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	2^338808+7885	101992	Stefano Morozzi	02/2022
6502	2^338808-105797	101992	Stefano Morozzi	02/2022
6503	2^338807-35899	101992	Stefano Morozzi	06/2022
6504	2^338808-89175	101992	Stefano Morozzi	01/2023
6505	2^338808-91475	101992	Stefano Morozzi	01/2023
6506	2^338805+29879	101991	Stefano Morozzi	01/2022
6507	2^338805+157925	101991	Stefano Morozzi	02/2022
6508	2^338804-6809	101991	Stefano Morozzi	03/2022
6509	2^338806-157095	101991	Stefano Morozzi	03/2022
6510	2^338804-133173	101991	Stefano Morozzi	04/2022
6511	2^338805-115189	101991	Stefano Morozzi	01/2023
6512	2^338802+150403	101990	Stefano Morozzi	11/2021
6513	2^338801+154587	101990	Stefano Morozzi	01/2022
6514	2^338802-180603	101990	Stefano Morozzi	02/2022
6515	2^338803-31921	101990	Stefano Morozzi	03/2022
6516	2^338803-81735	101990	Stefano Morozzi	03/2022
6517	2^338803+195141	101990	Stefano Morozzi	11/2022
6518	2^338800+160141	101989	Stefano Morozzi	03/2022
6519	2^338797-82489	101989	Stefano Morozzi	03/2022
6524	2^338796+93	101988	Donovan Johnson	06/2008
6520	2^338795+455	101988	Stefano Morozzi	11/2021
6521	2^338795-102075	101988	Stefano Morozzi	12/2021
6522	2^338794-3483	101988	Stefano Morozzi	01/2022
6523	2^338796+179641	101988	Stefano Morozzi	01/2022
6525	2^338793-5155	101987	Stefano Morozzi	02/2022
6526	2^338793+111107	101987	Stefano Morozzi	03/2022
6527	2^338791+112083	101987	Stefano Morozzi	04/2022
6528	2^338792-85097	101987	Stefano Morozzi	06/2022
6529	(61*10^101986+47)/9	101987	Robert Price	07/2022
6530	2^338787+53309	101986	Stefano Morozzi	01/2022
6531	2^338787-153817	101986	Stefano Morozzi	01/2022
6532	2^338789+56229	101986	Stefano Morozzi	01/2022
6533	2^338790+6429	101986	Stefano Morozzi	01/2022
6534	2^338788+131701	101986	Stefano Morozzi	02/2022
6535	2^338785+104639	101985	Stefano Morozzi	01/2022
6536	2^338784+37591	101985	Stefano Morozzi	04/2022
6537	2^338786-9831	101985	Stefano Morozzi	04/2022
6538	2^338783+109065	101984	Stefano Morozzi	03/2022
6539	2^338779+86711	101983	Stefano Morozzi	04/2022
6540	2^338778+113589	101983	Stefano Morozzi	05/2022
6541	2^338775-30369	101982	Stefano Morozzi	02/2022
6542	2^338774+159135	101982	Stefano Morozzi	03/2022
6543	2^338776+113001	101982	Stefano Morozzi	04/2022
6544	2^338774+117039	101982	Stefano Morozzi	09/2022
6545	2^338775+167109	101982	Stefano Morozzi	09/2022
6546	2^338774+147595	101982	Stefano Morozzi	11/2022
6547	2^338772+42733	101981	Stefano Morozzi	09/2022
6548	2^338771-138805	101981	Stefano Morozzi	12/2022
6549	2^338768-181007	101980	Stefano Morozzi	02/2022
6550	2^338768+108807	101980	Stefano Morozzi	03/2022
6551	2^338767+169155	101980	Stefano Morozzi	09/2022
6552	2^338769+95369	101980	Stefano Morozzi	11/2022
6553	2^338769+195965	101980	Stefano Morozzi	11/2022
6554	2^338770-12725	101980	Stefano Morozzi	12/2022
6555	2^338768-140843	101980	Stefano Morozzi	01/2023
6556	2^338764+138013	101979	Stefano Morozzi	04/2022
6557	2^338765-160323	101979	Stefano Morozzi	06/2022
6562	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
6558	2^338761+103671	101978	Stefano Morozzi	01/2022
6559	2^338763-7651	101978	Stefano Morozzi	03/2022
6560	2^338763+65591	101978	Stefano Morozzi	06/2022
6561	2^338762-111875	101978	Stefano Morozzi	12/2022
6563	2^338757-5151	101977	Stefano Morozzi	02/2022
6564	2^338760-79037	101977	Stefano Morozzi	02/2022
6565	2^338757-82143	101977	Stefano Morozzi	03/2022
6566	2^338757+137007	101977	Stefano Morozzi	04/2022
6567	2^338755+158531	101976	Stefano Morozzi	03/2022
6568	2^338752-153353	101975	Stefano Morozzi	01/2022
6569	2^338751+8001	101975	Stefano Morozzi	02/2022
6570	2^338752+32977	101975	Stefano Morozzi	02/2022
6571	2^338753-79233	101975	Stefano Morozzi	02/2022
6572	2^338752-88157	101975	Stefano Morozzi	12/2022
6573	2^338750-175625	101974	Stefano Morozzi	12/2021
6574	2^338747-2731	101974	Stefano Morozzi	12/2021
6575	2^338750-29597	101974	Stefano Morozzi	02/2022
6576	2^338748+35095	101974	Stefano Morozzi	03/2022
6577	2^338747+137475	101974	Stefano Morozzi	04/2022
6578	2^338747+162005	101974	Stefano Morozzi	04/2022
6579	2^338750+162237	101974	Stefano Morozzi	04/2022
6580	2^338747-184365	101974	Stefano Morozzi	04/2022
6581	2^338748+64341	101974	Stefano Morozzi	05/2022
6582	2^338746+59577	101973	Stefano Morozzi	03/2022
6583	2^338746+62055	101973	Stefano Morozzi	04/2022
6584	2^338744+194065	101973	Stefano Morozzi	09/2022
6585	2^338741+25359	101972	Stefano Morozzi	12/2021
6586	2^338743+176981	101972	Stefano Morozzi	12/2021
6587	2^338741+183029	101972	Stefano Morozzi	02/2022
6588	2^338743-130309	101972	Stefano Morozzi	02/2022
6589	2^338741+86349	101972	Stefano Morozzi	04/2022
6590	2^338741+111561	101972	Stefano Morozzi	04/2022
6591	2^338743+172301	101972	Stefano Morozzi	11/2022
6592	2^338741-189969	101972	Stefano Morozzi	01/2023
6593	2^338739+76959	101971	Stefano Morozzi	12/2021
6594	2^338739-105957	101971	Stefano Morozzi	02/2022
6595	2^338739+190149	101971	Stefano Morozzi	05/2022
6596	2^338738+64947	101971	Stefano Morozzi	05/2022
6597	2^338740+119947	101971	Stefano Morozzi	11/2022
6598	2^338740-186837	101971	Stefano Morozzi	12/2022
6599	2^338737+127547	101970	Stefano Morozzi	12/2021
6600	2^338737+128591	101970	Stefano Morozzi	01/2022
6601	2^338735-153165	101970	Stefano Morozzi	01/2022
6602	2^338734+13719	101970	Stefano Morozzi	05/2022
6603	2^338734-138225	101970	Stefano Morozzi	12/2022
6604	2^338735-186129	101970	Stefano Morozzi	12/2022
6610	25295^10744+10744^25295	101969	Hans Havermann	01/2019
6611	25712^9243+9243^25712	101969	Hans Havermann	01/2019
6605	2^338731-150895	101969	Stefano Morozzi	12/2021
6606	2^338731+54911	101969	Stefano Morozzi	01/2022
6607	2^338731+85863	101969	Stefano Morozzi	03/2022
6608	2^338732+185047	101969	Stefano Morozzi	03/2022
6609	2^338733+193791	101969	Stefano Morozzi	09/2022
6612	2^338729+69221	101968	Stefano Morozzi	09/2022
6613	2^338728+123355	101968	Stefano Morozzi	11/2022
6614	2^338730-87063	101968	Stefano Morozzi	12/2022
6615	2^338726+128199	101967	Stefano Morozzi	01/2022
6616	2^338727+127745	101967	Stefano Morozzi	01/2022
6617	2^338724+32971	101967	Stefano Morozzi	02/2022
6618	2^338727+189683	101967	Stefano Morozzi	05/2022
6619	2^338727+118293	101967	Stefano Morozzi	09/2022
6620	2^338723-76651	101966	Stefano Morozzi	12/2021
6621	2^338721+79037	101966	Stefano Morozzi	01/2022
6622	2^338723-132621	101966	Stefano Morozzi	03/2022
6623	2^338722+137313	101966	Stefano Morozzi	04/2022
6624	2^338722+162915	101966	Stefano Morozzi	04/2022
6625	2^338718-126861	101965	Stefano Morozzi	12/2021
6626	2^338718-109127	101965	Stefano Morozzi	04/2022
6631	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
6627	2^338714+30835	101964	Stefano Morozzi	01/2022
6628	2^338714+156715	101964	Stefano Morozzi	02/2022
6629	2^338715+19923	101964	Stefano Morozzi	09/2022
6630	2^338716+173253	101964	Stefano Morozzi	11/2022
6632	2^338711+125399	101963	Stefano Morozzi	12/2021
6633	2^338713-30895	101963	Stefano Morozzi	02/2022
6634	2^338712-132545	101963	Stefano Morozzi	03/2022
6635	2^338713+87825	101963	Stefano Morozzi	04/2022
6636	2^338712+190333	101963	Stefano Morozzi	06/2022
6637	2^338709-154429	101962	Stefano Morozzi	02/2022
6638	2^338710+140545	101962	Stefano Morozzi	06/2022
6639	2^338706-102917	101961	Stefano Morozzi	01/2022
6640	2^338705+34727	101961	Stefano Morozzi	03/2022
6641	2^338706-165633	101961	Stefano Morozzi	01/2023
6642	2^338707-116115	101961	Stefano Morozzi	01/2023
6643	2^338698+104083	101959	Stefano Morozzi	01/2022
6644	2^338700-184565	101959	Stefano Morozzi	04/2022
6645	2^338700+189777	101959	Stefano Morozzi	05/2022
6646	2^338698+41779	101959	Stefano Morozzi	09/2022
6647	2^338699+148533	101959	Stefano Morozzi	11/2022
6648	2^338700+97381	101959	Stefano Morozzi	11/2022
6649	2^338696+181671	101958	Stefano Morozzi	02/2022
6650	2^338697+146651	101958	Stefano Morozzi	11/2022
6651	2^338692+106297	101957	Stefano Morozzi	01/2022
6652	2^338692+33195	101957	Stefano Morozzi	02/2022
6653	2^338692+110505	101957	Stefano Morozzi	03/2022
6654	2^338692+190093	101957	Stefano Morozzi	05/2022
6655	2^338692+173343	101957	Stefano Morozzi	11/2022
6656	2^338693+144975	101957	Stefano Morozzi	11/2022
6657	2^338688+82203	101956	Stefano Morozzi	02/2022
6658	2^338689+82365	101956	Stefano Morozzi	02/2022
6659	2^338686-81303	101955	Stefano Morozzi	03/2022
6660	2^338687+40461	101955	Stefano Morozzi	06/2022
6661	2^338687+65283	101955	Stefano Morozzi	06/2022
6666	2^338682-19865	101954	Enzo Doria	06/2013
6667	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
6662	(8*10^101954-269)/9	101954	Robert Price	09/2021
6663	2^338683+50303	101954	Stefano Morozzi	11/2021
6664	2^338682-107205	101954	Stefano Morozzi	03/2022
6665	2^338682+13839	101954	Stefano Morozzi	05/2022
6668	2^338678-180005	101953	Stefano Morozzi	02/2022
6669	2^338680+15855	101953	Stefano Morozzi	06/2022
6670	2^338678+93175	101953	Stefano Morozzi	09/2022
6671	2^338674-175967	101952	Stefano Morozzi	12/2021
6672	2^338677-177373	101952	Stefano Morozzi	12/2021
6673	2^338677+102999	101952	Stefano Morozzi	01/2022
6674	2^338676+33381	101952	Stefano Morozzi	03/2022
6675	2^338677-82699	101952	Stefano Morozzi	03/2022
6676	2^338676-34299	101952	Stefano Morozzi	04/2022
6677	2^338675+188445	101952	Stefano Morozzi	05/2022
6678	2^338676+165271	101952	Stefano Morozzi	06/2022
6679	2^338674-187551	101952	Stefano Morozzi	12/2022
6680	2^338671-55041	101951	Stefano Morozzi	02/2022
6681	2^338673-80203	101951	Stefano Morozzi	02/2022
6682	2^338672-182063	101951	Stefano Morozzi	03/2022
6683	2^338672+36667	101951	Stefano Morozzi	04/2022
6684	2^338668+2583	101950	Stefano Morozzi	12/2021
6685	2^338670-157001	101950	Stefano Morozzi	03/2022
6686	2^338669-8353	101950	Stefano Morozzi	04/2022
6687	2^338670+40635	101950	Stefano Morozzi	06/2022
6695	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
6688	2^338665+1577	101949	Stefano Morozzi	12/2021
6689	2^338665-51133	101949	Stefano Morozzi	12/2021
6690	2^338664+4345	101949	Stefano Morozzi	01/2022
6691	2^338666-128943	101949	Stefano Morozzi	01/2022
6692	2^338664+131535	101949	Stefano Morozzi	01/2022
6693	2^338667+14943	101949	Stefano Morozzi	05/2022
6694	2^338665+166637	101949	Stefano Morozzi	09/2022
6696	2^338662+31587	101948	Stefano Morozzi	02/2022
6697	2^338663-58375	101948	Stefano Morozzi	04/2022
6698	2^338663-107869	101948	Stefano Morozzi	04/2022
6699	2^338663+90435	101948	Stefano Morozzi	06/2022
6700	2^338661+70457	101948	Stefano Morozzi	11/2022
6701	2^338662+70519	101948	Stefano Morozzi	11/2022
6702	2^338663-39447	101948	Stefano Morozzi	01/2023
6703	2^338658-159191	101947	Stefano Morozzi	04/2022
6704	2^338659-159687	101947	Stefano Morozzi	04/2022
6705	2^338659+15543	101947	Stefano Morozzi	05/2022
6706	2^338658+44395	101947	Stefano Morozzi	09/2022
6707	2^338658+192537	101947	Stefano Morozzi	09/2022
6708	2^338659-90531	101947	Stefano Morozzi	01/2023
6709	2^338659-114759	101947	Stefano Morozzi	01/2023
6710	2^338654+51027	101946	Stefano Morozzi	12/2021
6711	2^338656-152115	101946	Stefano Morozzi	12/2021
6712	2^338654+32415	101946	Stefano Morozzi	02/2022
6713	2^338654+39799	101946	Stefano Morozzi	05/2022
6714	2^338655+144579	101946	Stefano Morozzi	09/2022
6715	2^338657+97509	101946	Stefano Morozzi	11/2022
6716	2^338653+126629	101945	Stefano Morozzi	12/2021
6717	2^338653+33279	101945	Stefano Morozzi	02/2022
6718	2^338652-107097	101945	Stefano Morozzi	03/2022
6719	2^338653+94475	101945	Stefano Morozzi	09/2022
6720	2^338651+194073	101945	Stefano Morozzi	09/2022
6721	2^338652-89157	101945	Stefano Morozzi	01/2023
6722	2^338649-154663	101944	Stefano Morozzi	02/2022
6723	2^338650+61399	101944	Stefano Morozzi	04/2022
6724	2^338650-35655	101944	Stefano Morozzi	06/2022
6725	2^338650+169623	101944	Stefano Morozzi	09/2022
6726	2^338649-40743	101944	Stefano Morozzi	01/2023
6727	2^338645+150311	101943	Stefano Morozzi	11/2021
6728	2^338645+28481	101943	Stefano Morozzi	01/2022
6729	2^338647-77895	101943	Stefano Morozzi	01/2022
6730	2^338647-84607	101943	Stefano Morozzi	04/2022
6731	2^338647+164523	101943	Stefano Morozzi	05/2022
6732	2^338645+64845	101943	Stefano Morozzi	05/2022
6733	2^338644-35969	101943	Stefano Morozzi	12/2022
6734	2^338645-15715	101943	Stefano Morozzi	01/2023
6735	2^338641-152541	101942	Stefano Morozzi	12/2021
6736	2^338643-56487	101942	Stefano Morozzi	03/2022
6737	2^338642-186525	101942	Stefano Morozzi	12/2022
6738	2^338638+100575	101941	Stefano Morozzi	12/2021
6739	2^338639-127461	101941	Stefano Morozzi	12/2021
6740	2^338640+187657	101941	Stefano Morozzi	04/2022
6741	2^338640+44431	101941	Stefano Morozzi	09/2022
6742	2^338635+1961	101940	Stefano Morozzi	12/2021
6743	2^338637+102125	101940	Stefano Morozzi	12/2021
6744	2^338636-135329	101940	Stefano Morozzi	06/2022
6749	28594^3673+3673^28594	101939	Hans Havermann	02/2019
6745	2^338631+110741	101939	Stefano Morozzi	03/2022
6746	2^338631+112119	101939	Stefano Morozzi	04/2022
6747	2^338634-83097	101939	Stefano Morozzi	04/2022
6748	2^338633+139701	101939	Stefano Morozzi	05/2022
6750	2^338630-150341	101938	Stefano Morozzi	12/2021

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Probable Primes Top 10000

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