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	22576^15875+15875^22576	94836	Hans Havermann	09/2020
8502	(16*10^94822+53)/3	94823	Robert Price	12/2016
8503	8*6^121849-7	94818	Lelio R Paula	10/2014
8504	(85*10^94802+473)/9	94803	Robert Price	03/2017
8505	21767^21852-21852^21767	94790	Norbert Schneider	06/2020
8506	2^314870-108761	94786	Enzo Doria	03/2014
8507	5*2^314841-3	94778	Lelio R Paula	08/2014
8508	(2^314842+550)/2	94777	Stefano Morozzi	09/2020
8509	11738^23289-23289^11738	94777	Norbert Schneider	05/2022
8510	(2^314787+2630)/2	94761	Stefano Morozzi	09/2020
8511	6^121772+113	94758	Lelio R Paula	05/2016
8512	(2^314740+3642)/2	94746	Stefano Morozzi	09/2020
8513	6^121756-16253	94745	Enzo Doria	02/2013
8514	2^314718-112793	94740	Enzo Doria	06/2014
8515	2^314697-1847293	94734	Enzo Doria	07/2015
8516	22836^14065+14065^22836	94727	Hans Havermann	09/2020
8518	2^314548-249	94689	Yves Minet	02/2012
8517	5^135469+42	94689	Lelio R Paula	04/2016
8519	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
8520	25773^4712+4712^25773	94670	Hans Havermann	08/2020
8521	(2^314485+3614)/2	94670	Stefano Morozzi	09/2020
8522	(2*10^94604+547)/9	94604	Robert Price	10/2017
8523	(2^314164+2562)/2	94573	Stefano Morozzi	09/2020
8524	3*2^314152+5	94570	Lelio R Paula	08/2014
8525	2*6^121530-5	94570	Lelio R Paula	10/2014
8526	7*10^94563+87	94564	Robert Price	11/2016
8527	2^314114-109677	94558	Enzo Doria	04/2014
8528	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
8529	2^314059+76583	94542	Enzo Doria	05/2016
8530	2^314041-4035	94536	Lelio R Paula	03/2016
8531	(2^314028+3102)/2	94532	Stefano Morozzi	09/2020
8532	(2^314012+618)/2	94527	Stefano Morozzi	09/2020
8533	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
8534	11^90760-4710	94517	Enzo Doria	01/2013
8535	21675^21796+21796^21675	94507	Norbert Schneider	04/2020
8536	2^313942+100280245065	94506	Paul Bourdelais	10/2021
8537	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
8538	94*10^94493-3	94495	Robert Price	11/2016
8539	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
8540	(2^313859+2706)/2	94481	Stefano Morozzi	09/2020
8541	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
8542	7^111792-32	94476	Lelio R Paula	04/2016
8543	(2^313800+822)/2	94463	Stefano Morozzi	01/2021
8544	9*10^94462-47	94463	Robert Price	11/2021
8545	11*10^94460+3	94462	Robert Price	07/2021
8546	(202*10^94441-1)/3	94443	Robert Price	05/2020
8547	11^90680-5850	94434	Enzo Doria	01/2013
8548	(752^32833-1)/751	94432	Michael Stocker	05/2020
8549	2^313675-110125	94426	Enzo Doria	04/2014
8550	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
8551	2^313609-112225	94406	Enzo Doria	06/2014
8552	2^313584+72901	94399	Enzo Doria	04/2016
8553	(2^313567+1310)/2	94393	Stefano Morozzi	02/2021
8554	(2^313562+730)/2	94392	Stefano Morozzi	09/2020
8555	2^313510-112865	94376	Enzo Doria	06/2014
8556	7*10^94373+87	94374	Robert Price	11/2016
8557	(9^98897+8^98897)/17	94371	Robert Price	12/2012
8558	2^313453-114703	94359	Enzo Doria	04/2015
8559	8*10^94357-51	94358	Robert Price	10/2017
8560	25903^4392+4392^25903	94356	Hans Havermann	09/2020
8561	31706^945+945^31706	94340	Hans Havermann	09/2020
8562	(379*10^94337-1)/9	94339	Robert Price	08/2017
8563	2^313344-313344+1	94326	Robert Price	10/2014
8564	(2^313313+3662)/2	94317	Stefano Morozzi	09/2020
8565	20^72481-49	94300	Lelio R Paula	05/2016
8566	(34*10^94293-259)/9	94294	Robert Price	12/2021
8567	44725!2+128	94289	Robert Price	03/2015
8568	4*10^94286+9	94287	Robert Price	05/2015
8569	17^76621+24	94279	Lelio R Paula	07/2016
8570	26274^3875+3875^26274	94279	Hans Havermann	09/2020
8571	4*10^94270-33	94271	Robert Price	04/2021
8572	2^313156-112859	94270	Enzo Doria	06/2014
8573	(49*10^94262-211)/9	94263	Robert Price	06/2022
8574	6^121130-59	94258	Lelio R Paula	05/2016
8575	3^197542+28	94252	Robert Price	11/2013
8576	(2^313076+3550)/2	94245	Stefano Morozzi	09/2020
8577	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
8578	2^313045-5955	94236	Lelio R Paula	03/2016
8579	22099^18358+18358^22099	94227	Hans Havermann	08/2020
8580	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
8581	2^312909-1865203	94195	Enzo Doria	03/2016
8582	25013^5830+5830^25013	94191	Hans Havermann	09/2020
8583	2^312848-149	94177	Lelio R Paula	11/2012
8584	(2^312819+3278)/2	94168	Stefano Morozzi	02/2021
8585	4^156403-77597	94164	Mike Oakes	04/2011
8586	18^75004-85	94151	Lelio R Paula	06/2016
8587	19^73622-48	94145	Lelio R Paula	06/2016
8588	(11^90397-3^90397)/8	94138	Robert Price	04/2011
8589	(3^197287+5)/16	94129	Lelio R Paula	04/2013
8590	(23*10^94123-29)/3	94124	Robert Price	03/2022
8591	24220^7691+7691^24220	94119	Hans Havermann	09/2020
8592	12^87212-37	94118	Lelio R Paula	06/2016
8593	11^90376+76	94117	Lelio R Paula	05/2016
8594	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
8595	(2^312622+534)/2	94109	Stefano Morozzi	09/2020
8596	(10^94096+191)/3	94096	Robert Price	11/2017
8597	23794^9005+9005^23794	94093	Hans Havermann	09/2020
8598	2^312562-112685	94091	Enzo Doria	06/2014
8599	137^44026-2	94072	Lelio R Paula	10/2017
8600	s(164441)	94052	Robert Price	05/2020
8601	2^312404-869688105	94043	Lelio R Paula	09/2016
8602	2^312387+2793533	94038	Enzo Doria	03/2016
8604	10^94016+91	94017	Robert Price	04/2011
8603	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
8605	10^94016-188963	94016	Patrick De Geest	08/2013
8606	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
8607	(401*10^94010+13)/9	94012	Robert Price	09/2021
8608	23866^8691+8691^23866	94010	Hans Havermann	08/2020
8609	6^120802+7661	94003	Mike Oakes	04/2011
8610	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
8611	(2^312245+702)/2	93995	Stefano Morozzi	09/2020
8612	(56*10^93993+493)/9	93994	Robert Price	10/2021
8613	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
8614	2^312201+51	93982	Lelio R Paula	11/2012
8615	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
8616	(781*10^93942-7)/9	93944	Robert Price	12/2021
8617	3^196892+58	93942	Lelio R Paula	05/2016
8618	2^312060+18915	93940	Lelio R Paula	03/2016
8619	42^57867-41	93933	Norbert Schneider	08/2018
8620	8*10^93921+83	93922	Robert Price	11/2021
8621	2^311992-16209	93919	Enzo Doria	04/2013
8622	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
8623	2^311965-39	93911	Lelio R Paula	11/2012
8624	2^311920-111689	93898	Enzo Doria	05/2014
8625	130^44414+129	93889	Norbert Schneider	01/2019
8626	(2^311892+2730)/2	93889	Stefano Morozzi	09/2020
8627	7*10^93887-47	93888	Robert Price	02/2017
8628	9*10^93878-37	93879	Robert Price	06/2021
8629	(28*10^93874+323)/9	93875	Robert Price	10/2021
8630	(2^311778+1530)/2	93855	Stefano Morozzi	09/2020
8631	12^86965-13	93851	Lelio R Paula	06/2016
8632	24862^5953+5953^24862	93848	Hans Havermann	09/2020
8633	22299^16148+16148^22299	93837	Hans Havermann	08/2020
8634	2^311705+16095	93833	Lelio R Paula	03/2016
8635	(2^311701+3002)/2	93832	Stefano Morozzi	09/2020
8636	norm(Mod(x,x^3-x-1)^768329-1)	93831	Paul Vanderveen	09/2022
8638	2^311665-81	93821	Lelio R Paula	11/2012
8637	(2^311665+2654)/2	93821	Stefano Morozzi	09/2020
8639	(2^311648+3058)/2	93816	Stefano Morozzi	09/2020
8640	(2^311639+2738)/2	93813	Stefano Morozzi	01/2021
8641	730^32761+32761^730	93806	Norbert Schneider	09/2017
8642	11^90073+92	93802	Lelio R Paula	05/2016
8643	6*10^93792+41	93793	Robert Price	01/2017
8644	10^93790+64611	93791	Patrick De Geest	04/2020
8647	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
8645	10^93790-123456789	93790	Robert Price	02/2020
8646	10^93790-157517	93790	Patrick De Geest	04/2020
8648	(49*10^93782+293)/9	93783	Robert Price	03/2021
8649	12^86900-77	93781	Lelio R Paula	06/2016
8650	2^311508-109769	93774	Enzo Doria	04/2014
8651	2^311486-1859621	93767	Enzo Doria	03/2016
8652	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
8653	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
8654	2^311471+311469	93763	Renaud Lifchitz	01/2003
8655	(88*10^93760-1)/3	93762	Robert Price	10/2017
8656	2^311426+79459	93749	Enzo Doria	06/2016
8657	21537^21634+21634^21537	93745	Norbert Schneider	04/2020
8658	2^311409+111546435	93744	Paul Bourdelais	10/2021
8659	(2^311360+3078)/2	93729	Stefano Morozzi	09/2020
8660	(2^311341+2186)/2	93723	Stefano Morozzi	09/2020
8661	(2^311313+774)/2	93715	Stefano Morozzi	09/2020
8663	2^311294+5775	93709	Lelio R Paula	03/2016
8662	25155^5312+5312^25155	93709	Hans Havermann	09/2020
8664	2^311252-1017	93697	Lelio R Paula	03/2016
8665	2^311247-112041	93695	Enzo Doria	06/2014
8666	7*10^93692-83	93693	Robert Price	09/2017
8667	2^311205-109645	93683	Enzo Doria	04/2014
8668	5^134027-84	93681	Lelio R Paula	04/2016
8669	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
8670	(2^311027-2^155514+1)/5	93628		11/2006
8671	26748^3161+3161^26748	93614	Hans Havermann	08/2020
8672	3^196192-28	93608	Robert Price	12/2013
8673	216091#+261433	93606	Makoto Morimoto	12/2015
8674	5^133917+68	93604	Lelio R Paula	04/2016
8675	2^310924-1709	93598	Yves Minet	03/2013
8676	24555^6476+6476^24555	93587	Hans Havermann	08/2020
8677	(2^310867+734)/2	93580	Stefano Morozzi	09/2020
8678	(266*10^93577-11)/3	93579	Robert Price	09/2016
8679	(16*10^93577+161)/3	93578	Robert Price	05/2016
8680	3^196113-56	93570	Lelio R Paula	04/2016
8681	2^310806-110345	93562	Enzo Doria	05/2014
8682	3^196093+86	93561	Lelio R Paula	04/2016
8683	2^310780-2327	93555	Yves Minet	10/2013
8684	30^63332+41	93550	Lelio R Paula	08/2012
8685	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
8686	8*5^133807+7	93528	Lelio R Paula	10/2014
8687	2^310686+8193	93526	Lelio R Paula	03/2016
8688	22681^13282+13282^22681	93520	Hans Havermann	09/2020
8689	2^310646+63	93514	Lelio R Paula	11/2012
8690	(77*10^93508+31)/9	93509	Robert Price	10/2015
8691	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
8692	(2*10^93497+7)/9	93497	Erik Branger	03/2011
8693	3^195958-112852	93496	Enzo Doria	07/2014
8694	2^310583+16385	93495	Lelio R Paula	03/2016
8695	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
8696	9*7^110614+2	93481	Lelio R Paula	11/2014
8697	(19*10^93467+83)/3	93468	Robert Price	08/2020
8698	2^310469-8295	93461	Lelio R Paula	03/2016
8699	2^310459-1159	93458	Yves Minet	11/2012
8700	6^120075-95	93437	Lelio R Paula	05/2016
8701	(2^310362+1758)/2	93428	Stefano Morozzi	09/2020
8702	148^43041-147	93411	Norbert Schneider	05/2019
8703	2^310289+98327	93407	Yves Minet	11/2010
8704	21769^19510+19510^21769	93395	Hans Havermann	08/2020
8705	2^310217-113143	93385	Enzo Doria	07/2014
8706	7^110494-68	93379	Lelio R Paula	04/2016
8707	2^310184-113093	93375	Enzo Doria	07/2014
8708	2^310180-110417	93374	Enzo Doria	05/2014
8709	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
8710	(2^310173+3150)/2	93372	Stefano Morozzi	09/2020
8711	3^195669+68	93358	Lelio R Paula	04/2016
8712	10^93356+91	93357	Robert Price	04/2011
8713	10^93356-28313	93356	Patrick De Geest	08/2013
8714	(85*10^93346+23)/9	93347	Robert Price	11/2015
8715	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
8716	10^93333+191061	93334	Patrick De Geest	09/2022
8718	10^93333-4000001	93333	Robert Price	07/2021
8717	10^93333-44807	93333	Patrick De Geest	09/2022
8719	3^195556+8680	93304	Lelio R Paula	04/2016
8720	2^309942-109991	93302	Enzo Doria	04/2014
8721	2^309926-1867301	93298	Enzo Doria	03/2016
8722	2^309924+85951	93297	Yves Minet	03/2011
8723	2^309896-4229	93288	Yves Minet	08/2018
8724	(86*10^93263-77)/9	93264	Robert Price	05/2016
8725	6^119836-125	93251	Lelio R Paula	05/2016
8726	(77*10^93249-257)/9	93250	Robert Price	10/2017
8727	21822^18749+18749^21822	93245	Hans Havermann	09/2020
8728	3^195430-2	93244	Theodore Burton	02/2007
8729	(13*10^93236+47)/3	93237	Robert Price	01/2017
8730	(67*10^93226-7)/3	93228	Robert Price	10/2017
8731	(86*10^93217-221)/9	93218	Robert Price	06/2017
8732	2^309637-16329	93211	Enzo Doria	04/2013
8733	(41*10^93207+49)/9	93208	Robert Price	04/2016
8734	14^81312-57	93194	Lelio R Paula	06/2016
8735	41^57783-40	93192	Theodore Burton	02/2007
8736	3*10^93179-97	93180	Robert Price	08/2017
8737	5*7^110252-4	93175	Lelio R Paula	11/2014
8738	22022^16959+16959^22022	93140	Hans Havermann	08/2020
8739	83061!4-512	93137	Robert Price	11/2019
8740	25169^5016+5016^25169	93135	Hans Havermann	08/2020
8741	(483641^16384+1)/2	93135	Richard Fischer	02/2021
8742	2^309380-27	93133	Lelio R Paula	11/2012
8743	25653^4268+4268^25653	93127	Hans Havermann	08/2020
8744	(2^309355+1826)/2	93125	Stefano Morozzi	02/2021
8745	(2^309334+2710)/2	93119	Stefano Morozzi	09/2020
8746	23*10^93116-7	93118	Robert Price	03/2016
8747	(2^309270+3214)/2	93100	Stefano Morozzi	09/2020
8748	(29*10^93082+1)/3	93083	Robert Price	11/2015
8749	(2^309198+3738)/2	93078	Stefano Morozzi	09/2020
8750	(58*10^93062-13)/9	93063	Robert Price	09/2015

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