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	(2^349111-5)/3	105093	Lelio R Paula	12/2013
5502	675^37142+37142^675	105087	Norbert Schneider	08/2018
5503	2^348981-2797573	105054	Enzo Doria	04/2016
5504	2^348869-6555	105021	Lelio R Paula	01/2017
5505	5^150217+78	104998	Lelio R Paula	11/2016
5506	(88*10^104989-1)/3	104991	Robert Price	04/2020
5507	(28*10^104972+149)/3	104973	Robert Price	12/2019
5508	24927^16262+16262^24927	104972	Hans Havermann	10/2020
5509	2^348703-113005	104971	Enzo Doria	06/2014
5510	(191*10^104956-17)/3	104958	Robert Price	11/2021
5512	2^348612-809	104943	Yves Minet	05/2013
5511	(73*10^104942-1)/9	104943	Robert Price	01/2015
5513	2^348583-350407	104934	Enzo Doria	06/2015
5514	2^348531-949	104919	Yves Minet	05/2012
5515	20^80636-59	104910	Lelio R Paula	12/2016
5516	8*10^104893-13	104894	Robert Price	08/2019
5518	2^348437+35	104890	Lelio R Paula	09/2011
5517	25208^14487+14487^25208	104890	Hans Havermann	09/2020
5519	2^348348+135	104864	Lelio R Paula	09/2011
5520	(29*10^104858+349)/9	104859	Robert Price	06/2021
5521	6*10^104852-31	104853	Robert Price	07/2020
5523	(2^348284+9)/25	104843	Lelio R Paula	12/2013
5522	75^55914-74	104843	Norbert Schneider	01/2015
5524	2^348268+255255	104840	Lelio R Paula	01/2017
5525	35540^891+891^35540	104839	Hans Havermann	09/2020
5526	5^149985-52	104836	Lelio R Paula	11/2016
5527	2^348224-20249	104826	Enzo Doria	06/2013
5528	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
5529	2^348212-20105	104823	Enzo Doria	06/2013
5530	24647^17898+17898^24647	104819	Hans Havermann	10/2020
5531	20^80562+19	104814	Lelio R Paula	12/2016
5532	2*10^104811-87	104812	Robert Price	04/2018
5533	2^348149-20053	104804	Enzo Doria	06/2013
5534	2^348095-171	104788	Lelio R Paula	09/2011
5535	25383^13412+13412^25383	104769	Hans Havermann	09/2020
5536	2^348003-20377	104760	Enzo Doria	06/2013
5537	2^347994-741	104757	Lelio R Paula	12/2016
5538	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
5539	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
5540	25137^14702+14702^25137	104756	Hans Havermann	09/2020
5541	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
5542	2^347910-109937	104732	Enzo Doria	04/2014
5543	(88*10^104709-637)/9	104710	Robert Price	11/2020
5544	(13*10^104702+71)/3	104703	Robert Price	06/2021
5545	5^149794+28	104702	Lelio R Paula	11/2016
5546	105^51800-2	104698	Lelio R Paula	10/2017
5547	(16^86939+3^86939)/19	104684	Robert Price	06/2013
5548	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
5549	2^347731-18609	104678	Enzo Doria	05/2013
5550	4*6^134519+7	104677	Lelio R Paula	11/2014
5551	(34*10^104672-259)/9	104673	Robert Price	12/2021
5552	25321^13588+13588^25321	104656	Hans Havermann	09/2020
5553	2^347612-18545	104642	Enzo Doria	05/2013
5556	6^134465+95	104635	Lelio R Paula	11/2016
5554	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
5555	(166*10^104633-7)/3	104635	Robert Price	11/2020
5557	2^347517-17301	104614	Enzo Doria	05/2013
5558	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
5559	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
5560	3^219222-310	104596	Lelio R Paula	11/2016
5561	25993^10554+10554^25993	104581	Hans Havermann	09/2020
5562	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
5563	2^347372-17853	104570	Enzo Doria	05/2013
5564	2^347314+99	104552	Lelio R Paula	09/2011
5565	2^347300-22233	104548	Enzo Doria	06/2013
5566	2^347287-19845	104544	Enzo Doria	06/2013
5567	2^347258-231191	104536	Harrison Mesh	06/2022
5568	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
5569	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
5570	7*2^347239-3	104531	Lelio R Paula	09/2014
5571	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
5572	5*3^219047+8	104513	Lelio R Paula	09/2014
5573	2^347148-109073	104502	Enzo Doria	04/2014
5574	2^347129-20145	104497	Enzo Doria	06/2013
5575	4*10^104461-57	104462	Robert Price	10/2018
5576	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
5577	2^346923-19585	104435	Enzo Doria	05/2013
5578	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
5579	2^346854+346854^2+1	104414	Robert Price	06/2014
5580	2^346834+11715	104408	Lelio R Paula	04/2015
5581	24276^19961+19961^24276	104392	Hans Havermann	09/2020
5582	79^55009+78	104387	Norbert Schneider	02/2015
5583	3^218744+58	104368	Lelio R Paula	11/2016
5584	9*10^104361+89	104362	Robert Price	11/2019
5585	25048^14665+14665^25048	104358	Hans Havermann	09/2020
5586	2^346649+65	104352	Lelio R Paula	09/2011
5587	2^346638-17265	104349	Enzo Doria	05/2013
5588	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
5589	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
5590	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
5591	26092^9967+9967^26092	104331	Hans Havermann	09/2020
5592	5*10^104326+77	104327	Robert Price	12/2018
5593	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
5595	2^346527-111817	104316	Enzo Doria	05/2014
5594	6^134055+101	104316	Lelio R Paula	11/2016
5596	92105!4+8	104312	Robert Price	09/2019
5597	6^134013+163	104283	Lelio R Paula	11/2016
5598	(22*10^104272-61)/3	104273	Robert Price	03/2022
5599	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
5601	18^83049-89	104250	Lelio R Paula	01/2017
5600	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
5602	(166*10^104230+11)/3	104232	Robert Price	03/2021
5603	2^346213+484049	104221	Enzo Doria	04/2017
5604	18^83021-91	104214	Lelio R Paula	01/2017
5605	10^104212+128779	104213	Patrick De Geest	05/2016
5606	10^104212+237447	104213	Patrick De Geest	05/2016
5607	10^104212+242139	104213	Patrick De Geest	05/2016
5608	10^104212+269199	104213	Patrick De Geest	05/2016
5609	24254^19803+19803^24254	104213	Hans Havermann	09/2020
5610	(10^104212-71)/1	104212	Serge Batalov	12/2014
5611	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
5612	2^346078+7695	104180	Lelio R Paula	12/2016
5613	2^346055-19537	104173	Enzo Doria	05/2013
5614	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
5615	2^346037-20125	104168	Enzo Doria	06/2013
5616	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
5617	6^133854-17993	104159	Enzo Doria	03/2013
5618	2^345990+1874239	104154	Enzo Doria	06/2016
5619	2^345988-20373	104153	Enzo Doria	06/2013
5620	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
5621	(26*10^104132-503)/9	104133	Robert Price	07/2018
5622	3*5^148968+8	104125	Lelio R Paula	11/2014
5623	(7*10^104113+53)/3	104114	Robert Price	05/2018
5624	p(21253)#/2+8	104113	Robert Price	01/2017
5625	33582^1259+1259^33582	104106	Hans Havermann	09/2020
5626	32958^1441+1441^32958	104104	Hans Havermann	09/2020
5627	29127^3748+3748^29127	104095	Hans Havermann	09/2020
5628	322^41507+41507^322	104094	Norbert Schneider	12/2014
5629	6^133768-17423	104092	Enzo Doria	03/2013
5630	2^345786-19557	104092	Enzo Doria	05/2013
5631	171^46606-2	104072	Lelio R Paula	10/2017
5632	(29*10^104071+91)/3	104072	Robert Price	04/2020
5633	2^345704-149	104068	Lelio R Paula	09/2011
5634	25821^10712+10712^25821	104056	Hans Havermann	09/2020
5635	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
5636	6^133704-17273	104042	Enzo Doria	02/2013
5637	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
5638	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
5639	2^345547+11	104021	Lelio R Paula	09/2011
5640	(19*10^104014-49)/3	104015	Robert Price	05/2019
5641	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
5642	2^345504+723	104008	Lelio R Paula	09/2011
5643	2^345498-20037	104006	Enzo Doria	06/2013
5645	18^82854-37	104005	Lelio R Paula	01/2017
5644	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
5646	2^345486-109065	104002	Enzo Doria	04/2014
5647	2^345487-1851507	104002	Enzo Doria	08/2015
5648	2^345476+777	103999	Lelio R Paula	09/2011
5649	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
5650	4*10^103981-83	103982	Robert Price	10/2018
5651	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
5652	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
5653	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
5654	(19*10^103907+77)/3	103908	Robert Price	05/2019
5655	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
5656	2^345106-112181	103888	Enzo Doria	06/2014
5657	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
5658	2^345079+99	103880	Lelio R Paula	09/2011
5659	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
5660	11^99736-1500	103865	Enzo Doria	12/2012
5661	(569^37699-1)/568	103863	Serge Batalov	06/2022
5662	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
5663	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
5664	3*10^103844+31	103845	Robert Price	06/2021
5665	23927^21814+21814^23927	103813	Hans Havermann	09/2020
5666	2^344842-20157	103808	Enzo Doria	06/2013
5667	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
5668	2^344802-20765	103796	Enzo Doria	06/2013
5669	2^344794-3821	103794	Yves Minet	05/2011
5670	2^344782-109103	103790	Enzo Doria	04/2014
5671	3^217521-112292	103784	Enzo Doria	06/2014
5672	2^344759-3505	103783	Lelio R Paula	11/2016
5673	2^344735-147	103776	Lelio R Paula	09/2011
5674	L(496533)-p(496533)	103770	Robert Price	02/2018
5675	2*10^103749-69	103750	Robert Price	03/2018
5676	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
5677	2^344607-108891	103738	Enzo Doria	03/2014
5678	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
5679	(1097^34123-1)/1096	103738	Serge Batalov	06/2022
5680	(148*10^103718-1)/3	103720	Robert Price	03/2020
5681	2^344541-19561	103718	Enzo Doria	05/2013
5682	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
5683	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
5684	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
5685	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
5686	2^344444-455	103688	Yves Minet	03/2012
5687	(4*10^103678-43)/3	103679	Robert Price	01/2022
5688	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
5689	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
5691	2^344317-109933	103650	Enzo Doria	04/2014
5690	26055^9508+9508^26055	103650	Hans Havermann	09/2020
5692	2^344309-1852033	103648	Enzo Doria	08/2015
5693	25729^10672+10672^25729	103643	Hans Havermann	09/2020
5694	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
5695	3*10^103637+61	103638	Robert Price	09/2020
5696	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
5697	2^344213-21253	103619	Enzo Doria	06/2013
5698	2^344196-465	103614	Lelio R Paula	11/2016
5699	2^344187-20001	103611	Enzo Doria	06/2013
5700	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
5701	(237^43627-1)/236	103601	Serge Batalov	06/2022
5702	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
5703	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
5704	2^344085-20365	103580	Enzo Doria	06/2013
5705	5^148169+54	103566	Lelio R Paula	11/2016
5706	2^344017-108795	103560	Enzo Doria	03/2014
5707	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
5708	2^343971-5077	103546	Lelio R Paula	09/2011
5709	(7*10^103531+71)/3	103532	Robert Price	05/2018
5710	2^343899+141	103524	Lelio R Paula	08/2011
5711	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
5712	6^133029-67	103517	Lelio R Paula	11/2016
5713	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
5714	66*10^103507+7	103509	Robert Price	07/2020
5715	26297^8614+8614^26297	103485	Hans Havermann	09/2020
5716	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
5717	26499^8036+8036^26499	103480	Hans Havermann	09/2020
5718	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
5719	5^148014-24	103458	Lelio R Paula	11/2016
5720	28316^4503+4503^28316	103453	Hans Havermann	09/2020
5721	(22*10^103450+53)/3	103451	Robert Price	07/2019
5722	2^343604+9931	103436	Yves Minet	01/2011
5723	2^343601-21189	103435	Enzo Doria	06/2013
5724	(10^103423+173)/3	103423	Robert Price	05/2021
5725	2^343508-115229	103407	Enzo Doria	06/2015
5726	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
5727	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
5728	3^216685-113056	103386	Enzo Doria	07/2014
5729	24829^14580+14580^24829	103382	Hans Havermann	08/2020
5730	91355!4+1024	103381	Robert Price	09/2019
5731	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
5732	11^99262-20	103371	Lelio R Paula	12/2016
5733	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
5734	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
5735	2^343356-2791889	103361	Enzo Doria	03/2016
5736	(25*10^103360-241)/9	103361	Robert Price	05/2018
5737	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
5738	24826^14511+14511^24826	103319	Hans Havermann	09/2020
5739	2^343182-171	103309	Lelio R Paula	08/2011
5740	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
5741	(10680^25639-1)/10679	103285	Serge Batalov	06/2022
5742	(7427^26683-1)/7426	103282	Serge Batalov	06/2022
5743	2^343079-1835611	103278	Enzo Doria	05/2015
5744	2^343063-1147	103273	Yves Minet	06/2013
5745	24741^14930+14930^24741	103271	Hans Havermann	09/2020
5746	(16*10^103255-73)/3	103256	Robert Price	07/2020
5747	(219^44119-1)/218	103256	Serge Batalov	06/2022
5748	9*6^132689+7	103254	Lelio R Paula	11/2014
5749	2^342979-18085	103247	Enzo Doria	05/2013
5750	(16*10^103244-31)/3	103245	Robert Price	03/2019

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