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 ?
8501	(2^253660+490)/2	76359	Stefano Morozzi	01/2020
8502	19227^9352+9352^19227	76349	Hans Havermann	01/2020
8503	(2^253617+2874)/2	76347	Stefano Morozzi	01/2020
8504	2^253561-110533	76330	Enzo Doria	05/2014
8505	(2^253546+954)/2	76325	Stefano Morozzi	01/2020
8506	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
8507	9*5^109182+2	76316	Lelio R Paula	10/2014
8508	11^73279-3690	76313	Enzo Doria	12/2012
8509	(598*10^76309-31)/9	76311	Robert Price	02/2017
8510	11^73274-24000	76308	Enzo Doria	12/2012
8511	7^90291-6	76305	Theodore Burton	11/2005
8512	(2^253479+3650)/2	76305	Stefano Morozzi	01/2020
8513	(2^253460+2902)/2	76299	Stefano Morozzi	01/2020
8514	6*10^76295-29	76296	Robert Price	08/2020
8515	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
8516	(2^253399+3254)/2	76281	Stefano Morozzi	01/2020
8517	69247!4+4	76280	Robert Price	09/2019
8518	6^98025+145	76279	Lelio R Paula	01/2015
8519	(2^253382+1978)/2	76276	Stefano Morozzi	01/2020
8520	2^253355+1155	76268	Lelio R Paula	05/2013
8521	(73*10^76262+413)/9	76263	Robert Price	10/2017
8522	2^253292-71219	76249	Enzo Doria	04/2016
8523	7^90221-36	76246	Lelio R Paula	02/2015
8524	(2^253273+3486)/2	76243	Stefano Morozzi	01/2020
8525	(2^253238+894)/2	76232	Stefano Morozzi	01/2020
8526	18^60727-3473	76229	Enzo Doria	03/2013
8527	(2^253210+1170)/2	76224	Stefano Morozzi	01/2020
8528	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
8529	(8*10^76220-83)/3	76221	Robert Price	10/2017
8530	18568^12717+12717^18568	76211	Hans Havermann	01/2020
8531	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
8532	(5168^20521-1)/5167	76198	Serge Batalov	08/2020
8533	19443^8294+8294^19443	76193	Hans Havermann	12/2019
8534	11^73163-2010	76192	Enzo Doria	12/2012
8535	19006^10201+10201^19006	76189	Hans Havermann	12/2019
8536	2^253060+54615	76179	Lelio R Paula	05/2013
8537	(2^253049+3966)/2	76176	Stefano Morozzi	01/2020
8538	2^253029+1869761	76170	Enzo Doria	05/2016
8539	(2^253028+1906)/2	76169	Stefano Morozzi	01/2020
8540	(1078^25111-1)/1077	76150	Serge Batalov	08/2020
8541	2^252955-111007	76148	Enzo Doria	05/2014
8542	2*5^108931+7	76140	Lelio R Paula	10/2014
8543	(86*10^76128+121)/9	76129	Robert Price	03/2017
8544	22154*29^52050+9	76123	Curtis Bright	05/2015
8545	18915^10574+10574^18915	76119	Hans Havermann	01/2020
8546	3^159530-112358	76116	Enzo Doria	06/2014
8547	11^73089-48	76115	Lelio R Paula	02/2015
8548	86^39337-85	76098	Norbert Schneider	10/2015
8549	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
8550	6^97783+77	76090	Lelio R Paula	01/2015
8551	(2^252716+1842)/2	76075	Stefano Morozzi	01/2020
8552	2^252712-105	76074	Lelio R Paula	03/2012
8553	(10^76069-19)/9	76069	Robert Price	10/2017
8556	131^35927+2	76068	Lelio R Paula	05/2013
8554	(41*10^76067+373)/9	76068	Robert Price	04/2017
8555	(10807^18859-1)/10806	76068	Serge Batalov	08/2020
8557	2^252683-139	76066	Lelio R Paula	03/2012
8558	137^35597-136	76061	Norbert Schneider	05/2015
8559	3^159413+106	76060	Lelio R Paula	01/2015
8560	(2^252593+1682)/2	76038	Stefano Morozzi	01/2020
8561	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
8562	(6716^19867-1)/6715	76030	Serge Batalov	08/2020
8563	22235^2626+2626^22235	76029	Hans Havermann	12/2019
8564	(2^252557-9)/71	76026	Lelio R Paula	07/2012
8566	(85*10^76021-103)/9	76022	Robert Price	10/2017
8565	(2^252539+2690)/2	76022	Stefano Morozzi	01/2020
8567	11^72989+80	76011	Lelio R Paula	02/2015
8568	99877!6-36	75996	Robert Price	11/2018
8569	2^252449-459523	75995	Enzo Doria	05/2015
8570	20^58408+73	75991	Lelio R Paula	01/2015
8571	2^252418-1421	75986	Yves Minet	01/2013
8572	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
8573	20871^4366+4366^20871	75973	Hans Havermann	01/2020
8574	2^252365-110689	75970	Enzo Doria	05/2014
8575	11^72949-1020	75969	Enzo Doria	11/2012
8576	(2^252335+2394)/2	75961	Stefano Morozzi	01/2020
8577	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
8578	2^252261-110595	75939	Enzo Doria	05/2014
8579	7^89853+76	75935	Lelio R Paula	01/2015
8580	(3043^21799-1)/3042	75930	Serge Batalov	08/2020
8581	3^159132+56	75926	Lelio R Paula	01/2015
8582	730^26513+26513^730	75916	Norbert Schneider	11/2016
8583	7*10^75911-57	75912	Robert Price	06/2020
8584	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
8585	5^108596-14846	75906	Enzo Doria	02/2013
8586	(1377^24179-1)/1376	75894	Serge Batalov	07/2020
8587	(2^252082+2734)/2	75884	Stefano Morozzi	01/2020
8588	5^108560-14846	75881	Enzo Doria	02/2013
8589	2^252051-110359	75875	Enzo Doria	05/2014
8590	2^251971-110509	75851	Enzo Doria	05/2014
8591	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
8592	2^251842-4715	75812	Yves Minet	05/2019
8593	99655!6-2	75811	Robert Price	07/2017
8594	(2^251823+3290)/2	75806	Stefano Morozzi	01/2020
8595	14*10^75798+1089	75800	Jens K. Andersen	11/2007
8596	2^251784-455	75795	Yves Minet	03/2012
8597	2^251780-1289	75794	Yves Minet	01/2013
8598	2^251760-215609	75788	Paul Bourdelais	03/2013
8599	21947^2838+2838^21947	75784	Hans Havermann	01/2020
8600	99^37973+2	75781	Lelio R Paula	05/2013
8601	(185*10^75777+7)/3	75779	Robert Price	02/2017
8602	5*2^251690+3	75767	Lelio R Paula	06/2014
8603	6^97366+95	75766	Lelio R Paula	01/2015
8604	(4742^20611-1)/4741	75762	Serge Batalov	08/2020
8605	s(23010)	75760	Hans Havermann	11/2017
8606	(2^251666+1882)/2	75759	Stefano Morozzi	01/2020
8607	8*6^97337-7	75744	Lelio R Paula	10/2014
8608	24045^1412+1412^24045	75738	Hans Havermann	01/2020
8609	2^251588-111677	75736	Enzo Doria	05/2014
8610	(2^251580+2086)/2	75733	Stefano Morozzi	01/2020
8611	5^108346-13256	75731	Enzo Doria	02/2013
8612	(2^251570+1182)/2	75730	Stefano Morozzi	01/2020
8613	(31^50777+1)/32	75726	Robert Price	07/2013
8614	(10^75707+77)/3	75707	Robert Price	01/2017
8615	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
8616	2^251466+193	75699	Lelio R Paula	03/2012
8617	(2^251463+1338)/2	75698	Stefano Morozzi	01/2020
8618	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
8619	2^251422-109991	75686	Enzo Doria	04/2014
8620	91(10^23+1)(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)	75680	Makoto Kamada	03/2019
8621	(2^251355+3806)/2	75666	Stefano Morozzi	01/2020
8622	(2^251347+1278)/2	75663	Stefano Morozzi	01/2020
8623	4*5^108245-3	75661	Lelio R Paula	10/2014
8624	(25*10^75653+143)/3	75654	Robert Price	08/2020
8625	(2^251261+846)/2	75637	Stefano Morozzi	01/2020
8626	(2^251195+3770)/2	75617	Stefano Morozzi	01/2020
8627	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
8628	12^70066+95	75614	Lelio R Paula	02/2015
8629	(2^251181+1130)/2	75613	Stefano Morozzi	01/2020
8630	-E20534/2063	75607	Thomas Ritschel	02/2017
8631	19^59120-50	75600	Lelio R Paula	01/2015
8632	18^60222-4697	75596	Enzo Doria	03/2013
8633	18^60211-4355	75582	Enzo Doria	03/2013
8634	7*2^251014-9	75564	Lelio R Paula	06/2014
8635	6^97101-25	75560	Lelio R Paula	01/2015
8636	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
8637	(2^250974+3838)/2	75551	Stefano Morozzi	01/2020
8638	3^158331-140	75544	Lelio R Paula	01/2015
8639	(12235^18481-1)/12234	75539	Serge Batalov	08/2020
8640	(29*10^75532-107)/3	75533	Robert Price	08/2020
8643	(37^48157-1)/36	75519	Robert Price	03/2012
8641	(19*10^75518-43)/3	75519	Robert Price	10/2017
8642	2^250868-4229	75519	Yves Minet	08/2018
8644	10^75516+31467	75517	Patrick De Geest	03/2016
8646	10^75516-10^2256-1	75516	Serge Batalov	01/2011
8645	10^75516-66591	75516	Patrick De Geest	03/2016
8647	2^250851-187	75514	Lelio R Paula	03/2012
8648	(2^250836+466)/2	75509	Stefano Morozzi	01/2020
8649	22273^2454+2454^22273	75503	Hans Havermann	01/2020
8650	(43*10^75498-7)/9	75499	Robert Price	12/2014
8651	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
8652	4*5^107971-3	75470	Lelio R Paula	10/2014
8653	(25*10^75465+71)/3	75466	Robert Price	01/2017
8654	(2^250690+1222)/2	75465	Stefano Morozzi	01/2020
8656	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
8655	(2^250674+1354)/2	75461	Stefano Morozzi	01/2020
8657	(2^250670+1878)/2	75459	Stefano Morozzi	01/2020
8658	(182*10^75456+1)/3	75458	Robert Price	02/2017
8659	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
8660	(14583^18121-1)/14582	75449	Serge Batalov	08/2020
8661	10^75441+13	75442	Robert Price	01/2011
8662	10^75441-9923	75441	Patrick De Geest	05/2013
8663	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
8664	5*7^89231-6	75410	Lelio R Paula	10/2014
8666	2^250503-16995	75409	Lelio R Paula	05/2013
8665	11^72411-28	75409	Lelio R Paula	02/2015
8667	3*5^107860-8	75392	Lelio R Paula	10/2014
8668	(34*10^75387-403)/9	75388	Robert Price	10/2017
8671	2^250426+29835	75386	Lelio R Paula	05/2013
8669	8*3^157999-7	75386	Lelio R Paula	05/2014
8670	(15671^17971-1)/15670	75386	Serge Batalov	08/2020
8672	(2^250417+2642)/2	75383	Stefano Morozzi	01/2020
8673	(88*10^75381-43)/9	75382	Robert Price	11/2015
8674	(2^250394+2902)/2	75376	Stefano Morozzi	01/2020
8675	2^250382-111755	75373	Enzo Doria	05/2014
8676	2^250374-2798051	75371	Eric Chen	03/2016
8677	(22*10^75368-1)/3	75369	Robert Price	12/2014
8678	2^250369-4543	75369	Yves Minet	03/2019
8679	20078^5667+5667^20078	75360	Hans Havermann	02/2020
8680	(2^250318+2242)/2	75353	Stefano Morozzi	01/2020
8681	(21398^17401-1)/21397	75349	Serge Batalov	08/2020
8683	(19*10^75338+119)/3	75339	Robert Price	02/2017
8682	21517^3172+3172^21517	75339	Hans Havermann	01/2020
8684	2^250223-1859167	75325	Enzo Doria	03/2016
8685	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
8686	(2^250164+1578)/2	75307	Stefano Morozzi	01/2020
8687	3^157831-98	75305	Lelio R Paula	01/2015
8688	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
8689	92^38335-91	75282	Norbert Schneider	01/2016
8690	(2^250026+2398)/2	75266	Stefano Morozzi	01/2020
8691	2^250020+18915	75264	Lelio R Paula	05/2013
8692	2^250002+8193	75259	Lelio R Paula	05/2013
8693	(2^249996+1678)/2	75256	Stefano Morozzi	01/2020
8694	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
8695	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
8696	(5*10^75244+91)/3	75245	Robert Price	11/2016
8697	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
8698	14^65644+67	75237	Lelio R Paula	01/2015
8699	68383!4+32	75236	Robert Price	09/2019
8700	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
8701	129^35638+2	75218	Lelio R Paula	05/2013
8702	2^249853-110475	75214	Enzo Doria	05/2014
8703	(5704^20021-1)/5703	75199	Serge Batalov	08/2020
8704	20574^4517+4517^20574	75195	Hans Havermann	01/2020
8705	(11720^18481-1)/11719	75194	Serge Batalov	08/2020
8706	2^249762+75409	75186	Enzo Doria	04/2016
8707	565^27318+27318^565	75181	Norbert Schneider	12/2016
8708	(2^249741-7)/685	75177	Lelio R Paula	06/2012
8709	2^249726-112181	75176	Enzo Doria	06/2014
8710	2^249721+11715	75174	Lelio R Paula	05/2013
8711	(2^249705+654)/2	75169	Stefano Morozzi	01/2020
8713	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
8712	(15220^17971-1)/15219	75158	Serge Batalov	08/2020
8714	2^249658-47355	75155	Lelio R Paula	05/2013
8715	155^34311+2	75153	Lelio R Paula	05/2013
8716	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
8717	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
8718	2^249522+8415	75114	Lelio R Paula	05/2013
8719	2^249489-110911	75104	Enzo Doria	05/2014
8720	(28*10^75078+131)/3	75079	Robert Price	02/2017
8721	(206*10^75073-17)/9	75075	Robert Price	03/2017
8722	(2^249384+3330)/2	75072	Stefano Morozzi	01/2020
8723	(5947^19891-1)/5946	75071	Serge Batalov	08/2020
8724	2^249368-110573	75068	Enzo Doria	05/2014
8725	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
8726	19167^8248+8248^19167	75065	Hans Havermann	02/2020
8727	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
8728	(26*10^75055-173)/3	75056	Robert Price	10/2017
8730	2^249272+193	75039	Lelio R Paula	03/2012
8729	17433^17692-17692^17433	75039	Norbert Schneider	11/2019
8731	14^65468+43	75035	Lelio R Paula	01/2015
8732	37^47844+36	75030	Norbert Schneider	05/2014
8733	(52*10^75027-7)/9	75028	Robert Price	12/2014
8734	17943^15178+15178^17943	75024	Hans Havermann	02/2020
8735	(2^249219+494)/2	75023	Stefano Morozzi	01/2020
8736	20^57653+89	75009	Lelio R Paula	01/2015
8737	(2^249084+2682)/2	74982	Stefano Morozzi	01/2020
8738	2^249061-1868353	74975	Enzo Doria	04/2016
8739	(2^249056+1006)/2	74974	Stefano Morozzi	01/2020
8740	7^88713+2*3^88713	74972	Mike Oakes	07/2010
8741	18325^12334+12334^18325	74970	Hans Havermann	02/2020
8742	2*6^96313+5	74947	Lelio R Paula	10/2014
8744	(8*10^74944+49)/3	74945	Robert Price	03/2016
8743	(1258^24179-1)/1257	74945	Serge Batalov	07/2020
8745	300^30247+30247^300	74926	Norbert Schneider	11/2014
8746	2^248866-171	74917	Lelio R Paula	03/2012
8747	(714^26251-1)/713	74910	Serge Batalov	08/2020
8748	6*5^107168-7	74908	Lelio R Paula	10/2014
8749	11^71926+78	74904	Lelio R Paula	02/2015
8750	2^248824+1869391	74904	Enzo Doria	05/2016

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Probable Primes Top 10000

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