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	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
5502	26818^8783+8783^26818	105761	Hans Havermann	09/2020
5505	2^351305+1872467	105754	Enzo Doria	05/2016
5504	3^221649+16	105754	Lelio R Paula	11/2016
5503	32511^1790+1790^32511	105754	Hans Havermann	09/2020
5506	8*3^221637-5	105749	Lelio R Paula	09/2014
5507	2^351279-2780449	105746	Enzo Doria	03/2016
5508	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
5509	15^89903-26	105735	Lelio R Paula	02/2017
5511	2^351213-73	105726	Lelio R Paula	10/2011
5510	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
5512	2^351192-4589	105720	Yves Minet	07/2011
5513	20^81250-33	105709	Lelio R Paula	12/2016
5514	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
5515	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
5516	2^351076-113159	105685	Enzo Doria	07/2014
5517	93^53688-2	105684	Lelio R Paula	09/2013
5518	2^351060-4559	105680	Yves Minet	07/2011
5519	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
5520	11^101473-750	105674	Enzo Doria	11/2012
5521	3*5^151181-8	105672	Lelio R Paula	11/2014
5522	15^89831-34	105650	Lelio R Paula	02/2017
5524	11^101448-360	105648	Enzo Doria	08/2012
5523	3*7^125011+4	105648	Lelio R Paula	11/2014
5525	2^350943-113269	105645	Enzo Doria	07/2014
5526	2*10^105636-91	105637	Robert Price	04/2020
5527	24231^22880+22880^24231	105634	Hans Havermann	09/2020
5528	35296^983+983^35296	105626	Hans Havermann	09/2020
5529	2^350868-19725	105622	Enzo Doria	06/2013
5530	2^350858-59291	105619	Enzo Doria	10/2015
5531	2^350851+135	105617	Lelio R Paula	10/2011
5532	2^350841-741	105614	Lelio R Paula	01/2017
5533	3*10^105582+77	105583	Robert Price	09/2018
5534	24915^17284+17284^24915	105581	Hans Havermann	09/2020
5535	(5*10^105576-53)/3	105577	Robert Price	09/2020
5536	8*10^105571+3	105572	Robert Price	08/2015
5537	2^350674-78557	105564	Jorge Menendez	03/2018
5538	2*5^151026-3	105563	Lelio R Paula	11/2014
5539	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
5540	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
5541	3^221211+236	105545	Lelio R Paula	11/2016
5542	(32*10^105530-77)/9	105531	Robert Price	06/2018
5543	10^105515+33	105516	Lelio R Paula	11/2016
5544	24644^19125+19125^24644	105516	Hans Havermann	10/2020
5545	10^105515-41033	105515	Patrick De Geest	12/2016
5546	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
5547	2^350455-430567	105498	Harrison Mesh	06/2022
5548	17^85732-72	105489	Lelio R Paula	01/2017
5549	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
5550	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
5551	25233^15118+15118^25233	105462	Hans Havermann	09/2020
5552	26261^10366+10366^26261	105454	Hans Havermann	09/2020
5553	2^350307-110329	105453	Enzo Doria	05/2014
5554	2^350253-20365	105437	Enzo Doria	06/2013
5555	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
5556	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
5557	4*10^105415-69	105416	Robert Price	01/2022
5558	(22*10^105407+179)/3	105408	Robert Price	02/2022
5559	2^350139-109009	105403	Enzo Doria	04/2014
5560	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
5561	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
5562	3*5^150763+4	105380	Lelio R Paula	11/2014
5563	12^97643+91	105375	Lelio R Paula	02/2017
5564	6*5^150744-7	105367	Lelio R Paula	11/2014
5565	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
5566	4*10^105364-39	105365	Robert Price	09/2020
5568	2^349996-112169	105360	Enzo Doria	06/2014
5567	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
5569	(418*10^105343+23)/9	105345	Robert Price	02/2020
5570	25490^13563+13563^25490	105334	Hans Havermann	10/2020
5571	11^101142-1080	105329	Enzo Doria	12/2012
5572	(68*10^105320-41)/9	105321	Robert Price	10/2013
5573	24800^17649+17649^24800	105319	Hans Havermann	09/2020
5574	3^220712-9934	105307	Enzo Doria	05/2014
5575	7*10^105296+9	105297	Robert Price	09/2015
5576	89*10^105284-7	105286	Robert Price	04/2020
5577	2^349739+1873373	105282	Enzo Doria	06/2016
5578	7^124574+24	105278	Lelio R Paula	11/2016
5579	2^349708-20957	105273	Enzo Doria	06/2013
5580	34115^1218+1218^34115	105267	Hans Havermann	09/2020
5581	2^349649-20469	105255	Enzo Doria	06/2013
5582	2^349607-20109	105243	Enzo Doria	06/2013
5583	(85*10^105242+473)/9	105243	Robert Price	01/2020
5584	2^349594-19085	105239	Enzo Doria	05/2013
5585	2^349530+1874479	105220	Enzo Doria	06/2016
5586	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
5587	(106*10^105199+17)/3	105201	Robert Price	04/2021
5588	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
5589	3^220464-112852	105189	Enzo Doria	07/2014
5590	2^349419-17349	105186	Enzo Doria	05/2013
5591	2^349400-2579	105180	Yves Minet	07/2014
5592	8*5^150471+3	105176	Lelio R Paula	11/2014
5593	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
5594	655^37342+37342^655	105165	Norbert Schneider	08/2018
5595	13^94403+94	105160	Lelio R Paula	12/2016
5596	2^349301-112309	105151	Enzo Doria	06/2014
5597	30291^2960+2960^30291	105149	Hans Havermann	09/2020
5598	27350^6981+6981^27350	105132	Hans Havermann	09/2020
5600	9*2^349220+5	105127	Lelio R Paula	09/2014
5599	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
5601	7*3^220317+8	105119	Lelio R Paula	09/2014
5602	7^124386+88	105119	Lelio R Paula	11/2016
5603	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
5604	2^349171-19657	105111	Enzo Doria	06/2013
5605	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
5606	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
5607	(2^349111-5)/3	105093	Lelio R Paula	12/2013
5608	675^37142+37142^675	105087	Norbert Schneider	08/2018
5609	2^348981-2797573	105054	Enzo Doria	04/2016
5610	2^348869-6555	105021	Lelio R Paula	01/2017
5611	5^150217+78	104998	Lelio R Paula	11/2016
5612	(88*10^104989-1)/3	104991	Robert Price	04/2020
5613	(28*10^104972+149)/3	104973	Robert Price	12/2019
5614	24927^16262+16262^24927	104972	Hans Havermann	10/2020
5615	2^348703-113005	104971	Enzo Doria	06/2014
5616	(191*10^104956-17)/3	104958	Robert Price	11/2021
5618	2^348612-809	104943	Yves Minet	05/2013
5617	(73*10^104942-1)/9	104943	Robert Price	01/2015
5619	2^348583-350407	104934	Enzo Doria	06/2015
5620	2^348531-949	104919	Yves Minet	05/2012
5621	20^80636-59	104910	Lelio R Paula	12/2016
5622	8*10^104893-13	104894	Robert Price	08/2019
5624	2^348437+35	104890	Lelio R Paula	09/2011
5623	25208^14487+14487^25208	104890	Hans Havermann	09/2020
5625	2^348348+135	104864	Lelio R Paula	09/2011
5626	(29*10^104858+349)/9	104859	Robert Price	06/2021
5627	6*10^104852-31	104853	Robert Price	07/2020
5629	(2^348284+9)/25	104843	Lelio R Paula	12/2013
5628	75^55914-74	104843	Norbert Schneider	01/2015
5630	2^348268+255255	104840	Lelio R Paula	01/2017
5631	35540^891+891^35540	104839	Hans Havermann	09/2020
5632	5^149985-52	104836	Lelio R Paula	11/2016
5633	2^348224-20249	104826	Enzo Doria	06/2013
5634	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
5635	2^348212-20105	104823	Enzo Doria	06/2013
5636	24647^17898+17898^24647	104819	Hans Havermann	10/2020
5637	20^80562+19	104814	Lelio R Paula	12/2016
5638	2*10^104811-87	104812	Robert Price	04/2018
5639	2^348149-20053	104804	Enzo Doria	06/2013
5640	2^348095-171	104788	Lelio R Paula	09/2011
5641	25383^13412+13412^25383	104769	Hans Havermann	09/2020
5642	2^348003-20377	104760	Enzo Doria	06/2013
5643	2^347994-741	104757	Lelio R Paula	12/2016
5644	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
5645	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
5646	25137^14702+14702^25137	104756	Hans Havermann	09/2020
5647	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
5648	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
5649	2^347910-109937	104732	Enzo Doria	04/2014
5650	(88*10^104709-637)/9	104710	Robert Price	11/2020
5651	(13*10^104702+71)/3	104703	Robert Price	06/2021
5652	5^149794+28	104702	Lelio R Paula	11/2016
5653	105^51800-2	104698	Lelio R Paula	10/2017
5654	(16^86939+3^86939)/19	104684	Robert Price	06/2013
5655	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
5656	2^347731-18609	104678	Enzo Doria	05/2013
5657	4*6^134519+7	104677	Lelio R Paula	11/2014
5658	(34*10^104672-259)/9	104673	Robert Price	12/2021
5659	25321^13588+13588^25321	104656	Hans Havermann	09/2020
5660	2^347612-18545	104642	Enzo Doria	05/2013
5663	6^134465+95	104635	Lelio R Paula	11/2016
5661	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
5662	(166*10^104633-7)/3	104635	Robert Price	11/2020
5664	2^347517-17301	104614	Enzo Doria	05/2013
5665	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
5666	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
5667	3^219222-310	104596	Lelio R Paula	11/2016
5668	25993^10554+10554^25993	104581	Hans Havermann	09/2020
5669	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
5670	2^347372-17853	104570	Enzo Doria	05/2013
5671	2^347314+99	104552	Lelio R Paula	09/2011
5672	2^347300-22233	104548	Enzo Doria	06/2013
5673	2^347287-19845	104544	Enzo Doria	06/2013
5674	2^347258-231191	104536	Harrison Mesh	06/2022
5675	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
5676	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
5677	7*2^347239-3	104531	Lelio R Paula	09/2014
5678	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
5679	5*3^219047+8	104513	Lelio R Paula	09/2014
5680	2^347148-109073	104502	Enzo Doria	04/2014
5681	2^347129-20145	104497	Enzo Doria	06/2013
5682	4*10^104461-57	104462	Robert Price	10/2018
5683	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
5684	2^346923-19585	104435	Enzo Doria	05/2013
5685	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
5686	2^346854+346854^2+1	104414	Robert Price	06/2014
5687	2^346834+11715	104408	Lelio R Paula	04/2015
5688	24276^19961+19961^24276	104392	Hans Havermann	09/2020
5689	79^55009+78	104387	Norbert Schneider	02/2015
5690	3^218744+58	104368	Lelio R Paula	11/2016
5691	9*10^104361+89	104362	Robert Price	11/2019
5692	25048^14665+14665^25048	104358	Hans Havermann	09/2020
5693	2^346649+65	104352	Lelio R Paula	09/2011
5694	2^346638-17265	104349	Enzo Doria	05/2013
5695	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
5696	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
5697	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
5698	26092^9967+9967^26092	104331	Hans Havermann	09/2020
5699	5*10^104326+77	104327	Robert Price	12/2018
5700	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
5702	2^346527-111817	104316	Enzo Doria	05/2014
5701	6^134055+101	104316	Lelio R Paula	11/2016
5703	92105!4+8	104312	Robert Price	09/2019
5704	6^134013+163	104283	Lelio R Paula	11/2016
5705	(22*10^104272-61)/3	104273	Robert Price	03/2022
5706	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
5708	18^83049-89	104250	Lelio R Paula	01/2017
5707	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
5709	(166*10^104230+11)/3	104232	Robert Price	03/2021
5710	2^346213+484049	104221	Enzo Doria	04/2017
5711	18^83021-91	104214	Lelio R Paula	01/2017
5712	10^104212+128779	104213	Patrick De Geest	05/2016
5713	10^104212+237447	104213	Patrick De Geest	05/2016
5714	10^104212+242139	104213	Patrick De Geest	05/2016
5715	10^104212+269199	104213	Patrick De Geest	05/2016
5716	24254^19803+19803^24254	104213	Hans Havermann	09/2020
5717	(10^104212-71)/1	104212	Serge Batalov	12/2014
5718	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
5719	2^346078+7695	104180	Lelio R Paula	12/2016
5720	2^346055-19537	104173	Enzo Doria	05/2013
5721	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
5722	2^346037-20125	104168	Enzo Doria	06/2013
5723	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
5724	6^133854-17993	104159	Enzo Doria	03/2013
5725	2^345990+1874239	104154	Enzo Doria	06/2016
5726	2^345988-20373	104153	Enzo Doria	06/2013
5727	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
5728	(26*10^104132-503)/9	104133	Robert Price	07/2018
5729	3*5^148968+8	104125	Lelio R Paula	11/2014
5730	(7*10^104113+53)/3	104114	Robert Price	05/2018
5731	p(21253)#/2+8	104113	Robert Price	01/2017
5732	33582^1259+1259^33582	104106	Hans Havermann	09/2020
5733	32958^1441+1441^32958	104104	Hans Havermann	09/2020
5734	29127^3748+3748^29127	104095	Hans Havermann	09/2020
5735	322^41507+41507^322	104094	Norbert Schneider	12/2014
5736	6^133768-17423	104092	Enzo Doria	03/2013
5737	2^345786-19557	104092	Enzo Doria	05/2013
5738	171^46606-2	104072	Lelio R Paula	10/2017
5739	(29*10^104071+91)/3	104072	Robert Price	04/2020
5740	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
5741	2^345704-149	104068	Lelio R Paula	09/2011
5742	25821^10712+10712^25821	104056	Hans Havermann	09/2020
5743	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
5744	6^133704-17273	104042	Enzo Doria	02/2013
5745	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
5746	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
5747	2^345547+11	104021	Lelio R Paula	09/2011
5748	(19*10^104014-49)/3	104015	Robert Price	05/2019
5749	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
5750	2^345504+723	104008	Lelio R Paula	09/2011

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