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 ?
6501	2^338889+195975	102016	Stefano Morozzi	11/2022
6502	2^338889-117873	102016	Stefano Morozzi	02/2023
6503	2^338886+177159	102015	Stefano Morozzi	12/2021
6504	2^338885+40425	102015	Stefano Morozzi	06/2022
6505	2^338884-13053	102015	Stefano Morozzi	12/2022
6506	2^338885-112569	102015	Stefano Morozzi	12/2022
6507	2^338880+11341	102014	Stefano Morozzi	03/2022
6508	2^338880-160383	102014	Stefano Morozzi	06/2022
6509	2^338880-161627	102014	Stefano Morozzi	12/2022
6510	2^338879-1059	102013	Stefano Morozzi	12/2021
6511	2^338879-54525	102013	Stefano Morozzi	02/2022
6512	2^338877-82813	102013	Stefano Morozzi	03/2022
6513	2^338878-185883	102013	Stefano Morozzi	06/2022
6514	2^338879-60355	102013	Stefano Morozzi	06/2022
6515	2^338878+43719	102013	Stefano Morozzi	09/2022
6516	2^338879+122049	102013	Stefano Morozzi	11/2022
6517	2^338874-15063	102012	Stefano Morozzi	01/2023
6518	2^338874+148993	102012	Stefano Morozzi	02/2023
6519	2^338871+7679	102011	Stefano Morozzi	02/2022
6520	2^338872+61141	102011	Stefano Morozzi	03/2022
6521	2^338872-183923	102011	Stefano Morozzi	04/2022
6522	2^338873+19527	102011	Stefano Morozzi	09/2022
6523	2^338870+70719	102011	Stefano Morozzi	11/2022
6524	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
6525	2^338870-37571	102011	Stefano Morozzi	12/2022
6526	2^338872-138573	102011	Stefano Morozzi	12/2022
6527	2^338873-63843	102011	Stefano Morozzi	12/2022
6528	2^338868-5985	102010	Stefano Morozzi	02/2022
6529	2^338867+38079	102010	Stefano Morozzi	05/2022
6530	2^338868+140437	102010	Stefano Morozzi	06/2022
6531	2^338868-110175	102010	Stefano Morozzi	06/2022
6532	2^338868+123337	102010	Stefano Morozzi	11/2022
6533	2^338867-13327	102010	Stefano Morozzi	12/2022
6534	2^338868-11279	102010	Stefano Morozzi	12/2022
6535	2^338868-115685	102010	Stefano Morozzi	01/2023
6536	2^338864+158191	102009	Stefano Morozzi	02/2022
6537	2^338865-39699	102009	Stefano Morozzi	01/2023
6538	2^338865-40789	102009	Stefano Morozzi	01/2023
6539	2^338862+60433	102008	Stefano Morozzi	03/2022
6540	2^338861-9453	102008	Stefano Morozzi	04/2022
6541	2^338861+98067	102008	Stefano Morozzi	11/2022
6542	2^338862+146545	102008	Stefano Morozzi	11/2022
6543	2^338863-186207	102008	Stefano Morozzi	12/2022
6544	2^338860-41429	102008	Stefano Morozzi	01/2023
6545	2^338862-115833	102008	Stefano Morozzi	01/2023
6546	2^338863+74259	102008	Stefano Morozzi	02/2023
6547	2^338863-193017	102008	Stefano Morozzi	02/2023
6548	2^338858-190185	102007	Stefano Morozzi	01/2023
6549	2^338855+102141	102006	Stefano Morozzi	12/2021
6550	2^338856-27173	102006	Stefano Morozzi	12/2021
6551	2^338856-102839	102006	Stefano Morozzi	01/2022
6552	2^338855+79629	102006	Stefano Morozzi	01/2022
6553	2^338856+47755	102006	Stefano Morozzi	11/2022
6554	2^338850+27987	102005	Stefano Morozzi	01/2022
6555	2^338853+111791	102005	Stefano Morozzi	04/2022
6556	2^338852+145797	102005	Stefano Morozzi	11/2022
6557	2^338852-88497	102005	Stefano Morozzi	12/2022
6558	2^338850+124843	102005	Stefano Morozzi	02/2023
6559	2^338853-167695	102005	Stefano Morozzi	02/2023
6560	2^338847+176013	102004	Stefano Morozzi	12/2021
6561	2^338847-2365	102004	Stefano Morozzi	12/2021
6562	2^338848+158941	102004	Stefano Morozzi	03/2022
6563	2^338848+16671	102004	Stefano Morozzi	06/2022
6564	2^338847-35061	102004	Stefano Morozzi	06/2022
6565	2^338848+145063	102004	Stefano Morozzi	11/2022
6566	2^338847-61885	102004	Stefano Morozzi	12/2022
6567	2^338845+135831	102003	Stefano Morozzi	03/2022
6568	2^338846+85695	102003	Stefano Morozzi	03/2022
6569	2^338845+186525	102003	Stefano Morozzi	04/2022
6570	2^338846-163473	102003	Stefano Morozzi	12/2022
6571	2^338844-16077	102003	Stefano Morozzi	01/2023
6572	2^338844-165143	102003	Stefano Morozzi	01/2023
6573	2^338843-127261	102002	Stefano Morozzi	12/2021
6574	2^338843+107205	102002	Stefano Morozzi	02/2022
6575	2^338842-33185	102002	Stefano Morozzi	04/2022
6576	2^338842+14227	102002	Stefano Morozzi	05/2022
6577	2^338842+147973	102002	Stefano Morozzi	11/2022
6585	8*10^102000+51	102001	Robert Price	08/2019
6578	2^338838+150837	102001	Stefano Morozzi	11/2021
6579	2^338838+141397	102001	Stefano Morozzi	06/2022
6580	2^338839+194363	102001	Stefano Morozzi	09/2022
6581	2^338838+95637	102001	Stefano Morozzi	11/2022
6582	2^338839+171545	102001	Stefano Morozzi	11/2022
6583	2^338837-40071	102001	Stefano Morozzi	01/2023
6584	2^338838-90251	102001	Stefano Morozzi	01/2023
6586	2^338835-150625	102000	Stefano Morozzi	12/2021
6587	2^338834-32877	102000	Stefano Morozzi	04/2022
6591	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
6588	2^338833-100905	101999	Stefano Morozzi	12/2021
6589	2^338831+54419	101999	Stefano Morozzi	01/2022
6590	2^338831-63687	101999	Stefano Morozzi	12/2022
6599	2^338829-113239	101998	Enzo Doria	07/2014
6600	2^338828-113297	101998	Enzo Doria	07/2014
6592	2^338830+25017	101998	Stefano Morozzi	11/2021
6593	2^338831+321	101998	Stefano Morozzi	11/2021
6594	2^338827-26197	101998	Stefano Morozzi	12/2021
6595	2^338829+52727	101998	Stefano Morozzi	01/2022
6596	2^338827-55461	101998	Stefano Morozzi	02/2022
6597	2^338828-65859	101998	Stefano Morozzi	01/2023
6598	2^338829+99365	101998	Stefano Morozzi	02/2023
6601	2^338825-27453	101997	Stefano Morozzi	12/2021
6602	2^338824+89355	101997	Stefano Morozzi	05/2022
6603	2^338825-10995	101997	Stefano Morozzi	06/2022
6604	2^338824+149865	101997	Stefano Morozzi	02/2023
6605	2^338822+111175	101996	Stefano Morozzi	03/2022
6606	2^338822+187819	101996	Stefano Morozzi	04/2022
6607	2^338823+139545	101996	Stefano Morozzi	05/2022
6608	2^338823-184905	101996	Stefano Morozzi	06/2022
6609	2^338821-38919	101996	Stefano Morozzi	12/2022
6610	2^338820+41317	101995	Stefano Morozzi	06/2022
6611	2^338817+46019	101995	Stefano Morozzi	11/2022
6612	2^338820+148083	101995	Stefano Morozzi	11/2022
6613	2^338817-163251	101995	Stefano Morozzi	12/2022
6614	2^338819-63705	101995	Stefano Morozzi	12/2022
6615	2^338817-92509	101995	Stefano Morozzi	02/2023
6616	2^338815+151175	101994	Stefano Morozzi	12/2021
6617	2^338814-30011	101994	Stefano Morozzi	02/2022
6618	2^338814+12309	101994	Stefano Morozzi	04/2022
6619	2^338816-60647	101994	Stefano Morozzi	06/2022
6620	2^338816+171043	101994	Stefano Morozzi	11/2022
6621	2^338814-11513	101994	Stefano Morozzi	12/2022
6622	2^338811-126999	101993	Stefano Morozzi	12/2021
6623	2^338811+131621	101993	Stefano Morozzi	02/2022
6624	2^338812-107637	101993	Stefano Morozzi	03/2022
6625	2^338813+192725	101993	Stefano Morozzi	09/2022
6626	2^338812+94731	101993	Stefano Morozzi	11/2022
6627	2^338813+49205	101993	Stefano Morozzi	02/2023
6628	2^338809-152755	101992	Stefano Morozzi	01/2022
6629	2^338808+156531	101992	Stefano Morozzi	01/2022
6630	2^338808+7885	101992	Stefano Morozzi	02/2022
6631	2^338808-105797	101992	Stefano Morozzi	02/2022
6632	2^338807-35899	101992	Stefano Morozzi	06/2022
6633	2^338808-89175	101992	Stefano Morozzi	01/2023
6634	2^338808-91475	101992	Stefano Morozzi	01/2023
6635	2^338805+29879	101991	Stefano Morozzi	01/2022
6636	2^338805+157925	101991	Stefano Morozzi	02/2022
6637	2^338804-6809	101991	Stefano Morozzi	03/2022
6638	2^338806-157095	101991	Stefano Morozzi	03/2022
6639	2^338804-133173	101991	Stefano Morozzi	04/2022
6640	2^338805-115189	101991	Stefano Morozzi	01/2023
6641	2^338802+150403	101990	Stefano Morozzi	11/2021
6642	2^338801+154587	101990	Stefano Morozzi	01/2022
6643	2^338802-180603	101990	Stefano Morozzi	02/2022
6644	2^338803-31921	101990	Stefano Morozzi	03/2022
6645	2^338803-81735	101990	Stefano Morozzi	03/2022
6646	2^338803+195141	101990	Stefano Morozzi	11/2022
6647	2^338800+160141	101989	Stefano Morozzi	03/2022
6648	2^338797-82489	101989	Stefano Morozzi	03/2022
6653	2^338796+93	101988	Donovan Johnson	06/2008
6649	2^338795+455	101988	Stefano Morozzi	11/2021
6650	2^338795-102075	101988	Stefano Morozzi	12/2021
6651	2^338794-3483	101988	Stefano Morozzi	01/2022
6652	2^338796+179641	101988	Stefano Morozzi	01/2022
6654	2^338793-5155	101987	Stefano Morozzi	02/2022
6655	2^338793+111107	101987	Stefano Morozzi	03/2022
6656	2^338791+112083	101987	Stefano Morozzi	04/2022
6657	2^338792-85097	101987	Stefano Morozzi	06/2022
6658	(61*10^101986+47)/9	101987	Robert Price	07/2022
6659	2^338787+53309	101986	Stefano Morozzi	01/2022
6660	2^338787-153817	101986	Stefano Morozzi	01/2022
6661	2^338789+56229	101986	Stefano Morozzi	01/2022
6662	2^338790+6429	101986	Stefano Morozzi	01/2022
6663	2^338788+131701	101986	Stefano Morozzi	02/2022
6664	2^338785+104639	101985	Stefano Morozzi	01/2022
6665	2^338784+37591	101985	Stefano Morozzi	04/2022
6666	2^338786-9831	101985	Stefano Morozzi	04/2022
6667	2^338783+109065	101984	Stefano Morozzi	03/2022
6668	2^338779+86711	101983	Stefano Morozzi	04/2022
6669	2^338778+113589	101983	Stefano Morozzi	05/2022
6670	2^338775-30369	101982	Stefano Morozzi	02/2022
6671	2^338774+159135	101982	Stefano Morozzi	03/2022
6672	2^338776+113001	101982	Stefano Morozzi	04/2022
6673	2^338774+117039	101982	Stefano Morozzi	09/2022
6674	2^338775+167109	101982	Stefano Morozzi	09/2022
6675	2^338774+147595	101982	Stefano Morozzi	11/2022
6676	2^338772+42733	101981	Stefano Morozzi	09/2022
6677	2^338771-138805	101981	Stefano Morozzi	12/2022
6678	2^338768-181007	101980	Stefano Morozzi	02/2022
6679	2^338768+108807	101980	Stefano Morozzi	03/2022
6680	2^338767+169155	101980	Stefano Morozzi	09/2022
6681	2^338769+95369	101980	Stefano Morozzi	11/2022
6682	2^338769+195965	101980	Stefano Morozzi	11/2022
6683	2^338770-12725	101980	Stefano Morozzi	12/2022
6684	2^338768-140843	101980	Stefano Morozzi	01/2023
6685	2^338764+138013	101979	Stefano Morozzi	04/2022
6686	2^338765-160323	101979	Stefano Morozzi	06/2022
6687	2^338765+124545	101979	Stefano Morozzi	02/2023
6693	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
6688	2^338761+103671	101978	Stefano Morozzi	01/2022
6689	2^338763-7651	101978	Stefano Morozzi	03/2022
6690	2^338763+65591	101978	Stefano Morozzi	06/2022
6691	2^338762-111875	101978	Stefano Morozzi	12/2022
6692	2^338762-192237	101978	Stefano Morozzi	02/2023
6694	2^338757-5151	101977	Stefano Morozzi	02/2022
6695	2^338760-79037	101977	Stefano Morozzi	02/2022
6696	2^338757-82143	101977	Stefano Morozzi	03/2022
6697	2^338757+137007	101977	Stefano Morozzi	04/2022
6698	2^338755+158531	101976	Stefano Morozzi	03/2022
6699	2^338755+74081	101976	Stefano Morozzi	02/2023
6700	2^338752-153353	101975	Stefano Morozzi	01/2022
6701	2^338751+8001	101975	Stefano Morozzi	02/2022
6702	2^338752+32977	101975	Stefano Morozzi	02/2022
6703	2^338753-79233	101975	Stefano Morozzi	02/2022
6704	2^338752-88157	101975	Stefano Morozzi	12/2022
6705	2^338750-175625	101974	Stefano Morozzi	12/2021
6706	2^338747-2731	101974	Stefano Morozzi	12/2021
6707	2^338750-29597	101974	Stefano Morozzi	02/2022
6708	2^338748+35095	101974	Stefano Morozzi	03/2022
6709	2^338747+137475	101974	Stefano Morozzi	04/2022
6710	2^338747+162005	101974	Stefano Morozzi	04/2022
6711	2^338750+162237	101974	Stefano Morozzi	04/2022
6712	2^338747-184365	101974	Stefano Morozzi	04/2022
6713	2^338748+64341	101974	Stefano Morozzi	05/2022
6714	2^338750+24445	101974	Stefano Morozzi	02/2023
6715	2^338746+59577	101973	Stefano Morozzi	03/2022
6716	2^338746+62055	101973	Stefano Morozzi	04/2022
6717	2^338744+194065	101973	Stefano Morozzi	09/2022
6718	2^338741+25359	101972	Stefano Morozzi	12/2021
6719	2^338743+176981	101972	Stefano Morozzi	12/2021
6720	2^338741+183029	101972	Stefano Morozzi	02/2022
6721	2^338743-130309	101972	Stefano Morozzi	02/2022
6722	2^338741+86349	101972	Stefano Morozzi	04/2022
6723	2^338741+111561	101972	Stefano Morozzi	04/2022
6724	2^338743+172301	101972	Stefano Morozzi	11/2022
6725	2^338741-189969	101972	Stefano Morozzi	01/2023
6726	2^338739+76959	101971	Stefano Morozzi	12/2021
6727	2^338739-105957	101971	Stefano Morozzi	02/2022
6728	2^338739+190149	101971	Stefano Morozzi	05/2022
6729	2^338738+64947	101971	Stefano Morozzi	05/2022
6730	2^338740+119947	101971	Stefano Morozzi	11/2022
6731	2^338740-186837	101971	Stefano Morozzi	12/2022
6732	2^338737+127547	101970	Stefano Morozzi	12/2021
6733	2^338737+128591	101970	Stefano Morozzi	01/2022
6734	2^338735-153165	101970	Stefano Morozzi	01/2022
6735	2^338734+13719	101970	Stefano Morozzi	05/2022
6736	2^338734-138225	101970	Stefano Morozzi	12/2022
6737	2^338735-186129	101970	Stefano Morozzi	12/2022
6743	25295^10744+10744^25295	101969	Hans Havermann	01/2019
6744	25712^9243+9243^25712	101969	Hans Havermann	01/2019
6738	2^338731-150895	101969	Stefano Morozzi	12/2021
6739	2^338731+54911	101969	Stefano Morozzi	01/2022
6740	2^338731+85863	101969	Stefano Morozzi	03/2022
6741	2^338732+185047	101969	Stefano Morozzi	03/2022
6742	2^338733+193791	101969	Stefano Morozzi	09/2022
6745	2^338729+69221	101968	Stefano Morozzi	09/2022
6746	2^338728+123355	101968	Stefano Morozzi	11/2022
6747	2^338730-87063	101968	Stefano Morozzi	12/2022
6748	2^338726+128199	101967	Stefano Morozzi	01/2022
6749	2^338727+127745	101967	Stefano Morozzi	01/2022
6750	2^338724+32971	101967	Stefano Morozzi	02/2022

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Probable Primes Top 10000

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