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 ?
7501	8*10^102000+51	102001	Robert Price	08/2019
7502	2^338835-150625	102000	Stefano Morozzi	12/2021
7503	2^338834-32877	102000	Stefano Morozzi	04/2022
7507	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
7504	2^338833-100905	101999	Stefano Morozzi	12/2021
7505	2^338831+54419	101999	Stefano Morozzi	01/2022
7506	2^338831-63687	101999	Stefano Morozzi	12/2022
7515	2^338829-113239	101998	Enzo Doria	07/2014
7516	2^338828-113297	101998	Enzo Doria	07/2014
7508	2^338830+25017	101998	Stefano Morozzi	11/2021
7509	2^338831+321	101998	Stefano Morozzi	11/2021
7510	2^338827-26197	101998	Stefano Morozzi	12/2021
7511	2^338829+52727	101998	Stefano Morozzi	01/2022
7512	2^338827-55461	101998	Stefano Morozzi	02/2022
7513	2^338828-65859	101998	Stefano Morozzi	01/2023
7514	2^338829+99365	101998	Stefano Morozzi	02/2023
7517	2^338825-27453	101997	Stefano Morozzi	12/2021
7518	2^338824+89355	101997	Stefano Morozzi	05/2022
7519	2^338825-10995	101997	Stefano Morozzi	06/2022
7520	2^338824+149865	101997	Stefano Morozzi	02/2023
7521	2^338822+111175	101996	Stefano Morozzi	03/2022
7522	2^338822+187819	101996	Stefano Morozzi	04/2022
7523	2^338823+139545	101996	Stefano Morozzi	05/2022
7524	2^338823-184905	101996	Stefano Morozzi	06/2022
7525	2^338821-38919	101996	Stefano Morozzi	12/2022
7526	2^338820+41317	101995	Stefano Morozzi	06/2022
7527	2^338817+46019	101995	Stefano Morozzi	11/2022
7528	2^338820+148083	101995	Stefano Morozzi	11/2022
7529	2^338817-163251	101995	Stefano Morozzi	12/2022
7530	2^338819-63705	101995	Stefano Morozzi	12/2022
7531	2^338817-92509	101995	Stefano Morozzi	02/2023
7532	2^338815+151175	101994	Stefano Morozzi	12/2021
7533	2^338814-30011	101994	Stefano Morozzi	02/2022
7534	2^338814+12309	101994	Stefano Morozzi	04/2022
7535	2^338816-60647	101994	Stefano Morozzi	06/2022
7536	2^338816+171043	101994	Stefano Morozzi	11/2022
7537	2^338814-11513	101994	Stefano Morozzi	12/2022
7538	2^338811-126999	101993	Stefano Morozzi	12/2021
7539	2^338811+131621	101993	Stefano Morozzi	02/2022
7540	2^338812-107637	101993	Stefano Morozzi	03/2022
7541	2^338813+192725	101993	Stefano Morozzi	09/2022
7542	2^338812+94731	101993	Stefano Morozzi	11/2022
7543	2^338813+49205	101993	Stefano Morozzi	02/2023
7544	2^338809-152755	101992	Stefano Morozzi	01/2022
7545	2^338808+156531	101992	Stefano Morozzi	01/2022
7546	2^338808+7885	101992	Stefano Morozzi	02/2022
7547	2^338808-105797	101992	Stefano Morozzi	02/2022
7548	2^338807-35899	101992	Stefano Morozzi	06/2022
7549	2^338808-89175	101992	Stefano Morozzi	01/2023
7550	2^338808-91475	101992	Stefano Morozzi	01/2023
7551	2^338805+29879	101991	Stefano Morozzi	01/2022
7552	2^338805+157925	101991	Stefano Morozzi	02/2022
7553	2^338804-6809	101991	Stefano Morozzi	03/2022
7554	2^338806-157095	101991	Stefano Morozzi	03/2022
7555	2^338804-133173	101991	Stefano Morozzi	04/2022
7556	2^338805-115189	101991	Stefano Morozzi	01/2023
7557	2^338802+150403	101990	Stefano Morozzi	11/2021
7558	2^338801+154587	101990	Stefano Morozzi	01/2022
7559	2^338802-180603	101990	Stefano Morozzi	02/2022
7560	2^338803-31921	101990	Stefano Morozzi	03/2022
7561	2^338803-81735	101990	Stefano Morozzi	03/2022
7562	2^338803+195141	101990	Stefano Morozzi	11/2022
7563	2^338800+160141	101989	Stefano Morozzi	03/2022
7564	2^338797-82489	101989	Stefano Morozzi	03/2022
7569	2^338796+93	101988	Donovan Johnson	06/2008
7565	2^338795+455	101988	Stefano Morozzi	11/2021
7566	2^338795-102075	101988	Stefano Morozzi	12/2021
7567	2^338794-3483	101988	Stefano Morozzi	01/2022
7568	2^338796+179641	101988	Stefano Morozzi	01/2022
7570	2^338793-5155	101987	Stefano Morozzi	02/2022
7571	2^338793+111107	101987	Stefano Morozzi	03/2022
7572	2^338791+112083	101987	Stefano Morozzi	04/2022
7573	2^338792-85097	101987	Stefano Morozzi	06/2022
7574	(61*10^101986+47)/9	101987	Robert Price	07/2022
7575	2^338787+53309	101986	Stefano Morozzi	01/2022
7576	2^338787-153817	101986	Stefano Morozzi	01/2022
7577	2^338789+56229	101986	Stefano Morozzi	01/2022
7578	2^338790+6429	101986	Stefano Morozzi	01/2022
7579	2^338788+131701	101986	Stefano Morozzi	02/2022
7580	2^338785+104639	101985	Stefano Morozzi	01/2022
7581	2^338784+37591	101985	Stefano Morozzi	04/2022
7582	2^338786-9831	101985	Stefano Morozzi	04/2022
7583	2^338783+109065	101984	Stefano Morozzi	03/2022
7584	2^338779+86711	101983	Stefano Morozzi	04/2022
7585	2^338778+113589	101983	Stefano Morozzi	05/2022
7586	2^338775-30369	101982	Stefano Morozzi	02/2022
7587	2^338774+159135	101982	Stefano Morozzi	03/2022
7588	2^338776+113001	101982	Stefano Morozzi	04/2022
7589	2^338774+117039	101982	Stefano Morozzi	09/2022
7590	2^338775+167109	101982	Stefano Morozzi	09/2022
7591	2^338774+147595	101982	Stefano Morozzi	11/2022
7592	2^338772+42733	101981	Stefano Morozzi	09/2022
7593	2^338771-138805	101981	Stefano Morozzi	12/2022
7594	2^338768-181007	101980	Stefano Morozzi	02/2022
7595	2^338768+108807	101980	Stefano Morozzi	03/2022
7596	2^338767+169155	101980	Stefano Morozzi	09/2022
7597	2^338769+95369	101980	Stefano Morozzi	11/2022
7598	2^338769+195965	101980	Stefano Morozzi	11/2022
7599	2^338770-12725	101980	Stefano Morozzi	12/2022
7600	2^338768-140843	101980	Stefano Morozzi	01/2023
7601	2^338764+138013	101979	Stefano Morozzi	04/2022
7602	2^338765-160323	101979	Stefano Morozzi	06/2022
7603	2^338765+124545	101979	Stefano Morozzi	02/2023
7609	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
7604	2^338761+103671	101978	Stefano Morozzi	01/2022
7605	2^338763-7651	101978	Stefano Morozzi	03/2022
7606	2^338763+65591	101978	Stefano Morozzi	06/2022
7607	2^338762-111875	101978	Stefano Morozzi	12/2022
7608	2^338762-192237	101978	Stefano Morozzi	02/2023
7610	2^338757-5151	101977	Stefano Morozzi	02/2022
7611	2^338760-79037	101977	Stefano Morozzi	02/2022
7612	2^338757-82143	101977	Stefano Morozzi	03/2022
7613	2^338757+137007	101977	Stefano Morozzi	04/2022
7614	2^338755+158531	101976	Stefano Morozzi	03/2022
7615	2^338755+74081	101976	Stefano Morozzi	02/2023
7616	2^338752-153353	101975	Stefano Morozzi	01/2022
7617	2^338751+8001	101975	Stefano Morozzi	02/2022
7618	2^338752+32977	101975	Stefano Morozzi	02/2022
7619	2^338753-79233	101975	Stefano Morozzi	02/2022
7620	2^338752-88157	101975	Stefano Morozzi	12/2022
7621	2^338750-175625	101974	Stefano Morozzi	12/2021
7622	2^338747-2731	101974	Stefano Morozzi	12/2021
7623	2^338750-29597	101974	Stefano Morozzi	02/2022
7624	2^338748+35095	101974	Stefano Morozzi	03/2022
7625	2^338747+137475	101974	Stefano Morozzi	04/2022
7626	2^338747+162005	101974	Stefano Morozzi	04/2022
7627	2^338750+162237	101974	Stefano Morozzi	04/2022
7628	2^338747-184365	101974	Stefano Morozzi	04/2022
7629	2^338748+64341	101974	Stefano Morozzi	05/2022
7630	2^338750+24445	101974	Stefano Morozzi	02/2023
7631	2^338746+59577	101973	Stefano Morozzi	03/2022
7632	2^338746+62055	101973	Stefano Morozzi	04/2022
7633	2^338744+194065	101973	Stefano Morozzi	09/2022
7634	2^338741+25359	101972	Stefano Morozzi	12/2021
7635	2^338743+176981	101972	Stefano Morozzi	12/2021
7636	2^338741+183029	101972	Stefano Morozzi	02/2022
7637	2^338743-130309	101972	Stefano Morozzi	02/2022
7638	2^338741+86349	101972	Stefano Morozzi	04/2022
7639	2^338741+111561	101972	Stefano Morozzi	04/2022
7640	2^338743+172301	101972	Stefano Morozzi	11/2022
7641	2^338741-189969	101972	Stefano Morozzi	01/2023
7642	2^338739+76959	101971	Stefano Morozzi	12/2021
7643	2^338739-105957	101971	Stefano Morozzi	02/2022
7644	2^338739+190149	101971	Stefano Morozzi	05/2022
7645	2^338738+64947	101971	Stefano Morozzi	05/2022
7646	2^338740+119947	101971	Stefano Morozzi	11/2022
7647	2^338740-186837	101971	Stefano Morozzi	12/2022
7648	2^338737+127547	101970	Stefano Morozzi	12/2021
7649	2^338737+128591	101970	Stefano Morozzi	01/2022
7650	2^338735-153165	101970	Stefano Morozzi	01/2022
7651	2^338734+13719	101970	Stefano Morozzi	05/2022
7652	2^338734-138225	101970	Stefano Morozzi	12/2022
7653	2^338735-186129	101970	Stefano Morozzi	12/2022
7659	25295^10744+10744^25295	101969	Hans Havermann	01/2019
7660	25712^9243+9243^25712	101969	Hans Havermann	01/2019
7654	2^338731-150895	101969	Stefano Morozzi	12/2021
7655	2^338731+54911	101969	Stefano Morozzi	01/2022
7656	2^338731+85863	101969	Stefano Morozzi	03/2022
7657	2^338732+185047	101969	Stefano Morozzi	03/2022
7658	2^338733+193791	101969	Stefano Morozzi	09/2022
7661	2^338729+69221	101968	Stefano Morozzi	09/2022
7662	2^338728+123355	101968	Stefano Morozzi	11/2022
7663	2^338730-87063	101968	Stefano Morozzi	12/2022
7664	2^338726+128199	101967	Stefano Morozzi	01/2022
7665	2^338727+127745	101967	Stefano Morozzi	01/2022
7666	2^338724+32971	101967	Stefano Morozzi	02/2022
7667	2^338727+189683	101967	Stefano Morozzi	05/2022
7668	2^338727+118293	101967	Stefano Morozzi	09/2022
7669	2^338723-76651	101966	Stefano Morozzi	12/2021
7670	2^338721+79037	101966	Stefano Morozzi	01/2022
7671	2^338723-132621	101966	Stefano Morozzi	03/2022
7672	2^338722+137313	101966	Stefano Morozzi	04/2022
7673	2^338722+162915	101966	Stefano Morozzi	04/2022
7674	2^338723+199161	101966	Stefano Morozzi	02/2023
7675	2^338718-126861	101965	Stefano Morozzi	12/2021
7676	2^338718-109127	101965	Stefano Morozzi	04/2022
7681	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
7677	2^338714+30835	101964	Stefano Morozzi	01/2022
7678	2^338714+156715	101964	Stefano Morozzi	02/2022
7679	2^338715+19923	101964	Stefano Morozzi	09/2022
7680	2^338716+173253	101964	Stefano Morozzi	11/2022
7682	2^338711+125399	101963	Stefano Morozzi	12/2021
7683	2^338713-30895	101963	Stefano Morozzi	02/2022
7684	2^338712-132545	101963	Stefano Morozzi	03/2022
7685	2^338713+87825	101963	Stefano Morozzi	04/2022
7686	2^338712+190333	101963	Stefano Morozzi	06/2022
7687	2^338709-154429	101962	Stefano Morozzi	02/2022
7688	2^338710+140545	101962	Stefano Morozzi	06/2022
7689	2^338706-102917	101961	Stefano Morozzi	01/2022
7690	2^338705+34727	101961	Stefano Morozzi	03/2022
7691	2^338706-165633	101961	Stefano Morozzi	01/2023
7692	2^338707-116115	101961	Stefano Morozzi	01/2023
7693	2^338698+104083	101959	Stefano Morozzi	01/2022
7694	2^338700-184565	101959	Stefano Morozzi	04/2022
7695	2^338700+189777	101959	Stefano Morozzi	05/2022
7696	2^338698+41779	101959	Stefano Morozzi	09/2022
7697	2^338699+148533	101959	Stefano Morozzi	11/2022
7698	2^338700+97381	101959	Stefano Morozzi	11/2022
7699	2^338698-142181	101959	Stefano Morozzi	02/2023
7700	2^338696+181671	101958	Stefano Morozzi	02/2022
7701	2^338697+146651	101958	Stefano Morozzi	11/2022
7702	2^338695-116977	101958	Stefano Morozzi	02/2023
7703	2^338692+106297	101957	Stefano Morozzi	01/2022
7704	2^338692+33195	101957	Stefano Morozzi	02/2022
7705	2^338692+110505	101957	Stefano Morozzi	03/2022
7706	2^338692+190093	101957	Stefano Morozzi	05/2022
7707	2^338692+173343	101957	Stefano Morozzi	11/2022
7708	2^338693+144975	101957	Stefano Morozzi	11/2022
7709	2^338692+149281	101957	Stefano Morozzi	02/2023
7710	2^338688+82203	101956	Stefano Morozzi	02/2022
7711	2^338689+82365	101956	Stefano Morozzi	02/2022
7712	2^338688-92159	101956	Stefano Morozzi	02/2023
7713	2^338686-81303	101955	Stefano Morozzi	03/2022
7714	2^338687+40461	101955	Stefano Morozzi	06/2022
7715	2^338687+65283	101955	Stefano Morozzi	06/2022
7721	2^338682-19865	101954	Enzo Doria	06/2013
7722	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
7716	(8*10^101954-269)/9	101954	Robert Price	09/2021
7717	2^338683+50303	101954	Stefano Morozzi	11/2021
7718	2^338682-107205	101954	Stefano Morozzi	03/2022
7719	2^338682+13839	101954	Stefano Morozzi	05/2022
7720	2^338683-42837	101954	Stefano Morozzi	02/2023
7723	2^338678-180005	101953	Stefano Morozzi	02/2022
7724	2^338680+15855	101953	Stefano Morozzi	06/2022
7725	2^338678+93175	101953	Stefano Morozzi	09/2022
7726	2^338680+99217	101953	Stefano Morozzi	02/2023
7727	2^338674-175967	101952	Stefano Morozzi	12/2021
7728	2^338677-177373	101952	Stefano Morozzi	12/2021
7729	2^338677+102999	101952	Stefano Morozzi	01/2022
7730	2^338676+33381	101952	Stefano Morozzi	03/2022
7731	2^338677-82699	101952	Stefano Morozzi	03/2022
7732	2^338676-34299	101952	Stefano Morozzi	04/2022
7733	2^338675+188445	101952	Stefano Morozzi	05/2022
7734	2^338676+165271	101952	Stefano Morozzi	06/2022
7735	2^338674-187551	101952	Stefano Morozzi	12/2022
7736	2^338676-42243	101952	Stefano Morozzi	02/2023
7737	2^338671-55041	101951	Stefano Morozzi	02/2022
7738	2^338673-80203	101951	Stefano Morozzi	02/2022
7739	2^338672-182063	101951	Stefano Morozzi	03/2022
7740	2^338672+36667	101951	Stefano Morozzi	04/2022
7741	2^338668+2583	101950	Stefano Morozzi	12/2021
7742	2^338670-157001	101950	Stefano Morozzi	03/2022
7743	2^338669-8353	101950	Stefano Morozzi	04/2022
7744	2^338670+40635	101950	Stefano Morozzi	06/2022
7745	2^338665+1577	101949	Stefano Morozzi	12/2021
7746	2^338665-51133	101949	Stefano Morozzi	12/2021
7747	2^338664+4345	101949	Stefano Morozzi	01/2022
7748	2^338666-128943	101949	Stefano Morozzi	01/2022
7749	2^338664+131535	101949	Stefano Morozzi	01/2022
7750	2^338667+14943	101949	Stefano Morozzi	05/2022

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PRP Records

Probable Primes Top 10000

(295036 PRPs in the top)