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	2^308650+513	92913	Lelio R Paula	02/2016
5502	5*7^109936+6	92908	Lelio R Paula	10/2014
5503	2*10^92897+89	92898	Robert Price	07/2016
5504	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
5505	12^86073-29	92889	Lelio R Paula	06/2016
5506	2^308566-117	92888	Lelio R Paula	11/2012
5507	(17*10^92869-11)/3	92870	Robert Price	07/2015
5508	2^308459+75431	92856	Enzo Doria	04/2016
5509	2^308426-1866377	92846	Enzo Doria	03/2016
5510	24810^5521+5521^24810	92840	Hans Havermann	09/2020
5511	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
5512	2^308349-112111	92823	Enzo Doria	06/2014
5513	9*10^92821+19	92822	Robert Price	05/2016
5514	2^308337-75	92819	Lelio R Paula	11/2012
5515	4*3^194508+7	92805	Lelio R Paula	08/2014
5516	22*25^66379-113	92796	Curtis Bright	05/2015
5517	24538^6047+6047^24538	92792	Hans Havermann	09/2020
5518	11^89101-1080	92790	Enzo Doria	12/2012
5519	2^308236-1867859	92789	Enzo Doria	04/2016
5520	12^85963+25	92770	Lelio R Paula	06/2016
5521	23692^8221+8221^23692	92753	Hans Havermann	08/2020
5522	7^109750-66	92750	Lelio R Paula	04/2016
5523	9*10^92742+11	92743	Robert Kinser	01/2017
5524	(2^308054+778)/2	92734	Stefano Morozzi	09/2020
5525	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
5526	2^307997-110655	92717	Enzo Doria	05/2014
5527	L(443609)	92709	Renaud Lifchitz	11/2003
5528	10^92691+9	92692	Robert Price	03/2011
5529	10^92691-252291	92691	Patrick De Geest	08/2013
5530	(2^307883+3506)/2	92682	Stefano Morozzi	09/2020
5531	2^307879-2521	92681	Yves Minet	07/2014
5532	21269^21412+21412^21269	92666	Norbert Schneider	04/2020
5533	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
5534	14^80831+47	92643	Lelio R Paula	06/2016
5535	15^78744+92	92611	Lelio R Paula	07/2016
5536	65^51083-64	92610	Norbert Schneider	11/2014
5537	(2^307639+506)/2	92609	Stefano Morozzi	09/2020
5538	131^43737-130	92604	Norbert Schneider	02/2019
5539	6^118996-16943	92597	Enzo Doria	02/2013
5540	(16*10^92591+41)/3	92592	Robert Price	10/2017
5541	(2^307566+3094)/2	92587	Stefano Morozzi	09/2020
5542	(2^307528+1578)/2	92575	Stefano Morozzi	09/2020
5543	(3^194014-7)/2	92568	Lelio R Paula	04/2013
5544	(2^307498+570)/2	92566	Stefano Morozzi	09/2020
5545	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
5546	(26*10^92546-77)/3	92547	Robert Price	02/2017
5547	3^193954+340	92540	Lelio R Paula	04/2016
5548	2^307407-307407^2	92539	Henri Lifchitz	05/2005
5549	24299^6430+6430^24299	92536	Hans Havermann	08/2020
5550	(17*10^92513-11)/3	92514	Robert Price	07/2015
5551	2^307318-4211	92512	Yves Minet	06/2011
5552	2^307280+193	92501	Lelio R Paula	11/2012
5553	20^71075-33	92471	Lelio R Paula	05/2016
5554	2^307126-78795	92455	Lelio R Paula	02/2016
5555	2^307125-49789	92454	Henri Lifchitz	08/2005
5556	2^307099+23	92447	Lelio R Paula	11/2012
5557	129^43798+128	92440	Norbert Schneider	01/2019
5558	21826^17181+17181^21826	92435	Hans Havermann	09/2020
5559	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
5560	(2^307022+1038)/2	92423	Stefano Morozzi	09/2020
5561	7*10^92414-69	92415	Robert Price	01/2017
5562	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
5563	22280^14037+14037^22280	92402	Hans Havermann	09/2020
5564	2^306915+1873373	92391	Enzo Doria	06/2016
5565	2^306908+12915	92389	Lelio R Paula	02/2016
5566	21620^18759+18759^21620	92387	Hans Havermann	09/2020
5567	(2^306897+1142)/2	92385	Stefano Morozzi	09/2020
5568	19^72244-80	92383	Lelio R Paula	06/2016
5570	2^306849+75	92371	Lelio R Paula	11/2012
5569	(397*10^92369+53)/9	92371	Robert Price	11/2017
5571	2^306813-869688105	92360	Lelio R Paula	08/2016
5572	(2^306797+2694)/2	92355	Stefano Morozzi	09/2020
5573	21713^17914+17914^21713	92350	Hans Havermann	09/2020
5574	2^306672-109059	92318	Enzo Doria	04/2014
5575	(430463^16384+1)/2	92307	Richard Fischer	09/2020
5576	6^118604-17063	92292	Enzo Doria	02/2013
5577	21969^15878+15878^21969	92288	Hans Havermann	08/2020
5578	21690^17959+17959^21690	92276	Hans Havermann	08/2020
5579	(7613^23773-1)/7612	92273	Serge Batalov	08/2020
5580	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
5581	2^306467-1835611	92256	Enzo Doria	04/2015
5582	2^306433+76427	92246	Enzo Doria	05/2016
5583	2^306430-113313	92245	Enzo Doria	07/2014
5584	(23*10^92244-59)/9	92245	Robert Price	03/2017
5585	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
5586	21436^20043+20043^21436	92217	Hans Havermann	09/2020
5587	(25*10^92186+59)/3	92187	Robert Price	05/2016
5588	2^306213-286183	92180	Enzo Doria	06/2015
5589	10^92178+61	92179	Robert Price	04/2011
5590	10^92178-175509	92178	Patrick De Geest	07/2013
5591	2^306200+1185	92176	Lelio R Paula	02/2016
5592	(2^306171+1514)/2	92167	Stefano Morozzi	09/2020
5593	2^306153+11	92162	Lelio R Paula	11/2012
5594	(2^306141-7)/5	92157	Lelio R Paula	06/2013
5595	21725^17454+17454^21725	92156	Hans Havermann	09/2020
5596	(26*10^92152-23)/3	92153	Robert Price	08/2016
5597	(2*10^92152+67)/3	92152	Robert Price	04/2017
5598	21368^20457+20457^21368	92115	Hans Havermann	08/2020
5599	(2^305996+3018)/2	92114	Stefano Morozzi	09/2020
5600	410^92099+37^92099	92100	Mike Oakes	12/2010
5601	30504^1045+1045^30504	92096	Hans Havermann	08/2020
5602	24334^6085+6085^24334	92087	Hans Havermann	08/2020
5603	(4591^25147-1)/4590	92083	Serge Batalov	08/2020
5604	115^44684+114	92081	Norbert Schneider	07/2018
5605	(416771^16384+1)/2	92077	Richard Fischer	08/2020
5606	(2^305867-2^152934+1)/5	92075		11/2006
5607	2^305851-109495	92071	Enzo Doria	04/2014
5608	(416213^16384+1)/2	92067	Richard Fischer	08/2020
5609	12^85300+35	92055	Lelio R Paula	06/2016
5610	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
5611	21732^17201+17201^21732	92048	Hans Havermann	08/2020
5612	7*10^92043-39	92044	Robert Price	07/2020
5613	3^192911+92	92042	Lelio R Paula	04/2016
5614	2^305723-276271	92032	Enzo Doria	07/2015
5615	(2^305714+3738)/2	92029	Stefano Morozzi	09/2020
5616	(2^305682+3202)/2	92020	Stefano Morozzi	09/2020
5617	2^305676+93	92018	Donovan Johnson	06/2008
5618	3^192819+4	91999	Lelio R Paula	04/2013
5619	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
5620	2^305539+72911	91977	Enzo Doria	04/2016
5621	Phi(212014,10)	91960	Makoto Kamada	04/2019
5622	(2^305423+2666)/2	91942	Stefano Morozzi	09/2020
5623	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
5624	82077!4-128	91928	Robert Price	11/2019
5625	85^47642+84	91922	Norbert Schneider	10/2015
5626	10^91920+187651	91921	Patrick De Geest	07/2013
5627	10^91920-39	91920	Robert Price	05/2011
5628	(3975^25537-1)/3974	91913	Serge Batalov	08/2020
5629	(22*10^91903+41)/9	91904	Robert Price	02/2015
5631	2^305275-27	91897	Lelio R Paula	11/2012
5630	3^192607-7726	91897	Enzo Doria	05/2014
5632	(6958^23911-1)/6957	91874	Serge Batalov	08/2020
5633	(7*10^91856-61)/9	91856	Erik Branger	12/2009
5634	(89*10^91839-53)/9	91840	Robert Price	11/2015
5635	1678^28479+28479^1678	91839	Norbert Schneider	08/2020
5636	8*5^131351+7	91812	Lelio R Paula	10/2014
5637	3^192426-68	91811	Lelio R Paula	04/2016
5639	2^304973+117	91807	Lelio R Paula	11/2012
5638	(2^304974+234)/2	91807	Stefano Morozzi	09/2020
5640	2^304939-1863727	91796	Enzo Doria	03/2016
5641	2^304902+8415	91785	Lelio R Paula	02/2016
5642	18^73119+61	91785	Lelio R Paula	06/2016
5643	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
5644	2^304747+71355	91738	Lelio R Paula	02/2016
5645	8*3^192251+5	91728	Lelio R Paula	08/2014
5646	2^304674-87	91717	Lelio R Paula	11/2012
5647	(28*10^91715+701)/9	91716	Robert Price	11/2017
5649	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
5648	(2^304671+1046)/2	91715	Stefano Morozzi	09/2020
5650	(2^304667+3614)/2	91714	Stefano Morozzi	09/2020
5651	(5*10^91707-119)/3	91708	Robert Price	04/2016
5652	2^304633-112771	91704	Enzo Doria	06/2014
5653	(395347^16384+1)/2	91701	Richard Fischer	06/2020
5654	9*10^91693+23	91694	Robert Price	11/2017
5655	2^304578-16713	91688	Enzo Doria	05/2013
5656	6^117824-18713	91685	Enzo Doria	03/2013
5657	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
5658	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
5659	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
5660	2^304507-16645	91666	Enzo Doria	04/2013
5661	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
5662	21221^20860+20860^21221	91661	Hans Havermann	08/2020
5663	2^304471-1836127	91655	Enzo Doria	04/2015
5664	2^304433+32769	91644	Lelio R Paula	02/2016
5665	2^304410-16625	91637	Enzo Doria	04/2013
5666	183^40500-2	91630	Lelio R Paula	10/2017
5667	(203*10^91613+1)/3	91615	Robert Price	09/2017
5668	4*5^131052+7	91603	Lelio R Paula	10/2014
5669	21725^16458+16458^21725	91601	Hans Havermann	08/2020
5670	2^304278-4001	91597	Yves Minet	04/2017
5671	2^304272-1866377	91595	Enzo Doria	03/2016
5672	2^304268+19683	91594	Lelio R Paula	02/2016
5673	21718^16497+16497^21718	91594	Hans Havermann	08/2020
5674	22759^10576+10576^22759	91590	Hans Havermann	08/2020
5675	2^304162-161	91562	Lelio R Paula	11/2012
5676	5*7^108331+6	91552	Lelio R Paula	10/2014
5677	2^304082-2787821	91538	Enzo Doria	03/2016
5678	2^304015+64133	91518	David Broadhurst	06/2002
5679	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
5680	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
5681	(384007^16384+1)/2	91494	Richard Fischer	05/2020
5682	2^303930+1880527	91493	Enzo Doria	10/2016
5683	24810^4859+4859^24810	91464	Hans Havermann	08/2020
5684	3^191684-68	91457	Lelio R Paula	04/2016
5685	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
5686	11^87797-120	91432	Enzo Doria	07/2012
5687	2^303698-1847231	91423	Enzo Doria	07/2015
5688	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
5689	25660^3643+3643^25660	91388	Hans Havermann	08/2020
5690	2^303554+77299	91379	Enzo Doria	05/2016
5691	2^303542+12705	91376	Lelio R Paula	02/2016
5692	31^61269-2	91375	Lelio R Paula	09/2013
5693	2^303516-64875	91368	Lelio R Paula	02/2016
5694	(2^303497+1266)/2	91362	Stefano Morozzi	09/2020
5695	(2^303497+3710)/2	91362	Stefano Morozzi	09/2020
5696	21856^15121+15121^21856	91349	Hans Havermann	09/2020
5697	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
5698	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
5699	23081^9046+9046^23081	91319	Hans Havermann	09/2020
5700	2^303344-2786969	91316	Enzo Doria	03/2016
5701	6^117346+65	91313	Lelio R Paula	05/2016
5702	2^303321+855	91309	Lelio R Paula	02/2016
5703	12^84606+47	91306	Lelio R Paula	06/2016
5704	2^303288+1874311	91299	Enzo Doria	06/2016
5705	197^39788-2	91293	Lelio R Paula	10/2017
5706	11^87663-1710	91292	Enzo Doria	12/2012
5707	2^303224+2533	91280	Henri Lifchitz	05/2005
5708	6^117302+143	91279	Lelio R Paula	05/2016
5709	3^191306-112880	91277	Enzo Doria	07/2014
5710	(10052^22807-1)/10051	91276	Serge Batalov	08/2020
5711	2^303207+12915	91275	Lelio R Paula	02/2016
5712	2^303191-111259	91270	Enzo Doria	05/2014
5713	81539!4+32	91267	Robert Price	09/2019
5714	(2^303116+3570)/2	91247	Stefano Morozzi	09/2020
5715	10^91230+9^(91230+1)	91231	Robert Price	08/2016
5716	10^91230+7921	91231	Patrick De Geest	11/2016
5717	10^91230-911141	91230	Patrick De Geest	11/2016
5718	10^91229+348793	91230	Patrick De Geest	07/2019
5719	10^91229-2471	91229	Patrick De Geest	01/2019
5720	2996^26241+26241^2996	91228	Norbert Schneider	01/2020
5722	10^91225+5271	91226	Patrick De Geest	01/2019
5721	2816^26445+26445^2816	91226	Norbert Schneider	02/2020
5724	6^117232-17423	91225	Enzo Doria	02/2013
5723	10^91225-147219	91225	Patrick De Geest	07/2019
5725	7*10^91215+3	91216	Erik Branger	11/2009
5726	10^91215+230611	91216	Patrick De Geest	07/2019
5727	10^91215-4539	91215	Patrick De Geest	01/2019
5728	(2^303007+606)/2	91214	Stefano Morozzi	09/2020
5729	(2^302998+3102)/2	91212	Stefano Morozzi	09/2020
5730	10^91210+2421	91211	Patrick De Geest	01/2019
5731	10^91210-1737	91210	Patrick De Geest	01/2019
5732	97*10^91205-3	91207	Robert Price	01/2017
5733	2^302979-161181	91206	Enzo Doria	04/2013
5734	2^302949+81	91197	Henri Lifchitz	02/2007
5735	10^91194+200361	91195	Patrick De Geest	07/2019
5737	4*6^117192-5	91194	Lelio R Paula	10/2014
5736	10^91194-8663	91194	Patrick De Geest	01/2019
5738	2^302918+99	91188	Lelio R Paula	11/2012
5739	10^91186+268111	91187	Patrick De Geest	07/2019
5740	10^91186-7763	91186	Patrick De Geest	01/2019
5741	10^91181+550471	91182	Patrick De Geest	07/2019
5742	10^91181-1367	91181	Patrick De Geest	01/2019
5743	10^91178+71883	91179	Patrick De Geest	07/2019
5744	10^91178-4719	91178	Patrick De Geest	01/2019
5745	24686^4935+4935^24686	91173	Hans Havermann	08/2020
5746	10^91165+3043	91166	Patrick De Geest	01/2019
5747	10^91165-399413	91165	Patrick De Geest	07/2019
5748	10^91156+3861	91157	Patrick De Geest	01/2019
5749	10^91156-231497	91156	Patrick De Geest	07/2019
5750	2^302797+1869587	91151	Enzo Doria	05/2016

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