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	2^338590+60747	101926	Stefano Morozzi	03/2022
7252	2^338588+62397	101926	Stefano Morozzi	04/2022
7253	2^338589-9685	101926	Stefano Morozzi	04/2022
7254	2^338588+73765	101926	Stefano Morozzi	02/2023
7255	2^338589-16915	101926	Stefano Morozzi	02/2023
7262	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
7256	2^338586+1153	101925	Stefano Morozzi	12/2021
7257	2^338587-51709	101925	Stefano Morozzi	12/2021
7258	2^338586+105303	101925	Stefano Morozzi	01/2022
7259	2^338585-131773	101925	Stefano Morozzi	03/2022
7260	2^338587+168039	101925	Stefano Morozzi	09/2022
7261	2^338585-140719	101925	Stefano Morozzi	01/2023
7263	2^338584+100771	101924	Stefano Morozzi	11/2021
7264	2^338581-150415	101924	Stefano Morozzi	12/2021
7265	2^338581-2349	101924	Stefano Morozzi	12/2021
7266	2^338582+42933	101924	Stefano Morozzi	09/2022
7267	2^338584+93267	101924	Stefano Morozzi	09/2022
7268	2^338582-86697	101924	Stefano Morozzi	12/2022
7269	2^338582-138035	101924	Stefano Morozzi	12/2022
7270	2^338584-115569	101924	Stefano Morozzi	01/2023
7271	2^338581-92793	101924	Stefano Morozzi	02/2023
7272	2^338578+67593	101923	Stefano Morozzi	09/2022
7273	2^338580+142201	101923	Stefano Morozzi	09/2022
7274	2^338579-14635	101923	Stefano Morozzi	01/2023
7275	2^338579-164985	101923	Stefano Morozzi	01/2023
7276	2^338575-28815	101922	Stefano Morozzi	01/2022
7277	2^338575-33645	101922	Stefano Morozzi	04/2022
7278	2^338577-92239	101922	Stefano Morozzi	02/2023
7279	2^338573-156693	101921	Stefano Morozzi	03/2022
7280	2^338572+193305	101921	Stefano Morozzi	09/2022
7281	2^338573+173751	101921	Stefano Morozzi	02/2023
7282	2^338574+73707	101921	Stefano Morozzi	02/2023
7287	2^338568+37	101920	Lelio R Paula	07/2011
7283	2^338570-53933	101920	Stefano Morozzi	02/2022
7284	2^338569+87201	101920	Stefano Morozzi	04/2022
7285	2^338570-36897	101920	Stefano Morozzi	12/2022
7286	2^338570-61157	101920	Stefano Morozzi	12/2022
7288	2^338567-9619	101919	Stefano Morozzi	04/2022
7289	2^338565-141589	101919	Stefano Morozzi	01/2023
7290	2^338565+148821	101919	Stefano Morozzi	02/2023
7291	2^338564-56763	101918	Stefano Morozzi	03/2022
7292	2^338561+112007	101918	Stefano Morozzi	04/2022
7293	2^338561-9315	101918	Stefano Morozzi	04/2022
7294	2^338564+41965	101918	Stefano Morozzi	09/2022
7295	2^338561+121139	101918	Stefano Morozzi	11/2022
7296	2^338562+21799	101918	Stefano Morozzi	11/2022
7304	2^338559-1858777	101917	Enzo Doria	04/2016
7297	2^338558+4825	101917	Stefano Morozzi	01/2022
7298	2^338559-127935	101917	Stefano Morozzi	01/2022
7299	2^338560+154891	101917	Stefano Morozzi	01/2022
7300	2^338559+131885	101917	Stefano Morozzi	02/2022
7301	2^338558+93735	101917	Stefano Morozzi	09/2022
7302	2^338559-90957	101917	Stefano Morozzi	01/2023
7303	2^338559-190761	101917	Stefano Morozzi	01/2023
7305	2^338555+189981	101916	Stefano Morozzi	05/2022
7306	2^338553-125383	101915	Stefano Morozzi	12/2021
7307	2^338554-82821	101915	Stefano Morozzi	03/2022
7308	2^338548+76923	101914	Stefano Morozzi	12/2021
7309	2^338549+158517	101914	Stefano Morozzi	03/2022
7310	2^338549+85397	101914	Stefano Morozzi	03/2022
7311	2^338548+138121	101914	Stefano Morozzi	05/2022
7312	2^338550-110301	101914	Stefano Morozzi	06/2022
7313	2^338547+129321	101913	Stefano Morozzi	01/2022
7314	2^338547-153481	101913	Stefano Morozzi	01/2022
7315	2^338545-11059	101913	Stefano Morozzi	12/2022
7316	2^338544+107853	101912	Stefano Morozzi	02/2022
7317	2^338542+172813	101912	Stefano Morozzi	11/2022
7318	2^338544-12687	101912	Stefano Morozzi	12/2022
7319	2^338543-140677	101912	Stefano Morozzi	01/2023
7320	2^338541+152721	101911	Stefano Morozzi	01/2022
7321	2^338539+60825	101911	Stefano Morozzi	03/2022
7322	2^338539+160881	101911	Stefano Morozzi	03/2022
7323	2^338541-182523	101911	Stefano Morozzi	03/2022
7324	2^338540+87645	101911	Stefano Morozzi	04/2022
7325	2^338541+148305	101911	Stefano Morozzi	11/2022
7326	2^338541-163075	101911	Stefano Morozzi	12/2022
7327	2^338536-100785	101910	Stefano Morozzi	12/2021
7328	2^338535-51837	101910	Stefano Morozzi	12/2021
7329	2^338535-158745	101910	Stefano Morozzi	04/2022
7330	2^338536-189977	101910	Stefano Morozzi	01/2023
7331	2^338537-65623	101910	Stefano Morozzi	01/2023
7332	2^338532+39445	101909	Stefano Morozzi	05/2022
7333	2^338532+141415	101909	Stefano Morozzi	06/2022
7334	2^338532-136037	101909	Stefano Morozzi	06/2022
7335	2^338531+81081	101908	Stefano Morozzi	01/2022
7336	2^338530+59835	101908	Stefano Morozzi	03/2022
7337	2^338529+186551	101908	Stefano Morozzi	04/2022
7338	2^338531+61313	101908	Stefano Morozzi	04/2022
7339	2^338531-9277	101908	Stefano Morozzi	04/2022
7340	2^338528-92727	101908	Stefano Morozzi	02/2023
7341	2^338527+191205	101907	Stefano Morozzi	06/2022
7342	2^338525+99621	101907	Stefano Morozzi	02/2023
7343	2^338524+54421	101906	Stefano Morozzi	01/2022
7344	2^338522-155811	101906	Stefano Morozzi	02/2022
7345	2^338523-16291	101906	Stefano Morozzi	01/2023
7346	2^338522-142137	101906	Stefano Morozzi	02/2023
7347	2^338521+183131	101905	Stefano Morozzi	02/2022
7348	2^338520+34945	101905	Stefano Morozzi	03/2022
7349	2^338518-182885	101905	Stefano Morozzi	04/2022
7350	2^338518+114633	101905	Stefano Morozzi	05/2022
7351	2^338518-12621	101905	Stefano Morozzi	12/2022
7352	2^338518-187325	101905	Stefano Morozzi	12/2022
7360	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
7353	2^338517-125955	101904	Stefano Morozzi	12/2021
7354	2^338517+126437	101904	Stefano Morozzi	12/2021
7355	2^338517-53499	101904	Stefano Morozzi	01/2022
7356	2^338515+30369	101904	Stefano Morozzi	01/2022
7357	2^338517-184623	101904	Stefano Morozzi	04/2022
7358	2^338515+89333	101904	Stefano Morozzi	05/2022
7359	2^338515+198813	101904	Stefano Morozzi	02/2023
7363	24502^14419+14419^24502	101903	Hans Havermann	01/2019
7361	2^338512-827	101903	Stefano Morozzi	12/2021
7362	2^338514-6611	101903	Stefano Morozzi	03/2022
7364	2^338509+5139	101902	Stefano Morozzi	01/2022
7365	2^338509+40205	101902	Stefano Morozzi	06/2022
7366	2^338511+19959	101902	Stefano Morozzi	09/2022
7367	2^338510-37877	101902	Stefano Morozzi	12/2022
7368	2^338507-188655	101901	Stefano Morozzi	12/2022
7369	2^338507-114457	101901	Stefano Morozzi	01/2023
7370	2^338504-152615	101900	Stefano Morozzi	01/2022
7371	2^338502-4587	101900	Stefano Morozzi	02/2022
7372	2^338502-166275	101900	Stefano Morozzi	01/2023
7373	2^338500-26865	101899	Stefano Morozzi	12/2021
7374	2^338501-177471	101899	Stefano Morozzi	12/2021
7375	2^338499-3915	101899	Stefano Morozzi	01/2022
7376	2^338501+32051	101899	Stefano Morozzi	02/2022
7377	2^338499+183533	101899	Stefano Morozzi	03/2022
7378	2^338500+35625	101899	Stefano Morozzi	03/2022
7379	2^338499+87579	101899	Stefano Morozzi	04/2022
7380	2^338498-117683	101899	Stefano Morozzi	02/2023
7383	2^338497-17041	101898	Enzo Doria	05/2013
7381	2^338497+150405	101898	Stefano Morozzi	11/2021
7382	2^338495+100533	101898	Stefano Morozzi	12/2021
7384	2^338494+36057	101897	Stefano Morozzi	03/2022
7385	2^338492+39015	101897	Stefano Morozzi	05/2022
7386	2^338494+168007	101897	Stefano Morozzi	09/2022
7387	2^338490+61149	101896	Stefano Morozzi	03/2022
7388	2^338489+161369	101896	Stefano Morozzi	04/2022
7389	2^338491+22961	101896	Stefano Morozzi	11/2022
7390	2^338487-3555	101895	Stefano Morozzi	01/2022
7391	2^338487-183129	101895	Stefano Morozzi	04/2022
7392	2^338484+128767	101894	Stefano Morozzi	01/2022
7393	2^338484-31895	101894	Stefano Morozzi	03/2022
7394	2^338483-67899	101894	Stefano Morozzi	02/2023
7395	2^338483-192129	101894	Stefano Morozzi	02/2023
7396	2^338478+10893	101893	Stefano Morozzi	03/2022
7397	2^338479+87243	101893	Stefano Morozzi	04/2022
7398	2^338479+167619	101893	Stefano Morozzi	09/2022
7399	2^338480+197503	101893	Stefano Morozzi	11/2022
7400	2^338481-11421	101893	Stefano Morozzi	12/2022
7401	2^338479-89649	101893	Stefano Morozzi	01/2023
7402	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
7405	2^338475+54615	101892	Lelio R Paula	10/2016
7403	2^338475-59775	101892	Stefano Morozzi	04/2022
7404	2^338476-134237	101892	Stefano Morozzi	04/2022
7406	2^338474+100767	101891	Stefano Morozzi	11/2021
7407	2^338474+81165	101891	Stefano Morozzi	01/2022
7408	2^338474+41137	101891	Stefano Morozzi	06/2022
7409	2^338472-110445	101891	Stefano Morozzi	06/2022
7410	2^338473-89535	101891	Stefano Morozzi	01/2023
7411	2^338470+27777	101890	Stefano Morozzi	01/2022
7412	2^338468+31351	101890	Stefano Morozzi	01/2022
7413	2^338469-106339	101890	Stefano Morozzi	03/2022
7414	2^338471+187469	101890	Stefano Morozzi	04/2022
7415	2^338468+96613	101890	Stefano Morozzi	11/2022
7416	2^338469+46167	101890	Stefano Morozzi	11/2022
7417	2^338470+71527	101890	Stefano Morozzi	11/2022
7418	2^338469-112783	101890	Stefano Morozzi	12/2022
7419	2^338470-115665	101890	Stefano Morozzi	01/2023
7420	2^338467-25665	101889	Stefano Morozzi	12/2021
7421	2^338465+152139	101889	Stefano Morozzi	12/2021
7422	2^338466-28643	101889	Stefano Morozzi	01/2022
7423	2^338465+181517	101889	Stefano Morozzi	01/2022
7424	2^338466+115917	101889	Stefano Morozzi	06/2022
7425	2^338465-88291	101889	Stefano Morozzi	12/2022
7426	2^338464-104009	101888	Stefano Morozzi	02/2022
7427	2^338463+185169	101888	Stefano Morozzi	03/2022
7428	2^338464+60595	101888	Stefano Morozzi	03/2022
7429	2^338464-66377	101888	Stefano Morozzi	01/2023
7430	2^338458+60273	101887	Stefano Morozzi	03/2022
7431	2^338461+135867	101887	Stefano Morozzi	03/2022
7432	2^338455-4621	101886	Stefano Morozzi	02/2022
7433	2^338457+187827	101886	Stefano Morozzi	04/2022
7434	2^338455+173349	101886	Stefano Morozzi	11/2022
7435	2^338454+133737	101885	Stefano Morozzi	03/2022
7436	2^338454-158501	101885	Stefano Morozzi	04/2022
7437	2^338454-184217	101885	Stefano Morozzi	04/2022
7438	2^338453+164451	101885	Stefano Morozzi	05/2022
7439	2^338452-136137	101885	Stefano Morozzi	12/2022
7440	2^338450+106275	101884	Stefano Morozzi	01/2022
7441	2^338450+168439	101884	Stefano Morozzi	09/2022
7442	(133*10^101881+17)/3	101883	Robert Price	11/2021
7443	2^338445-80461	101883	Stefano Morozzi	02/2022
7444	2^338446-131211	101883	Stefano Morozzi	02/2022
7445	2^338448+187167	101883	Stefano Morozzi	04/2022
7446	2^338446-160115	101883	Stefano Morozzi	06/2022
7447	2^338447-164157	101883	Stefano Morozzi	01/2023
7448	2^338447-191001	101883	Stefano Morozzi	01/2023
7449	2^338444+127623	101882	Stefano Morozzi	12/2021
7450	2^338443-113827	101882	Stefano Morozzi	12/2022
7451	2^338441-5893	101881	Stefano Morozzi	02/2022
7452	2^338439-162565	101881	Stefano Morozzi	12/2022
7453	2^338436+153657	101880	Stefano Morozzi	01/2022
7454	2^338437-153159	101880	Stefano Morozzi	01/2022
7455	2^338436-83783	101880	Stefano Morozzi	04/2022
7456	2^338435+89109	101880	Stefano Morozzi	05/2022
7457	2^338435+13871	101880	Stefano Morozzi	05/2022
7458	2^338436+149691	101880	Stefano Morozzi	02/2023
7459	2^338434+81537	101879	Stefano Morozzi	01/2022
7460	2^338432+33495	101879	Stefano Morozzi	03/2022
7461	2^338432-7043	101879	Stefano Morozzi	03/2022
7462	2^338433-32629	101879	Stefano Morozzi	03/2022
7463	2^338430-9903	101878	Stefano Morozzi	04/2022
7471	2^338426-19797	101877	Enzo Doria	06/2013
7464	2^338427-77797	101877	Stefano Morozzi	01/2022
7465	2^338427-178687	101877	Stefano Morozzi	01/2022
7466	2^338428-54873	101877	Stefano Morozzi	02/2022
7467	2^338425+41357	101877	Stefano Morozzi	06/2022
7468	2^338428+90855	101877	Stefano Morozzi	06/2022
7469	2^338428-39807	101877	Stefano Morozzi	01/2023
7470	2^338425-192381	101877	Stefano Morozzi	02/2023
7472	2^338422-188787	101876	Stefano Morozzi	12/2022
7473	2^338423-187755	101876	Stefano Morozzi	12/2022
7474	2^338422-115865	101876	Stefano Morozzi	01/2023
7475	2^338420-178829	101875	Stefano Morozzi	01/2022
7476	2^338421-105423	101875	Stefano Morozzi	02/2022
7477	2^338419-82761	101875	Stefano Morozzi	03/2022
7478	2^338420+193143	101875	Stefano Morozzi	09/2022
7479	2^338419+199641	101875	Stefano Morozzi	02/2023
7480	2^338420-143103	101875	Stefano Morozzi	02/2023
7481	2^338418-50903	101874	Stefano Morozzi	12/2021
7482	2^338418+158355	101874	Stefano Morozzi	02/2022
7483	2^338418+159339	101874	Stefano Morozzi	03/2022
7484	2^338416+14953	101874	Stefano Morozzi	05/2022
7485	2^338416+166051	101874	Stefano Morozzi	06/2022
7486	2^338418-138765	101874	Stefano Morozzi	12/2022
7487	2^338417+49737	101874	Stefano Morozzi	02/2023
7488	2^338413-125919	101873	Stefano Morozzi	12/2021
7489	2^338414+26083	101873	Stefano Morozzi	12/2021
7490	2^338412-152379	101873	Stefano Morozzi	12/2021
7491	2^338413+54797	101873	Stefano Morozzi	01/2022
7492	2^338412+157951	101873	Stefano Morozzi	02/2022
7493	2^338414+81627	101873	Stefano Morozzi	02/2022
7494	2^338413+133679	101873	Stefano Morozzi	03/2022
7495	2^338413+197735	101873	Stefano Morozzi	11/2022
7496	2^338413-114301	101873	Stefano Morozzi	01/2023
7497	11*32^67682+395	101873	Eric Chen	04/2023
7498	2^338409-52183	101872	Stefano Morozzi	12/2021
7499	2^338411-3789	101872	Stefano Morozzi	01/2022
7500	2^338409+173237	101872	Stefano Morozzi	11/2022

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PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)