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 ?
5501	(5*10^122592+91)/3	122593	Robert Price	04/2018
5502	36751^2166+2166^36751	122589	Hans Havermann	03/2021
5503	(85*10^122585-1)/3	122587	Robert Price	02/2020
5504	29368^14931+14931^29368	122585	Hans Havermann	03/2021
5505	2^407179-112075	122574	Enzo Doria	06/2014
5506	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
5507	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
5508	(646*10^122533+11)/9	122535	Robert Price	10/2021
5509	2^407008-1867919	122522	Enzo Doria	04/2016
5510	11^117642-300	122512	Enzo Doria	10/2012
5511	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
5512	2^406949+72197	122504	Enzo Doria	04/2016
5513	(19*10^122501+149)/3	122502	Robert Price	05/2019
5514	28632^18977+18977^28632	122495	Hans Havermann	03/2021
5515	31815^7076+7076^31815	122481	Hans Havermann	03/2021
5516	2^406826-65	122467	Lelio R Paula	11/2013
5517	2^406821-2797363	122466	Enzo Doria	04/2016
5518	(7*10^122456-331)/9	122456	Robert Price	03/2022
5519	2^406758-17	122447	Lelio R Paula	11/2013
5520	29941^12282+12282^29941	122437	Hans Havermann	03/2021
5521	(30^82883-1)/29	122427	Robert Price	12/2011
5522	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
5523	28732^18215+18215^28732	122411	Hans Havermann	03/2021
5524	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
5525	4*10^122377+19	122378	Robert Price	10/2018
5526	28227^21634+21634^28227	122368	Hans Havermann	03/2021
5527	Phi(246362,10)	122365	Makoto Kamada	09/2019
5528	3*10^122345-97	122346	Robert Price	07/2018
5529	97^61575-2	122336	Lelio R Paula	12/2014
5530	2*10^122319+47	122320	Robert Price	12/2021
5531	208^52765+52765^208	122313	Norbert Schneider	11/2020
5533	2^406298+2799109	122308	Enzo Doria	04/2016
5532	2^406296+213691	122308	Enzo Doria	09/2023
5534	7*10^122294+57	122295	Robert Price	06/2019
5535	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
5536	2^406229-1849993	122288	Enzo Doria	08/2015
5537	3*10^122274+7	122275	Robert Price	07/2015
5538	2^406117+1876577	122254	Enzo Doria	07/2016
5539	29308^14835+14835^29308	122253	Hans Havermann	03/2021
5540	28119^22268+22268^28119	122253	Hans Havermann	03/2021
5541	32167^6312+6312^32167	122240	Hans Havermann	03/2021
5542	3^256199-2^256199	122238	Mike Oakes	06/2005
5543	27678^26053+26053^27678	122223	Hans Havermann	03/2021
5544	2^405992-78557	122216	Jorge Menendez	03/2018
5545	(8*10^122203+43)/3	122204	Robert Price	06/2018
5546	(58*10^122170+329)/9	122171	Robert Price	05/2019
5547	2^405774+179149	122151	Enzo Doria	06/2016
5548	2^405693+20417	122126	Enzo Doria	07/2023
5549	(218*10^122109+7)/9	122111	Robert Price	06/2022
5550	29189^15246+15246^29189	122103	Hans Havermann	03/2021
5552	34*10^122082-9	122084	Robert Price	06/2020
5551	33442^4473+4473^33442	122084	Hans Havermann	03/2021
5553	5*10^122082+41	122083	Robert Price	03/2019
5554	31849^6808+6808^31849	122078	Hans Havermann	03/2021
5556	2^405514-3311	122072	Yves Minet	12/2014
5557	2^405514-115511	122072	Enzo Doria	07/2015
5555	23*10^122070-7	122072	Robert Price	02/2020
5558	2^405422-113261	122045	Enzo Doria	07/2014
5559	95^61698-61698^95	122022	Norman Luhn	10/2024
5560	2^405173+71237	121970	Enzo Doria	04/2016
5561	fibonacci(583574)+2	121960	Jon Grantham	08/2023
5562	(154*10^121953+17)/9	121955	Robert Price	06/2022
5563	(34*10^121924+191)/9	121925	Robert Price	08/2021
5564	(2^405016+1)/257	121920	Lelio R Paula	04/2014
5565	28557^18590+18590^28557	121918	Hans Havermann	03/2021
5566	28641^18002+18002^28641	121877	Hans Havermann	03/2021
5567	2^404858+71329	121875	Enzo Doria	04/2016
5568	2^404813-114703	121861	Enzo Doria	04/2015
5569	2^404764+77791	121847	Enzo Doria	05/2016
5570	28830^16841+16841^28830	121847	Hans Havermann	03/2021
5571	(4*10^121825+89)/3	121826	Robert Price	08/2021
5572	317^48694+48694^317	121787	Norbert Schneider	08/2015
5573	2^404536-115259	121778	Enzo Doria	06/2015
5574	2^404501-631	121767	Yves Minet	07/2012
5575	5*10^121764-69	121765	Robert Price	02/2021
5576	28236^20485+20485^28236	121738	Hans Havermann	02/2021
5577	(382*10^121694-31)/9	121696	Robert Price	06/2022
5578	63^67620+2	121672	Lelio R Paula	08/2015
5579	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
5580	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
5581	(16*10^121633+167)/3	121634	Robert Price	06/2019
5582	29955^11494+11494^29955	121632	Hans Havermann	02/2021
5583	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
5584	31088^8163+8163^31088	121612	Hans Havermann	02/2021
5585	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
5586	(211^52301-1)/210	121560	Anonymous	04/2024
5587	(10^121543-79)/3	121543	Robert Price	01/2018
5588	801^41852-41852^801	121523	Norman Luhn	10/2024
5589	2^403676+76831	121519	Enzo Doria	05/2016
5590	715^42564-42564^715	121491	Norman Luhn	10/2024
5591	(7*10^121487+143)/3	121488	Robert Price	03/2018
5592	27965^22086+22086^27965	121484	Hans Havermann	02/2021
5593	(893*10^121470+7)/9	121472	Robert Price	06/2021
5594	(206*10^121462-11)/3	121464	Robert Price	02/2022
5595	26282^27481-27481^26282	121457	Frank Doornink	03/2024
5596	(77*10^121455+67)/9	121456	Robert Price	12/2021
5597	2^403363-113635	121425	Enzo Doria	08/2014
5598	25531^27552-27552^25531	121424	Frank Doornink	02/2024
5599	(17*10^121418-113)/3	121419	Robert Price	06/2021
5600	2^403336-1861469	121417	Enzo Doria	03/2016
5601	27929^22186+22186^27929	121382	Hans Havermann	02/2021
5602	p(24442)#/2-64	121381	Robert Price	04/2017
5603	11^116555-720	121380	Enzo Doria	11/2012
5604	(873^41263+1)/874	121353	Jinyuan Wang	12/2024
5605	2^403100-461267	121346	Enzo Doria	07/2015
5606	2^403093-112213	121344	Enzo Doria	06/2014
5607	29404^13385+13385^29404	121340	Hans Havermann	02/2021
5608	28106^20745+20745^28106	121332	Hans Havermann	02/2021
5609	(316^48539+1)/317	121330	Eric Chen	10/2017
5610	(23*10^121320-71)/3	121321	Robert Price	07/2020
5611	2^403004+1866361	121317	Enzo Doria	03/2016
5612	2^402953+89	121301	Lelio R Paula	10/2013
5613	2^402944-2788319	121299	Enzo Doria	03/2016
5614	(44*10^121297-719)/9	121298	Robert Price	12/2018
5615	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
5616	2^402828-113183	121264	Enzo Doria	07/2014
5617	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
5618	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
5619	282^49477-49477^282	121231	Norman Luhn	10/2024
5621	2^402715+1874223	121230	Enzo Doria	06/2016
5620	(35*10^121229-593)/9	121230	Robert Price	07/2018
5622	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
5623	291^49190-49190^291	121199	Norman Luhn	10/2024
5624	28719^16568+16568^28719	121174	Hans Havermann	02/2021
5625	7*10^121144+9	121145	Robert Price	09/2015
5626	27490^25467+25467^27490	121121	Hans Havermann	02/2021
5627	34575^3182+3182^34575	121106	Hans Havermann	02/2021
5628	5*10^121100-37	121101	Robert Price	11/2021
5629	F(579521)/516247738177	121101	Serge Batalov	07/2024
5630	25592^27467-27467^25592	121078	Frank Doornink	02/2024
5631	29954^10935+10935^29954	120979	Hans Havermann	02/2021
5632	33585^3992+3992^33585	120946	Hans Havermann	02/2021
5633	40296^1003+1003^40296	120941	Hans Havermann	02/2021
5634	2^401725-113251	120932	Enzo Doria	07/2014
5635	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
5636	2^401652+73711	120910	Enzo Doria	04/2016
5637	(2^401632+3)/79	120902	Lelio R Paula	04/2014
5638	40450^973+973^40450	120870	Hans Havermann	01/2021
5639	(8*10^120851-11)/3	120852	Robert Price	07/2023
5640	10^120841+88417	120842	Patrick De Geest	04/2020
5641	10^120841-123456789	120841	Robert Price	02/2020
5642	10^120841-176853	120841	Patrick De Geest	04/2020
5643	2^401406-2791331	120836	Enzo Doria	03/2016
5644	(28^83497+1)/29	120832	Robert Price	07/2013
5645	(22*10^120828+161)/3	120829	Robert Price	05/2019
5646	2^401369+1867367	120825	Enzo Doria	03/2016
5647	(5*10^120821+43)/3	120822	Robert Price	12/2021
5648	26990^27263-27263^26990	120808	Frank Doornink	03/2024
5649	(10^120782+29)/3	120782	Serge Batalov	12/2014
5650	2^401215-1657	120778	Yves Minet	07/2014
5651	2^401159+53	120761	Lelio R Paula	10/2013
5652	27782^22179+22179^27782	120739	Hans Havermann	01/2021
5653	242^50649-50649^242	120738	Norman Luhn	09/2024
5654	32974^4585+4585^32974	120730	Hans Havermann	02/2021
5655	2^401031-113047	120723	Enzo Doria	07/2014
5656	30598^8813+8813^30598	120713	Hans Havermann	02/2021
5657	(71*10^120703-287)/9	120704	Robert Price	09/2019
5658	25671^27370-27370^25671	120687	Frank Doornink	02/2024
5659	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
5660	34793^2940+2940^34793	120675	Hans Havermann	02/2021
5661	26028^27329-27329^26028	120670	Frank Doornink	03/2024
5662	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5663	(166*10^120654+11)/3	120656	Robert Price	03/2021
5664	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5665	8*10^120637-27	120638	Robert Price	10/2021
5666	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5667	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5668	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5669	9*10^120617-61	120618	Robert Price	06/2021
5670	(29*10^120590-71)/3	120591	Robert Price	07/2021
5671	2^400571-15	120584	Lelio R Paula	10/2013
5672	(10^120574+359)/9	120574	Serge Batalov	12/2014
5673	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5674	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5675	2^400424-216413	120540	Enzo Doria	04/2013
5676	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5677	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5678	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5679	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5680	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5681	2^400166+1874899	120462	Enzo Doria	06/2016
5682	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5683	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5684	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5685	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5686	2^399999+54173	120412	Norman Luhn	08/2023
5687	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5688	2^399966+73759	120402	Enzo Doria	04/2016
5689	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5690	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5692	2^399918-95	120388	Lelio R Paula	04/2013
5691	2^399918+214009	120388	Enzo Doria	10/2023
5693	(28*10^120381-67)/3	120382	Robert Price	10/2020
5694	(49*10^120380-139)/9	120381	Robert Price	03/2019
5695	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
5696	2^399792-1849259	120350	Enzo Doria	08/2015
5697	9*10^120342-7	120343	Robert Price	09/2015
5698	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
5699	(331*10^120332-7)/9	120334	Robert Price	04/2022
5700	(13*10^120306-37)/3	120307	Robert Price	01/2019
5701	(23*10^120299+37)/3	120300	Robert Price	02/2022
5702	25935^27254-27254^25935	120297	Frank Doornink	03/2024
5703	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
5704	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
5705	2^399526-1861721	120270	Enzo Doria	11/2015
5706	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
5707	32016^5687+5687^32016	120217	Hans Havermann	01/2021
5708	(205*10^120212-1)/3	120214	Robert Price	11/2021
5709	2^399322-2798111	120208	Enzo Doria	04/2016
5710	30438^8867+8867^30438	120163	Hans Havermann	02/2021
5711	3^251841-5*2^251841	120159	Jon Grantham	08/2023
5713	72^64693-71^64693	120157	Robert Price	03/2014
5712	(17*10^120156-161)/9	120157	Robert Price	02/2021
5714	2^399111-28489	120145	Enzo Doria	08/2015
5715	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
5716	30254^9333+9333^30254	120110	Hans Havermann	02/2021
5717	2^398972+6561	120103	Henri Lifchitz	10/2024
5718	30882^7745+7745^30882	120101	Hans Havermann	02/2021
5720	2^398877+105	120074	Donovan Johnson	01/2006
5719	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
5721	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
5722	U(686581)/4280145953	120067	Serge Batalov	07/2024
5723	2^398710+57	120024	Lelio R Paula	04/2013
5724	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
5725	2^398691-115057	120018	Enzo Doria	06/2015
5726	L(574219)	120005	Renaud Lifchitz	03/2004
5727	2^398571+60413	119982	Yves Minet	03/2011
5728	28623^15538+15538^28623	119971	Hans Havermann	02/2021
5729	p(24179)#/2-64	119949	Robert Price	04/2017
5730	2^398448+1872001	119945	Enzo Doria	05/2016
5731	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
5732	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
5733	(191*10^119941-17)/3	119943	Robert Price	11/2021
5734	634^42803+42803^634	119938	Norbert Schneider	07/2019
5735	31083^7220+7220^31083	119935	Hans Havermann	01/2021
5736	(68*10^119931-11)/3	119933	Robert Price	01/2020
5737	8*10^119930-3	119931	Ray Chandler	04/2011
5738	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
5739	(10^119880+179)/9	119880	Serge Batalov	12/2014
5740	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
5741	(10^119836+77)/3	119836	Robert Price	01/2018
5742	26681^27074-27074^26681	119835	Frank Doornink	03/2024
5743	28179^17870+17870^28179	119821	Hans Havermann	02/2021
5744	2^398029+1872527	119819	Enzo Doria	05/2016
5745	33142^4119+4119^33142	119802	Hans Havermann	01/2021
5746	2^397897-113541	119779	Enzo Doria	08/2014
5747	28636^15171+15171^28636	119728	Hans Havermann	02/2021
5748	87^61730-61730^87	119727	Norman Luhn	09/2024
5749	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
5750	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020

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