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 ?
7254	25295^10744+10744^25295	101969	Hans Havermann	01/2019
7255	25712^9243+9243^25712	101969	Hans Havermann	01/2019
7251	2^338731+85863	101969	Stefano Morozzi	03/2022
7252	2^338732+185047	101969	Stefano Morozzi	03/2022
7253	2^338733+193791	101969	Stefano Morozzi	09/2022
7256	2^338729+69221	101968	Stefano Morozzi	09/2022
7257	2^338728+123355	101968	Stefano Morozzi	11/2022
7258	2^338730-87063	101968	Stefano Morozzi	12/2022
7259	2^338726+128199	101967	Stefano Morozzi	01/2022
7260	2^338727+127745	101967	Stefano Morozzi	01/2022
7261	2^338724+32971	101967	Stefano Morozzi	02/2022
7262	2^338727+189683	101967	Stefano Morozzi	05/2022
7263	2^338727+118293	101967	Stefano Morozzi	09/2022
7264	2^338723-76651	101966	Stefano Morozzi	12/2021
7265	2^338721+79037	101966	Stefano Morozzi	01/2022
7266	2^338723-132621	101966	Stefano Morozzi	03/2022
7267	2^338722+137313	101966	Stefano Morozzi	04/2022
7268	2^338722+162915	101966	Stefano Morozzi	04/2022
7269	2^338723+199161	101966	Stefano Morozzi	02/2023
7270	2^338718-126861	101965	Stefano Morozzi	12/2021
7271	2^338718-109127	101965	Stefano Morozzi	04/2022
7276	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
7272	2^338714+30835	101964	Stefano Morozzi	01/2022
7273	2^338714+156715	101964	Stefano Morozzi	02/2022
7274	2^338715+19923	101964	Stefano Morozzi	09/2022
7275	2^338716+173253	101964	Stefano Morozzi	11/2022
7277	2^338711+125399	101963	Stefano Morozzi	12/2021
7278	2^338713-30895	101963	Stefano Morozzi	02/2022
7279	2^338712-132545	101963	Stefano Morozzi	03/2022
7280	2^338713+87825	101963	Stefano Morozzi	04/2022
7281	2^338712+190333	101963	Stefano Morozzi	06/2022
7282	2^338709-154429	101962	Stefano Morozzi	02/2022
7283	2^338710+140545	101962	Stefano Morozzi	06/2022
7284	2^338706-102917	101961	Stefano Morozzi	01/2022
7285	2^338705+34727	101961	Stefano Morozzi	03/2022
7286	2^338706-165633	101961	Stefano Morozzi	01/2023
7287	2^338707-116115	101961	Stefano Morozzi	01/2023
7288	2^338698+104083	101959	Stefano Morozzi	01/2022
7289	2^338700-184565	101959	Stefano Morozzi	04/2022
7290	2^338700+189777	101959	Stefano Morozzi	05/2022
7291	2^338698+41779	101959	Stefano Morozzi	09/2022
7292	2^338699+148533	101959	Stefano Morozzi	11/2022
7293	2^338700+97381	101959	Stefano Morozzi	11/2022
7294	2^338698-142181	101959	Stefano Morozzi	02/2023
7295	2^338696+181671	101958	Stefano Morozzi	02/2022
7296	2^338697+146651	101958	Stefano Morozzi	11/2022
7297	2^338695-116977	101958	Stefano Morozzi	02/2023
7298	2^338692+106297	101957	Stefano Morozzi	01/2022
7299	2^338692+33195	101957	Stefano Morozzi	02/2022
7300	2^338692+110505	101957	Stefano Morozzi	03/2022
7301	2^338692+190093	101957	Stefano Morozzi	05/2022
7302	2^338692+173343	101957	Stefano Morozzi	11/2022
7303	2^338693+144975	101957	Stefano Morozzi	11/2022
7304	2^338692+149281	101957	Stefano Morozzi	02/2023
7305	2^338688+82203	101956	Stefano Morozzi	02/2022
7306	2^338689+82365	101956	Stefano Morozzi	02/2022
7307	2^338688-92159	101956	Stefano Morozzi	02/2023
7308	2^338686-81303	101955	Stefano Morozzi	03/2022
7309	2^338687+40461	101955	Stefano Morozzi	06/2022
7310	2^338687+65283	101955	Stefano Morozzi	06/2022
7316	2^338682-19865	101954	Enzo Doria	06/2013
7317	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
7311	(8*10^101954-269)/9	101954	Robert Price	09/2021
7312	2^338683+50303	101954	Stefano Morozzi	11/2021
7313	2^338682-107205	101954	Stefano Morozzi	03/2022
7314	2^338682+13839	101954	Stefano Morozzi	05/2022
7315	2^338683-42837	101954	Stefano Morozzi	02/2023
7318	2^338678-180005	101953	Stefano Morozzi	02/2022
7319	2^338680+15855	101953	Stefano Morozzi	06/2022
7320	2^338678+93175	101953	Stefano Morozzi	09/2022
7321	2^338680+99217	101953	Stefano Morozzi	02/2023
7322	2^338674-175967	101952	Stefano Morozzi	12/2021
7323	2^338677-177373	101952	Stefano Morozzi	12/2021
7324	2^338677+102999	101952	Stefano Morozzi	01/2022
7325	2^338676+33381	101952	Stefano Morozzi	03/2022
7326	2^338677-82699	101952	Stefano Morozzi	03/2022
7327	2^338676-34299	101952	Stefano Morozzi	04/2022
7328	2^338675+188445	101952	Stefano Morozzi	05/2022
7329	2^338676+165271	101952	Stefano Morozzi	06/2022
7330	2^338674-187551	101952	Stefano Morozzi	12/2022
7331	2^338676-42243	101952	Stefano Morozzi	02/2023
7332	2^338671-55041	101951	Stefano Morozzi	02/2022
7333	2^338673-80203	101951	Stefano Morozzi	02/2022
7334	2^338672-182063	101951	Stefano Morozzi	03/2022
7335	2^338672+36667	101951	Stefano Morozzi	04/2022
7336	2^338668+2583	101950	Stefano Morozzi	12/2021
7337	2^338670-157001	101950	Stefano Morozzi	03/2022
7338	2^338669-8353	101950	Stefano Morozzi	04/2022
7339	2^338670+40635	101950	Stefano Morozzi	06/2022
7347	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
7340	2^338665+1577	101949	Stefano Morozzi	12/2021
7341	2^338665-51133	101949	Stefano Morozzi	12/2021
7342	2^338664+4345	101949	Stefano Morozzi	01/2022
7343	2^338666-128943	101949	Stefano Morozzi	01/2022
7344	2^338664+131535	101949	Stefano Morozzi	01/2022
7345	2^338667+14943	101949	Stefano Morozzi	05/2022
7346	2^338665+166637	101949	Stefano Morozzi	09/2022
7348	2^338662+31587	101948	Stefano Morozzi	02/2022
7349	2^338663-58375	101948	Stefano Morozzi	04/2022
7350	2^338663-107869	101948	Stefano Morozzi	04/2022
7351	2^338663+90435	101948	Stefano Morozzi	06/2022
7352	2^338661+70457	101948	Stefano Morozzi	11/2022
7353	2^338662+70519	101948	Stefano Morozzi	11/2022
7354	2^338663-39447	101948	Stefano Morozzi	01/2023
7355	2^338658-159191	101947	Stefano Morozzi	04/2022
7356	2^338659-159687	101947	Stefano Morozzi	04/2022
7357	2^338659+15543	101947	Stefano Morozzi	05/2022
7358	2^338658+44395	101947	Stefano Morozzi	09/2022
7359	2^338658+192537	101947	Stefano Morozzi	09/2022
7360	2^338659-90531	101947	Stefano Morozzi	01/2023
7361	2^338659-114759	101947	Stefano Morozzi	01/2023
7362	2^338659+124079	101947	Stefano Morozzi	02/2023
7363	2^338654+51027	101946	Stefano Morozzi	12/2021
7364	2^338656-152115	101946	Stefano Morozzi	12/2021
7365	2^338654+32415	101946	Stefano Morozzi	02/2022
7366	2^338654+39799	101946	Stefano Morozzi	05/2022
7367	2^338655+144579	101946	Stefano Morozzi	09/2022
7368	2^338657+97509	101946	Stefano Morozzi	11/2022
7369	2^338653+126629	101945	Stefano Morozzi	12/2021
7370	2^338653+33279	101945	Stefano Morozzi	02/2022
7371	2^338652-107097	101945	Stefano Morozzi	03/2022
7372	2^338653+94475	101945	Stefano Morozzi	09/2022
7373	2^338651+194073	101945	Stefano Morozzi	09/2022
7374	2^338652-89157	101945	Stefano Morozzi	01/2023
7375	2^338649-154663	101944	Stefano Morozzi	02/2022
7376	2^338650+61399	101944	Stefano Morozzi	04/2022
7377	2^338650-35655	101944	Stefano Morozzi	06/2022
7378	2^338650+169623	101944	Stefano Morozzi	09/2022
7379	2^338649-40743	101944	Stefano Morozzi	01/2023
7380	2^338645+150311	101943	Stefano Morozzi	11/2021
7381	2^338645+28481	101943	Stefano Morozzi	01/2022
7382	2^338647-77895	101943	Stefano Morozzi	01/2022
7383	2^338647-84607	101943	Stefano Morozzi	04/2022
7384	2^338647+164523	101943	Stefano Morozzi	05/2022
7385	2^338645+64845	101943	Stefano Morozzi	05/2022
7386	2^338644-35969	101943	Stefano Morozzi	12/2022
7387	2^338645-15715	101943	Stefano Morozzi	01/2023
7388	2^338641-152541	101942	Stefano Morozzi	12/2021
7389	2^338643-56487	101942	Stefano Morozzi	03/2022
7390	2^338642-186525	101942	Stefano Morozzi	12/2022
7391	2^338643-41715	101942	Stefano Morozzi	02/2023
7392	2^338638+100575	101941	Stefano Morozzi	12/2021
7393	2^338639-127461	101941	Stefano Morozzi	12/2021
7394	2^338640+187657	101941	Stefano Morozzi	04/2022
7395	2^338640+44431	101941	Stefano Morozzi	09/2022
7396	2^338635+1961	101940	Stefano Morozzi	12/2021
7397	2^338637+102125	101940	Stefano Morozzi	12/2021
7398	2^338636-135329	101940	Stefano Morozzi	06/2022
7399	2^338635+199485	101940	Stefano Morozzi	02/2023
7404	28594^3673+3673^28594	101939	Hans Havermann	02/2019
7400	2^338631+110741	101939	Stefano Morozzi	03/2022
7401	2^338631+112119	101939	Stefano Morozzi	04/2022
7402	2^338634-83097	101939	Stefano Morozzi	04/2022
7403	2^338633+139701	101939	Stefano Morozzi	05/2022
7405	2^338630-150341	101938	Stefano Morozzi	12/2021
7406	2^338630+12867	101938	Stefano Morozzi	04/2022
7407	2^338629+42147	101938	Stefano Morozzi	09/2022
7408	2^338628+121083	101938	Stefano Morozzi	11/2022
7409	2^338630+147235	101938	Stefano Morozzi	11/2022
7410	2^338628-37679	101938	Stefano Morozzi	12/2022
7411	2^338629-41383	101938	Stefano Morozzi	01/2023
7412	2^338628-91877	101938	Stefano Morozzi	02/2023
7413	2^338626-105875	101937	Stefano Morozzi	02/2022
7414	2^338625-111729	101937	Stefano Morozzi	12/2022
7415	2^338627+49299	101937	Stefano Morozzi	02/2023
7416	2^338621+33069	101936	Stefano Morozzi	02/2022
7417	2^338623-106405	101936	Stefano Morozzi	03/2022
7418	2^338621+61751	101936	Stefano Morozzi	04/2022
7419	2^338623-86577	101936	Stefano Morozzi	12/2022
7420	2^338620-150735	101935	Stefano Morozzi	12/2021
7421	2^338619-27765	101935	Stefano Morozzi	01/2022
7422	2^338619-77959	101935	Stefano Morozzi	01/2022
7423	2^338619-186367	101935	Stefano Morozzi	12/2022
7424	2^338618-64905	101935	Stefano Morozzi	01/2023
7425	2^338615+151655	101934	Stefano Morozzi	12/2021
7426	2^338616+5047	101934	Stefano Morozzi	01/2022
7427	2^338616+39705	101934	Stefano Morozzi	05/2022
7428	2^338617+149321	101934	Stefano Morozzi	02/2023
7429	2^338611+76659	101933	Stefano Morozzi	12/2021
7430	2^338613-109791	101933	Stefano Morozzi	04/2022
7431	2^338612+119583	101933	Stefano Morozzi	09/2022
7432	2^338611-140397	101933	Stefano Morozzi	01/2023
7433	2^338614-39653	101933	Stefano Morozzi	01/2023
7434	2^338609+130139	101932	Stefano Morozzi	01/2022
7435	2^338609+131327	101932	Stefano Morozzi	01/2022
7436	2^338608-155453	101932	Stefano Morozzi	02/2022
7437	2^338609+161721	101932	Stefano Morozzi	04/2022
7438	2^338609-10405	101932	Stefano Morozzi	06/2022
7439	2^338608+94017	101932	Stefano Morozzi	09/2022
7440	2^338610+170515	101932	Stefano Morozzi	11/2022
7441	2^338607+30611	101931	Stefano Morozzi	01/2022
7442	2^338607+106695	101931	Stefano Morozzi	02/2022
7443	2^338606-32291	101931	Stefano Morozzi	03/2022
7444	2^338606+15195	101931	Stefano Morozzi	05/2022
7445	2^338605+197789	101931	Stefano Morozzi	11/2022
7446	2^338607-90621	101931	Stefano Morozzi	01/2023
7447	2^338603-1195	101930	Stefano Morozzi	12/2021
7448	2^338601+108867	101930	Stefano Morozzi	03/2022
7449	2^338603+34311	101930	Stefano Morozzi	03/2022
7450	2^338598+57127	101929	Stefano Morozzi	02/2022
7451	2^338598+162645	101929	Stefano Morozzi	04/2022
7452	2^338599+43445	101929	Stefano Morozzi	09/2022
7453	2^338599+19485	101929	Stefano Morozzi	09/2022
7454	2^338598+46195	101929	Stefano Morozzi	11/2022
7455	2^338600-36393	101929	Stefano Morozzi	12/2022
7456	2^338596-1739	101928	Stefano Morozzi	12/2021
7457	2^338595-78687	101928	Stefano Morozzi	01/2022
7458	2^338595+181683	101928	Stefano Morozzi	02/2022
7459	2^338597-106045	101928	Stefano Morozzi	02/2022
7460	2^338595+119565	101928	Stefano Morozzi	09/2022
7461	2^338595+19623	101928	Stefano Morozzi	09/2022
7462	2^338595+21711	101928	Stefano Morozzi	11/2022
7463	2^338596-111129	101928	Stefano Morozzi	12/2022
7464	2^338591+53769	101927	Stefano Morozzi	01/2022
7465	2^338593+156989	101927	Stefano Morozzi	02/2022
7466	2^338592+36157	101927	Stefano Morozzi	03/2022
7467	2^338593+42099	101927	Stefano Morozzi	09/2022
7468	2^338591+46685	101927	Stefano Morozzi	11/2022
7469	2^338593+120437	101927	Stefano Morozzi	11/2022
7470	2^338591-165517	101927	Stefano Morozzi	01/2023
7471	2^338592-166107	101927	Stefano Morozzi	01/2023
7472	2^338592-189249	101927	Stefano Morozzi	01/2023
7473	2^338594-40493	101927	Stefano Morozzi	01/2023
7474	2^338590+182007	101926	Stefano Morozzi	02/2022
7475	2^338590+60747	101926	Stefano Morozzi	03/2022
7476	2^338588+62397	101926	Stefano Morozzi	04/2022
7477	2^338589-9685	101926	Stefano Morozzi	04/2022
7478	2^338588+73765	101926	Stefano Morozzi	02/2023
7479	2^338589-16915	101926	Stefano Morozzi	02/2023
7486	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
7480	2^338586+1153	101925	Stefano Morozzi	12/2021
7481	2^338587-51709	101925	Stefano Morozzi	12/2021
7482	2^338586+105303	101925	Stefano Morozzi	01/2022
7483	2^338585-131773	101925	Stefano Morozzi	03/2022
7484	2^338587+168039	101925	Stefano Morozzi	09/2022
7485	2^338585-140719	101925	Stefano Morozzi	01/2023
7487	2^338584+100771	101924	Stefano Morozzi	11/2021
7488	2^338581-150415	101924	Stefano Morozzi	12/2021
7489	2^338581-2349	101924	Stefano Morozzi	12/2021
7490	2^338582+42933	101924	Stefano Morozzi	09/2022
7491	2^338584+93267	101924	Stefano Morozzi	09/2022
7492	2^338582-86697	101924	Stefano Morozzi	12/2022
7493	2^338582-138035	101924	Stefano Morozzi	12/2022
7494	2^338584-115569	101924	Stefano Morozzi	01/2023
7495	2^338581-92793	101924	Stefano Morozzi	02/2023
7496	2^338578+67593	101923	Stefano Morozzi	09/2022
7497	2^338580+142201	101923	Stefano Morozzi	09/2022
7498	2^338579-14635	101923	Stefano Morozzi	01/2023
7499	2^338579-164985	101923	Stefano Morozzi	01/2023
7500	2^338575-28815	101922	Stefano Morozzi	01/2022

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Probable Primes Top 10000

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