann	12/2018
4294	(26*10^101537-167)/3	101538	Robert Price	10/2019
4295	2^337267-19	101528	Lelio R Paula	07/2011
4296	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
4297	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
4298	2^337183-19989	101503	Enzo Doria	06/2013
4299	2^337149+72425	101492	Enzo Doria	04/2016
4300	24041^16642+16642^24041	101483	Hans Havermann	12/2018
4301	33982^969+969^33982	101482	Hans Havermann	12/2018
4302	2^337101-20241	101478	Enzo Doria	06/2013
4303	2^337035-20001	101458	Enzo Doria	06/2013
4304	(7*10^101456+89)/3	101457	Robert Price	08/2020
4305	2^337017-16995	101453	Lelio R Paula	09/2016
4306	2^336979-115315	101441	Enzo Doria	06/2015
4307	2^336970-20885	101439	Enzo Doria	06/2013
4308	2^336958+79	101435	Lelio R Paula	10/2009
4309	2^336942+169	101430	Lelio R Paula	10/2009
4310	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
4311	4*10^101415-89	101416	Robert Price	11/2018
4312	(14*10^101410-89)/3	101411	Robert Price	05/2020
4313	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
4314	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
4315	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
4316	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
4317	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
4318	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
4319	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
4320	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
4321	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
4322	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
4323	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
4324	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
4325	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
4326	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
4327	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
4328	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
4329	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
4330	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
4331	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
4332	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
4333	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
4334	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
4335	24097^16150+16150^24097	101405	Hans Havermann	12/2018
4336	2^336842+94065	101400	Lelio R Paula	09/2016
4337	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
4338	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
4339	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
4340	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
4341	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
4342	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
4343	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
4344	10^101369+203811	101370	Patrick De Geest	11/2016
4345	10^101369-99	101369	Lelio R Paula	09/2016
4346	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
4347	2^336701-113563	101358	Enzo Doria	08/2014
4348	89717!4-512	101351	Robert Price	11/2019
4349	2^336644-109023	101340	Enzo Doria	04/2014
4350	2^336601-21081	101327	Enzo Doria	06/2013
4351	20^77869+63	101310	Lelio R Paula	09/2016
4352	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
4353	6^130179-137	101299	Lelio R Paula	10/2016
4354	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
4355	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
4356	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
4357	2^336369-19753	101258	Enzo Doria	05/2013
4358	23842^17653+17653^23842	101253	Hans Havermann	11/2018
4359	2^336350-344291	101252	Enzo Doria	07/2015
4360	(56*10^101222-47)/9	101223	Robert Price	02/2019
4361	2^336243-108777	101220	Enzo Doria	03/2014
4362	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
4363	23535^19954+19954^23535	101202	Hans Havermann	11/2018
4364	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
4365	2^336150-20393	101192	Enzo Doria	06/2013
4366	23996^16473+16473^23996	101186	Hans Havermann	11/2018
4367	2^336112-1865249	101180	Enzo Doria	03/2016
4368	2^336103-109015	101178	Enzo Doria	04/2014
4369	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
4370	13^90809-96	101157	Lelio R Paula	10/2016
4371	26199^7258+7258^26199	101150	Hans Havermann	11/2018
4372	19^79098-30	101147	Lelio R Paula	10/2016
4373	19^79095+88	101144	Lelio R Paula	10/2016
4374	15^85976+32	101116	Lelio R Paula	10/2016
4375	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
4376	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
4377	(4^167933+17)/3	101106	Robert Price	02/2017
4379	2^335858+153	101104	Lelio R Paula	10/2009
4378	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
4380	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
4381	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
4382	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
4383	6^129918-35	101096	Lelio R Paula	10/2016
4384	3^211885-70	101095	Lelio R Paula	09/2016
4386	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
4385	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
4387	2^335818-20033	101092	Enzo Doria	06/2013
4388	2^335813-110083	101090	Enzo Doria	04/2014
4389	2^335804+2155	101088	Lelio R Paula	09/2016
4390	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
4391	2^335784-16145	101082	Enzo Doria	04/2013
4392	11^97051+62	101069	Lelio R Paula	10/2016
4393	3*10^101065+11	101066	Robert Price	07/2018
4394	27820^4293+4293^27820	101064	Hans Havermann	10/2018
4395	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
4396	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
4397	2^335658-94395	101044	Lelio R Paula	09/2016
4398	24514^13215+13215^24514	101024	Hans Havermann	11/2018
4399	2^335586+169	101022	Lelio R Paula	10/2009
4400	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
4401	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
4402	(19*10^100997+737)/9	100998	Robert Price	07/2018
4403	47599!2+1024	100991	Robert Price	02/2015
4404	2^335468-18629	100986	Enzo Doria	05/2013
4405	2^335454-20961	100982	Enzo Doria	06/2013
4406	10^100978+61	100979	Lelio R Paula	09/2016
4407	10^100978-156437	100978	Patrick De Geest	11/2016
4408	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
4409	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
4410	2^335403-1859167	100967	Enzo Doria	03/2016
4411	23599^18976+18976^23599	100962	Hans Havermann	10/2018
4412	6*10^100958+43	100959	Robert Price	07/2020
4413	9*2^335364-5	100956	Lelio R Paula	08/2014
4414	2^335349+72287	100951	Enzo Doria	04/2016
4415	2^335329+16095	100945	Lelio R Paula	09/2016
4416	232823#+233663	100937	Makoto Morimoto	10/2017
4417	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
4418	2^335237-20893	100917	Enzo Doria	06/2013
4419	2^335222-19337	100912	Enzo Doria	05/2013
4420	2^335222-109985	100912	Enzo Doria	04/2014
4421	2^335182-17237	100900	Enzo Doria	05/2013
4422	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
4424	2^335043-16737	100858	Enzo Doria	05/2013
4423	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
4425	2^335038-20633	100857	Enzo Doria	06/2013
4426	2^335031+1873373	100855	Enzo Doria	06/2016
4427	23489^19650+19650^23489	100847	Hans Havermann	10/2018
4428	3^211354-8816	100842	Enzo Doria	05/2014
4429	2^334984-112757	100841	Enzo Doria	06/2014
4430	(746*10^100827+1)/9	100829	Robert Price	03/2020
4431	29451^2648+2648^29451	100809	Hans Havermann	09/2018
4432	25583^8716+8716^25583	100806	Hans Havermann	08/2018
4434	2^334857+48527	100803	Lelio R Paula	08/2011
4433	12^93406+29	100803	Lelio R Paula	10/2016
4435	28780^3179+3179^28780	100796	Hans Havermann	09/2018
4436	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
4437	2^334809-13	100788	Lelio R Paula	04/2011
4438	(82*10^100780-1)/9	100781	Robert Price	12/2014
4439	31395^1622+1622^31395	100780	Hans Havermann	09/2018
4440	(2^334779+47)/5	100778	Lelio R Paula	12/2013
4441	2^334751+2049	100771	Lelio R Paula	09/2016
4442	13^90443-98	100749	Lelio R Paula	10/2016
4443	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
4444	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
4445	(7*10^100737+71)/3	100738	Robert Price	05/2018
4446	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
4447	15^85639-28	100720	Lelio R Paula	10/2016
4448	27068^5259+5259^27068	100718	Hans Havermann	08/2018
4449	2^334562+577294575	100711	Lelio R Paula	09/2016
4450	4*3^211077-5	100710	Lelio R Paula	08/2014
4451	2^334524+145	100702	Lelio R Paula	07/2009
4452	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
4453	27648^4375+4375^27648	100666	Hans Havermann	09/2018
4454	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
4455	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
4456	2^334294-113111	100633	Enzo Doria	07/2014
4457	25581^8582+8582^25581	100626	Hans Havermann	08/2018
4458	6^129308-17723	100622	Enzo Doria	03/2013
4459	6^129305+95	100619	Lelio R Paula	10/2016
4460	2^334244-1167	100618	Lelio R Paula	09/2016
4461	(2^334233+3066)/2	100614	Stefano Morozzi	09/2020
4462	(76*10^100611+77)/9	100612	Robert Price	10/2019
4463	7*10^100606-93	100607	Robert Price	08/2020
4464	(26*10^100566+49)/3	100567	Robert Price	08/2019
4465	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
4466	24885^10984+10984^24885	100555	Hans Havermann	07/2018
4467	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
4468	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
4469	23578^18367+18367^23578	100538	Hans Havermann	07/2018
4470	13^90251+24	100535	Lelio R Paula	10/2016
4471	2^333963+789	100533	Lelio R Paula	08/2011
4472	2^333919-1840087	100520	Enzo Doria	06/2015
4473	(2^333916+1698)/2	100519	Stefano Morozzi	09/2020
4474	2^333911+72623	100518	Enzo Doria	04/2016
4475	24605^12168+12168^24605	100517	Hans Havermann	08/2018
4476	66*10^100502+7	100504	Robert Price	07/2020
4477	18^80064-67	100503	Lelio R Paula	10/2016
4478	5^143742-48	100472	Lelio R Paula	10/2016
4479	24095^14784+14784^24095	100472	Hans Havermann	08/2018
4480	2^333757-112123	100471	Enzo Doria	06/2014
4481	7*10^100457-57	100458	Robert Price	06/2020
4482	27358^4693+4693^27358	100444	Hans Havermann	07/2018
4483	8*10^100439-51	100440	Robert Price	08/2019
4484	2^333603-108861	100425	Enzo Doria	03/2014
4485	9*7^118818-2	100414	Lelio R Paula	11/2014
4486	2^333546-17097	100408	Enzo Doria	05/2013
4487	17^81597+72	100401	Lelio R Paula	10/2016
4488	p(20559)#/2+8	100384	Robert Price	01/2017
4489	11^96390-24	100380	Lelio R Paula	10/2016
4490	(2^333385+2730)/2	100359	Stefano Morozzi	09/2020
4492	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
4491	23565^18136+18136^23565	100353	Hans Havermann	07/2018
4493	2^333354+763	100350	Lelio R Paula	08/2011
4494	(25*10^100343-67)/3	100344	Robert Price	06/2019
4495	2^333289-109483	100330	Enzo Doria	04/2014
4496	2^333240-2790209	100316	Enzo Doria	03/2016
4497	23601^17798+17798^23601	100314	Hans Havermann	05/2018
4499	(2^333227-2^166614+1)/5	100311		11/2006
4498	2^333225+719	100311	Lelio R Paula	08/2011
4500	2^333221-2785333	100310	Enzo Doria	10/2015

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Probable Primes Top 10000

(271023 PRPs in the top)