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 ?
7251	2^338267+110481	101829	Stefano Morozzi	03/2022
7252	2^338267-166035	101829	Stefano Morozzi	01/2023
7253	2^338265-154893	101828	Stefano Morozzi	02/2022
7254	2^338264+163611	101828	Stefano Morozzi	05/2022
7255	2^338263-62767	101828	Stefano Morozzi	12/2022
7256	2^338261-188119	101827	Stefano Morozzi	12/2022
7257	2^338259-40327	101827	Stefano Morozzi	01/2023
7258	2^338256+5223	101826	Stefano Morozzi	01/2022
7259	2^338257+178425	101826	Stefano Morozzi	01/2022
7260	2^338256-180569	101826	Stefano Morozzi	02/2022
7261	2^338257-5965	101826	Stefano Morozzi	02/2022
7262	2^338258-9225	101826	Stefano Morozzi	04/2022
7263	2^338255-127021	101825	Stefano Morozzi	12/2021
7264	2^338253+159005	101825	Stefano Morozzi	03/2022
7265	2^338253+64817	101825	Stefano Morozzi	05/2022
7266	2^338254-85403	101825	Stefano Morozzi	06/2022
7267	2^338254+142947	101825	Stefano Morozzi	09/2022
7268	2^338253+121095	101825	Stefano Morozzi	11/2022
7269	2^338254+196725	101825	Stefano Morozzi	11/2022
7270	2^338254-91007	101825	Stefano Morozzi	01/2023
7271	2^338251+78975	101824	Stefano Morozzi	01/2022
7272	2^338252-178709	101824	Stefano Morozzi	01/2022
7273	2^338252+129703	101824	Stefano Morozzi	01/2022
7274	2^338252+132285	101824	Stefano Morozzi	02/2022
7275	2^338251-33381	101824	Stefano Morozzi	04/2022
7276	2^338252-13805	101824	Stefano Morozzi	12/2022
7277	2^338245-134755	101822	Stefano Morozzi	04/2022
7278	2^338244-59219	101822	Stefano Morozzi	04/2022
7279	2^338244-64703	101822	Stefano Morozzi	01/2023
7287	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
7280	2^338241+1391	101821	Stefano Morozzi	12/2021
7281	2^338242+151195	101821	Stefano Morozzi	12/2021
7282	2^338240-152495	101821	Stefano Morozzi	12/2021
7283	2^338240+81745	101821	Stefano Morozzi	02/2022
7284	2^338241-155551	101821	Stefano Morozzi	02/2022
7285	2^338242-108237	101821	Stefano Morozzi	04/2022
7286	2^338242+43045	101821	Stefano Morozzi	09/2022
7288	2^338238-126735	101820	Stefano Morozzi	12/2021
7289	2^338238+183855	101820	Stefano Morozzi	03/2022
7290	2^338238+141013	101820	Stefano Morozzi	06/2022
7291	2^338237+97227	101820	Stefano Morozzi	11/2022
7292	2^338238+48429	101820	Stefano Morozzi	11/2022
7293	2^338234-80925	101819	Stefano Morozzi	02/2022
7294	2^338234-154593	101819	Stefano Morozzi	02/2022
7295	2^338235-131787	101819	Stefano Morozzi	03/2022
7296	2^338233+89781	101819	Stefano Morozzi	05/2022
7297	2^338235+169971	101819	Stefano Morozzi	11/2022
7298	2^338233-113875	101819	Stefano Morozzi	12/2022
7305	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
7299	2^338232-175539	101818	Stefano Morozzi	12/2021
7300	2^338231+57345	101818	Stefano Morozzi	02/2022
7301	2^338232+36097	101818	Stefano Morozzi	03/2022
7302	2^338230+137403	101818	Stefano Morozzi	04/2022
7303	2^338231-59569	101818	Stefano Morozzi	04/2022
7304	2^338230-86633	101818	Stefano Morozzi	12/2022
7306	2^338228+159247	101817	Stefano Morozzi	03/2022
7307	2^338227-12631	101817	Stefano Morozzi	12/2022
7308	(34*10^101815+191)/9	101816	Robert Price	08/2021
7309	2^338224+185461	101816	Stefano Morozzi	03/2022
7310	2^338224+62295	101816	Stefano Morozzi	04/2022
7311	2^338225+162645	101816	Stefano Morozzi	04/2022
7312	2^338223+144209	101816	Stefano Morozzi	09/2022
7319	6^130841+103	101815	Lelio R Paula	10/2016
7313	2^338220+150405	101815	Stefano Morozzi	11/2021
7314	2^338219-4147	101815	Stefano Morozzi	01/2022
7315	2^338221+83391	101815	Stefano Morozzi	02/2022
7316	2^338221+62937	101815	Stefano Morozzi	04/2022
7317	2^338220-65697	101815	Stefano Morozzi	01/2023
7318	2^338220-139505	101815	Stefano Morozzi	01/2023
7320	2^338216+77473	101814	Stefano Morozzi	12/2021
7321	2^338218+155299	101814	Stefano Morozzi	01/2022
7322	2^338217-134745	101814	Stefano Morozzi	04/2022
7323	2^338218+73507	101814	Stefano Morozzi	11/2022
7324	2^338213-125631	101813	Stefano Morozzi	12/2021
7325	2^338215+25845	101813	Stefano Morozzi	12/2021
7326	2^338210-153537	101812	Stefano Morozzi	01/2022
7327	2^338209+60915	101812	Stefano Morozzi	03/2022
7328	2^338211-57297	101812	Stefano Morozzi	03/2022
7329	2^338211-110257	101812	Stefano Morozzi	06/2022
7330	2^338211+71549	101812	Stefano Morozzi	11/2022
7331	2^338208-178787	101811	Stefano Morozzi	01/2022
7332	2^338208+106153	101811	Stefano Morozzi	01/2022
7333	2^338207+16499	101811	Stefano Morozzi	06/2022
7334	2^338205+102471	101810	Stefano Morozzi	12/2021
7335	2^338199-176377	101809	Stefano Morozzi	12/2021
7336	2^338201-151233	101809	Stefano Morozzi	12/2021
7337	2^338202-152061	101809	Stefano Morozzi	12/2021
7338	2^338202+133785	101809	Stefano Morozzi	03/2022
7339	2^338200+135643	101809	Stefano Morozzi	03/2022
7340	2^338202+14169	101809	Stefano Morozzi	05/2022
7341	2^338202-85211	101809	Stefano Morozzi	06/2022
7342	2^338196+121147	101808	Stefano Morozzi	11/2022
7343	2^338196+73551	101808	Stefano Morozzi	11/2022
7344	2^338194-175845	101807	Stefano Morozzi	12/2021
7345	2^338195+56771	101807	Stefano Morozzi	02/2022
7346	2^338195+162365	101807	Stefano Morozzi	04/2022
7347	2^338194+67497	101807	Stefano Morozzi	09/2022
7348	2^338193-116335	101807	Stefano Morozzi	01/2023
7349	2^338194-15585	101807	Stefano Morozzi	01/2023
7350	2^338192+130387	101806	Stefano Morozzi	01/2022
7351	2^338190+89359	101806	Stefano Morozzi	05/2022
7352	2^338189+144605	101806	Stefano Morozzi	09/2022
7353	2^338190-113537	101806	Stefano Morozzi	12/2022
7354	2^338186+127245	101805	Stefano Morozzi	12/2021
7355	2^338186-130013	101805	Stefano Morozzi	02/2022
7356	2^338186+39235	101805	Stefano Morozzi	05/2022
7357	2^338185+77315	101804	Stefano Morozzi	12/2021
7358	2^338185+102519	101804	Stefano Morozzi	12/2021
7359	2^338183-76539	101804	Stefano Morozzi	12/2021
7360	2^338185+104489	101804	Stefano Morozzi	01/2022
7361	2^338179+35361	101803	Stefano Morozzi	03/2022
7362	2^338181+64235	101803	Stefano Morozzi	05/2022
7363	2^338181+94047	101803	Stefano Morozzi	09/2022
7364	2^338180+146131	101803	Stefano Morozzi	11/2022
7365	2^338179+123399	101803	Stefano Morozzi	11/2022
7366	2^338177+51807	101802	Stefano Morozzi	12/2021
7367	2^338177+107385	101802	Stefano Morozzi	02/2022
7368	2^338178+34287	101802	Stefano Morozzi	03/2022
7369	2^338178+184207	101802	Stefano Morozzi	03/2022
7370	2^338177-108901	101802	Stefano Morozzi	04/2022
7371	2^338177+141569	101802	Stefano Morozzi	06/2022
7372	2^338176+46221	101802	Stefano Morozzi	11/2022
7373	2^338175+25161	101801	Stefano Morozzi	11/2021
7374	2^338173-27901	101801	Stefano Morozzi	01/2022
7375	2^338174+23217	101801	Stefano Morozzi	11/2022
7376	2^338174+23793	101801	Stefano Morozzi	11/2022
7377	2^338173-36183	101801	Stefano Morozzi	12/2022
7378	2^338173-137053	101801	Stefano Morozzi	12/2022
7379	2^338174-36797	101801	Stefano Morozzi	12/2022
7380	2^338175-166509	101801	Stefano Morozzi	01/2023
7381	2^338169-155965	101800	Stefano Morozzi	02/2022
7382	2^338172+95797	101800	Stefano Morozzi	11/2022
7383	2^338166+183237	101799	Stefano Morozzi	02/2022
7384	2^338168-157835	101799	Stefano Morozzi	03/2022
7385	2^338166+137107	101799	Stefano Morozzi	04/2022
7386	2^338166+22897	101799	Stefano Morozzi	11/2022
7387	2^338166-161123	101799	Stefano Morozzi	12/2022
7388	2^338165-152139	101798	Stefano Morozzi	12/2021
7389	2^338163-178947	101798	Stefano Morozzi	02/2022
7390	2^338164-64329	101798	Stefano Morozzi	01/2023
7391	2^338159-127575	101797	Stefano Morozzi	12/2021
7392	2^338161+154259	101797	Stefano Morozzi	01/2022
7393	2^338160+139947	101797	Stefano Morozzi	05/2022
7394	2^338160+191815	101797	Stefano Morozzi	09/2022
7395	2^338160+22207	101797	Stefano Morozzi	11/2022
7396	2^338161+196157	101797	Stefano Morozzi	11/2022
7397	2^338162-138635	101797	Stefano Morozzi	12/2022
7398	2^338156-75269	101796	Stefano Morozzi	12/2021
7399	2^338156-151247	101796	Stefano Morozzi	12/2021
7400	2^338156+103273	101796	Stefano Morozzi	01/2022
7401	2^338156+167053	101796	Stefano Morozzi	09/2022
7402	2^338158+69303	101796	Stefano Morozzi	09/2022
7403	2^338158+171189	101796	Stefano Morozzi	11/2022
7404	2^338157-188989	101796	Stefano Morozzi	12/2022
7405	2^338158-188711	101796	Stefano Morozzi	12/2022
7406	2^338155+132621	101795	Stefano Morozzi	02/2022
7407	2^338155-82605	101795	Stefano Morozzi	03/2022
7408	2^338155-182631	101795	Stefano Morozzi	03/2022
7409	2^338155+187755	101795	Stefano Morozzi	04/2022
7410	2^338154-83975	101795	Stefano Morozzi	04/2022
7411	2^338154+163759	101795	Stefano Morozzi	05/2022
7412	2^338152-25767	101794	Stefano Morozzi	12/2021
7413	2^338152+181927	101794	Stefano Morozzi	02/2022
7414	2^338151+60779	101794	Stefano Morozzi	03/2022
7415	2^338151+189149	101794	Stefano Morozzi	05/2022
7416	2^338152+45567	101794	Stefano Morozzi	11/2022
7417	2^338147+29343	101793	Stefano Morozzi	01/2022
7418	2^338148+130803	101793	Stefano Morozzi	01/2022
7419	2^338146+166167	101793	Stefano Morozzi	06/2022
7420	2^338149-185073	101793	Stefano Morozzi	06/2022
7421	2^338149+41757	101793	Stefano Morozzi	09/2022
7422	2^338144+180697	101792	Stefano Morozzi	01/2022
7423	2^338143+8589	101792	Stefano Morozzi	02/2022
7424	2^338143-55611	101792	Stefano Morozzi	02/2022
7425	2^338143+60623	101792	Stefano Morozzi	03/2022
7426	2^338145-63609	101792	Stefano Morozzi	12/2022
7427	2^338141-77301	101791	Stefano Morozzi	12/2021
7428	2^338141+157145	101791	Stefano Morozzi	02/2022
7429	2^338140+84745	101791	Stefano Morozzi	03/2022
7430	2^338140+90073	101791	Stefano Morozzi	05/2022
7431	2^338142+96583	101791	Stefano Morozzi	11/2022
7432	2^338139-134719	101790	Stefano Morozzi	04/2022
7433	2^338138+95443	101790	Stefano Morozzi	11/2022
7434	2^338133+1445	101789	Stefano Morozzi	12/2021
7435	2^338133+172469	101789	Stefano Morozzi	11/2022
7436	2^338134+23235	101789	Stefano Morozzi	11/2022
7437	2^338132+105643	101788	Stefano Morozzi	01/2022
7438	2^338131+181871	101788	Stefano Morozzi	02/2022
7439	2^338132-184539	101788	Stefano Morozzi	04/2022
7440	2^338130+22383	101788	Stefano Morozzi	11/2022
7441	2^338132+170143	101788	Stefano Morozzi	11/2022
7442	2^338131-62599	101788	Stefano Morozzi	12/2022
7443	2^338128+128953	101787	Stefano Morozzi	01/2022
7444	2^338127+11021	101787	Stefano Morozzi	03/2022
7445	2^338127+192935	101787	Stefano Morozzi	09/2022
7446	2^338127+98621	101787	Stefano Morozzi	11/2022
7447	2^338123-25959	101786	Stefano Morozzi	12/2021
7448	2^338124-180765	101786	Stefano Morozzi	02/2022
7449	2^338125-7129	101786	Stefano Morozzi	03/2022
7450	2^338125-40071	101786	Stefano Morozzi	01/2023
7454	2^338122-20117	101785	Enzo Doria	06/2013
7455	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
7451	2^338122+32799	101785	Stefano Morozzi	02/2022
7452	2^338120+166411	101785	Stefano Morozzi	06/2022
7453	2^338122+90705	101785	Stefano Morozzi	06/2022
7456	2^338117+103761	101784	Stefano Morozzi	01/2022
7457	2^338118+53817	101784	Stefano Morozzi	01/2022
7458	2^338116+82585	101784	Stefano Morozzi	02/2022
7459	2^338118+39483	101784	Stefano Morozzi	05/2022
7460	2^338119+96659	101784	Stefano Morozzi	11/2022
7461	2^338115+61083	101783	Stefano Morozzi	03/2022
7462	2^338114+173287	101783	Stefano Morozzi	11/2022
7463	2^338113-139681	101783	Stefano Morozzi	01/2023
7464	2^338110-175365	101782	Stefano Morozzi	12/2021
7465	2^338110-3963	101782	Stefano Morozzi	01/2022
7466	2^338112+155061	101782	Stefano Morozzi	01/2022
7467	2^338112+137335	101782	Stefano Morozzi	04/2022
7468	2^338111-85627	101782	Stefano Morozzi	06/2022
7469	2^338111-90145	101782	Stefano Morozzi	01/2023
7478	35^65917-7092	101781	Enzo Doria	03/2013
7470	2^338107-1221	101781	Stefano Morozzi	12/2021
7471	2^338109+108539	101781	Stefano Morozzi	03/2022
7472	2^338109-7261	101781	Stefano Morozzi	03/2022
7473	2^338109-131961	101781	Stefano Morozzi	03/2022
7474	2^338108+39585	101781	Stefano Morozzi	05/2022
7475	2^338109+38147	101781	Stefano Morozzi	05/2022
7476	2^338108+17301	101781	Stefano Morozzi	09/2022
7477	2^338108-65859	101781	Stefano Morozzi	01/2023
7479	2^338105+79599	101780	Stefano Morozzi	01/2022
7480	2^338103-180675	101780	Stefano Morozzi	02/2022
7481	2^338103+19499	101780	Stefano Morozzi	09/2022
7482	2^338103-165319	101780	Stefano Morozzi	01/2023
7483	2^338100-100389	101779	Stefano Morozzi	12/2021
7484	2^338100+27595	101779	Stefano Morozzi	12/2021
7485	2^338101+101139	101779	Stefano Morozzi	12/2021
7486	2^338101+134985	101779	Stefano Morozzi	03/2022
7487	2^338102+186135	101779	Stefano Morozzi	03/2022
7488	2^338100+36885	101779	Stefano Morozzi	04/2022
7489	2^338102-8151	101779	Stefano Morozzi	04/2022
7490	2^338100+90637	101779	Stefano Morozzi	06/2022
7491	2^338101+68505	101779	Stefano Morozzi	09/2022
7492	2^338097+100229	101778	Stefano Morozzi	11/2021
7493	2^338097-25695	101778	Stefano Morozzi	12/2021
7494	2^338098-110043	101778	Stefano Morozzi	06/2022
7495	2^338099-191389	101778	Stefano Morozzi	01/2023
7496	2^338093-128403	101777	Stefano Morozzi	01/2022
7497	2^338093+33051	101777	Stefano Morozzi	02/2022
7498	2^338094+135555	101777	Stefano Morozzi	03/2022
7499	2^338095-32395	101777	Stefano Morozzi	03/2022
7500	2^338090-175353	101776	Stefano Morozzi	12/2021

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Probable Primes Top 10000

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