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 ?
9251	2^338468+31351	101890	Stefano Morozzi	01/2022
9252	2^338469-106339	101890	Stefano Morozzi	03/2022
9253	2^338471+187469	101890	Stefano Morozzi	04/2022
9254	2^338468+96613	101890	Stefano Morozzi	11/2022
9255	2^338469+46167	101890	Stefano Morozzi	11/2022
9256	2^338470+71527	101890	Stefano Morozzi	11/2022
9257	2^338469-112783	101890	Stefano Morozzi	12/2022
9258	2^338470-115665	101890	Stefano Morozzi	01/2023
9259	2^338467-25665	101889	Stefano Morozzi	12/2021
9260	2^338465+152139	101889	Stefano Morozzi	12/2021
9261	2^338466-28643	101889	Stefano Morozzi	01/2022
9262	2^338465+181517	101889	Stefano Morozzi	01/2022
9263	2^338466+115917	101889	Stefano Morozzi	06/2022
9264	2^338465-88291	101889	Stefano Morozzi	12/2022
9265	2^338464-104009	101888	Stefano Morozzi	02/2022
9266	2^338463+185169	101888	Stefano Morozzi	03/2022
9267	2^338464+60595	101888	Stefano Morozzi	03/2022
9268	2^338464-66377	101888	Stefano Morozzi	01/2023
9269	2^338458+60273	101887	Stefano Morozzi	03/2022
9270	2^338461+135867	101887	Stefano Morozzi	03/2022
9271	2^338455-4621	101886	Stefano Morozzi	02/2022
9272	2^338457+187827	101886	Stefano Morozzi	04/2022
9273	2^338455+173349	101886	Stefano Morozzi	11/2022
9274	2^338454+133737	101885	Stefano Morozzi	03/2022
9275	2^338454-158501	101885	Stefano Morozzi	04/2022
9276	2^338454-184217	101885	Stefano Morozzi	04/2022
9277	2^338453+164451	101885	Stefano Morozzi	05/2022
9278	2^338452-136137	101885	Stefano Morozzi	12/2022
9279	2^338450+106275	101884	Stefano Morozzi	01/2022
9280	2^338450+168439	101884	Stefano Morozzi	09/2022
9281	(133*10^101881+17)/3	101883	Robert Price	11/2021
9282	2^338445-80461	101883	Stefano Morozzi	02/2022
9283	2^338446-131211	101883	Stefano Morozzi	02/2022
9284	2^338448+187167	101883	Stefano Morozzi	04/2022
9285	2^338446-160115	101883	Stefano Morozzi	06/2022
9286	2^338447-164157	101883	Stefano Morozzi	01/2023
9287	2^338447-191001	101883	Stefano Morozzi	01/2023
9288	2^338444+127623	101882	Stefano Morozzi	12/2021
9289	2^338443-113827	101882	Stefano Morozzi	12/2022
9290	2^338441-5893	101881	Stefano Morozzi	02/2022
9291	2^338439-162565	101881	Stefano Morozzi	12/2022
9292	2^338436+153657	101880	Stefano Morozzi	01/2022
9293	2^338437-153159	101880	Stefano Morozzi	01/2022
9294	2^338436-83783	101880	Stefano Morozzi	04/2022
9295	2^338435+89109	101880	Stefano Morozzi	05/2022
9296	2^338435+13871	101880	Stefano Morozzi	05/2022
9297	2^338436+149691	101880	Stefano Morozzi	02/2023
9298	2^338434+81537	101879	Stefano Morozzi	01/2022
9299	2^338432+33495	101879	Stefano Morozzi	03/2022
9300	2^338432-7043	101879	Stefano Morozzi	03/2022
9301	2^338433-32629	101879	Stefano Morozzi	03/2022
9302	2^338430-9903	101878	Stefano Morozzi	04/2022
9310	2^338426-19797	101877	Enzo Doria	06/2013
9303	2^338427-77797	101877	Stefano Morozzi	01/2022
9304	2^338427-178687	101877	Stefano Morozzi	01/2022
9305	2^338428-54873	101877	Stefano Morozzi	02/2022
9306	2^338425+41357	101877	Stefano Morozzi	06/2022
9307	2^338428+90855	101877	Stefano Morozzi	06/2022
9308	2^338428-39807	101877	Stefano Morozzi	01/2023
9309	2^338425-192381	101877	Stefano Morozzi	02/2023
9311	2^338422-188787	101876	Stefano Morozzi	12/2022
9312	2^338423-187755	101876	Stefano Morozzi	12/2022
9313	2^338422-115865	101876	Stefano Morozzi	01/2023
9314	2^338420-178829	101875	Stefano Morozzi	01/2022
9315	2^338421-105423	101875	Stefano Morozzi	02/2022
9316	2^338419-82761	101875	Stefano Morozzi	03/2022
9317	2^338420+193143	101875	Stefano Morozzi	09/2022
9318	2^338419+199641	101875	Stefano Morozzi	02/2023
9319	2^338420-143103	101875	Stefano Morozzi	02/2023
9320	2^338418-50903	101874	Stefano Morozzi	12/2021
9321	2^338418+158355	101874	Stefano Morozzi	02/2022
9322	2^338418+159339	101874	Stefano Morozzi	03/2022
9323	2^338416+14953	101874	Stefano Morozzi	05/2022
9324	2^338416+166051	101874	Stefano Morozzi	06/2022
9325	2^338418-138765	101874	Stefano Morozzi	12/2022
9326	2^338417+49737	101874	Stefano Morozzi	02/2023
9327	2^338413-125919	101873	Stefano Morozzi	12/2021
9328	2^338414+26083	101873	Stefano Morozzi	12/2021
9329	2^338412-152379	101873	Stefano Morozzi	12/2021
9330	2^338413+54797	101873	Stefano Morozzi	01/2022
9331	2^338412+157951	101873	Stefano Morozzi	02/2022
9332	2^338414+81627	101873	Stefano Morozzi	02/2022
9333	2^338413+133679	101873	Stefano Morozzi	03/2022
9334	2^338413+197735	101873	Stefano Morozzi	11/2022
9335	2^338413-114301	101873	Stefano Morozzi	01/2023
9336	11*32^67682+395	101873	Eric Chen	04/2023
9337	2^338409-52183	101872	Stefano Morozzi	12/2021
9338	2^338411-3789	101872	Stefano Morozzi	01/2022
9339	2^338409+173237	101872	Stefano Morozzi	11/2022
9340	2^338406-184175	101871	Stefano Morozzi	04/2022
9341	2^338405+94451	101871	Stefano Morozzi	09/2022
9342	2^338406-161217	101871	Stefano Morozzi	12/2022
9343	2^338406+199929	101871	Stefano Morozzi	02/2023
9344	2^338404+55717	101870	Stefano Morozzi	01/2022
9345	2^338403+36261	101870	Stefano Morozzi	04/2022
9346	2^338402-34431	101870	Stefano Morozzi	04/2022
9347	2^338404-159215	101870	Stefano Morozzi	04/2022
9348	2^338403+18363	101870	Stefano Morozzi	09/2022
9349	2^338403+170235	101870	Stefano Morozzi	11/2022
9350	2^338399+23045	101869	Stefano Morozzi	11/2022
9351	2^338399-65535	101869	Stefano Morozzi	01/2023
9352	2^338395-127449	101868	Stefano Morozzi	12/2021
9353	2^338398-127637	101868	Stefano Morozzi	01/2022
9354	2^338398-166533	101868	Stefano Morozzi	01/2023
9355	2^338394+100317	101867	Stefano Morozzi	11/2021
9356	2^338393-152749	101867	Stefano Morozzi	01/2022
9357	2^338393+163025	101867	Stefano Morozzi	04/2022
9358	2^338393+89229	101867	Stefano Morozzi	05/2022
9359	2^338393+99647	101867	Stefano Morozzi	02/2023
9360	2^338394-192471	101867	Stefano Morozzi	02/2023
9361	2^338390+76627	101866	Stefano Morozzi	12/2021
9362	2^338389-85081	101866	Stefano Morozzi	06/2022
9363	2^338390+148113	101866	Stefano Morozzi	11/2022
9364	2^338389-14253	101866	Stefano Morozzi	01/2023
9365	2^338390-114297	101866	Stefano Morozzi	01/2023
9366	2^338391-64225	101866	Stefano Morozzi	01/2023
9367	2^338389-16971	101866	Stefano Morozzi	02/2023
9368	2^338387-75685	101865	Stefano Morozzi	12/2021
9369	2^338388-53459	101865	Stefano Morozzi	01/2022
9370	2^338388-36575	101865	Stefano Morozzi	12/2022
9371	2^338385-190311	101865	Stefano Morozzi	01/2023
9372	2^338384+131563	101864	Stefano Morozzi	01/2022
9373	2^338382+109069	101864	Stefano Morozzi	03/2022
9374	2^338384+168987	101864	Stefano Morozzi	09/2022
9375	2^338383-42367	101864	Stefano Morozzi	02/2023
9376	2^338380+77125	101863	Stefano Morozzi	12/2021
9377	2^338381-35539	101863	Stefano Morozzi	06/2022
9378	2^338378-125841	101862	Stefano Morozzi	12/2021
9379	2^338375+27815	101862	Stefano Morozzi	01/2022
9380	2^338375-28509	101862	Stefano Morozzi	01/2022
9381	2^338375+29985	101862	Stefano Morozzi	01/2022
9382	2^338377+157881	101862	Stefano Morozzi	02/2022
9383	2^338375+59589	101862	Stefano Morozzi	03/2022
9384	2^338378+36399	101862	Stefano Morozzi	04/2022
9385	2^338378-159773	101862	Stefano Morozzi	04/2022
9386	2^338378+14883	101862	Stefano Morozzi	05/2022
9387	2^338376+140173	101862	Stefano Morozzi	06/2022
9388	2^338375+18761	101862	Stefano Morozzi	09/2022
9389	2^338373-75103	101861	Stefano Morozzi	12/2021
9390	2^338372+128877	101861	Stefano Morozzi	01/2022
9391	2^338374-28731	101861	Stefano Morozzi	01/2022
9392	2^338374-128427	101861	Stefano Morozzi	01/2022
9393	2^338372+37875	101861	Stefano Morozzi	04/2022
9394	2^338373+161541	101861	Stefano Morozzi	04/2022
9395	2^338374+37759	101861	Stefano Morozzi	04/2022
9396	2^338372+93235	101861	Stefano Morozzi	09/2022
9397	2^338373-63273	101861	Stefano Morozzi	12/2022
9398	2^338369+29427	101860	Stefano Morozzi	01/2022
9399	2^338370+179133	101860	Stefano Morozzi	01/2022
9400	2^338369+131501	101860	Stefano Morozzi	01/2022
9401	2^338369+181649	101860	Stefano Morozzi	02/2022
9402	2^338370-4787	101860	Stefano Morozzi	02/2022
9403	2^338371-133491	101860	Stefano Morozzi	04/2022
9404	2^338371+42023	101860	Stefano Morozzi	09/2022
9405	2^338371+145323	101860	Stefano Morozzi	11/2022
9406	2^338371-138145	101860	Stefano Morozzi	12/2022
9413	2^338368-20369	101859	Enzo Doria	06/2013
9414	2^338366+74179	101859	Enzo Doria	04/2016
9407	2^338366+53853	101859	Stefano Morozzi	01/2022
9408	2^338365-31665	101859	Stefano Morozzi	03/2022
9409	2^338368-156345	101859	Stefano Morozzi	03/2022
9410	2^338366-159867	101859	Stefano Morozzi	04/2022
9411	2^338368-63509	101859	Stefano Morozzi	12/2022
9412	2^338365-190975	101859	Stefano Morozzi	01/2023
9415	2^338362-180845	101858	Stefano Morozzi	02/2022
9416	2^338364-155769	101858	Stefano Morozzi	02/2022
9417	2^338362+142843	101858	Stefano Morozzi	09/2022
9418	2^338362+170019	101858	Stefano Morozzi	11/2022
9419	2^338361-100875	101857	Stefano Morozzi	12/2021
9420	2^338361+154169	101857	Stefano Morozzi	01/2022
9421	2^338359-189645	101857	Stefano Morozzi	01/2023
9422	2^338356+101271	101856	Stefano Morozzi	12/2021
9423	2^338356+53383	101856	Stefano Morozzi	01/2022
9424	2^338355+59393	101856	Stefano Morozzi	03/2022
9425	2^338356+60775	101856	Stefano Morozzi	03/2022
9426	2^338356-106257	101856	Stefano Morozzi	03/2022
9427	2^338357-58921	101856	Stefano Morozzi	04/2022
9428	2^338356+94605	101856	Stefano Morozzi	09/2022
9429	2^338356+117813	101856	Stefano Morozzi	09/2022
9430	2^338358-38475	101856	Stefano Morozzi	12/2022
9431	2^338353-190291	101855	Stefano Morozzi	01/2023
9432	2^338350-152933	101854	Stefano Morozzi	01/2022
9433	2^338350+6337	101854	Stefano Morozzi	01/2022
9434	2^338350+168759	101854	Stefano Morozzi	09/2022
9437	27088^5755+5755^27088	101853	Hans Havermann	01/2019
9435	2^338347+125901	101853	Stefano Morozzi	11/2021
9436	2^338346-10643	101853	Stefano Morozzi	06/2022
9438	2^338343+152271	101852	Stefano Morozzi	12/2021
9439	2^338345+154107	101852	Stefano Morozzi	01/2022
9440	2^338342+155397	101852	Stefano Morozzi	01/2022
9441	2^338342-130767	101852	Stefano Morozzi	02/2022
9442	2^338345-30123	101852	Stefano Morozzi	02/2022
9443	2^338345+35747	101852	Stefano Morozzi	03/2022
9444	2^338345-133131	101852	Stefano Morozzi	04/2022
9445	2^338345-134559	101852	Stefano Morozzi	04/2022
9446	2^338342+170073	101852	Stefano Morozzi	11/2022
9447	2^338344+46567	101852	Stefano Morozzi	11/2022
9448	2^338344+97141	101852	Stefano Morozzi	11/2022
9449	2^338342-162213	101852	Stefano Morozzi	12/2022
9450	2^338339+2753	101851	Stefano Morozzi	12/2021
9451	2^338341+128415	101851	Stefano Morozzi	01/2022
9452	2^338338+2677	101850	Stefano Morozzi	12/2021
9453	2^338336+54607	101850	Stefano Morozzi	01/2022
9454	2^338338+109999	101850	Stefano Morozzi	03/2022
9455	2^338336+161575	101850	Stefano Morozzi	04/2022
9456	2^338335+51975	101849	Stefano Morozzi	12/2021
9457	2^338335-152607	101849	Stefano Morozzi	01/2022
9458	2^338334+55273	101849	Stefano Morozzi	01/2022
9459	2^338332+34315	101849	Stefano Morozzi	03/2022
9460	2^338335+158759	101849	Stefano Morozzi	03/2022
9461	2^338332+67621	101849	Stefano Morozzi	09/2022
9462	2^338332-66099	101849	Stefano Morozzi	01/2023
9463	2^338334-191043	101849	Stefano Morozzi	01/2023
9464	2^338331+83403	101848	Stefano Morozzi	02/2022
9465	2^338330-110865	101848	Stefano Morozzi	06/2022
9466	2^338330+71047	101848	Stefano Morozzi	11/2022
9467	2^338328-5295	101847	Stefano Morozzi	02/2022
9468	2^338327+143585	101847	Stefano Morozzi	09/2022
9469	2^338324-179667	101846	Stefano Morozzi	02/2022
9470	2^338322+21903	101846	Stefano Morozzi	11/2022
9471	2^338324+98047	101846	Stefano Morozzi	11/2022
9472	2^338323-87729	101846	Stefano Morozzi	12/2022
9473	2^338322-16667	101846	Stefano Morozzi	01/2023
9474	2^338325-142159	101846	Stefano Morozzi	02/2023
9475	2^338316-175857	101844	Stefano Morozzi	12/2021
9476	2^338318+54405	101844	Stefano Morozzi	01/2022
9477	2^338316+32961	101844	Stefano Morozzi	02/2022
9478	2^338317+68175	101844	Stefano Morozzi	09/2022
9479	2^338318-86171	101844	Stefano Morozzi	12/2022
9480	2^338315-178635	101843	Stefano Morozzi	01/2022
9481	2^338315+34899	101843	Stefano Morozzi	03/2022
9482	2^338314-106973	101843	Stefano Morozzi	03/2022
9483	2^338313+170411	101843	Stefano Morozzi	11/2022
9484	2^338315-88807	101843	Stefano Morozzi	12/2022
9485	2^338311-51799	101842	Stefano Morozzi	12/2021
9486	2^338309+157259	101842	Stefano Morozzi	02/2022
9487	2^338310+40903	101842	Stefano Morozzi	06/2022
9488	2^338309-168051	101842	Stefano Morozzi	02/2023
9489	2^338308-55853	101841	Stefano Morozzi	02/2022
9490	2^338307+134871	101841	Stefano Morozzi	03/2022
9491	2^338307+19689	101841	Stefano Morozzi	09/2022
9492	2^338308+66873	101841	Stefano Morozzi	09/2022
9493	2^338306+124399	101841	Stefano Morozzi	02/2023
9494	2^338306-91913	101841	Stefano Morozzi	02/2023
9495	2^338304+78757	101840	Stefano Morozzi	01/2022
9496	2^338304-5807	101840	Stefano Morozzi	02/2022
9497	2^338305+110879	101840	Stefano Morozzi	03/2022
9498	2^338304+91147	101840	Stefano Morozzi	06/2022
9499	2^338304-64475	101840	Stefano Morozzi	01/2023
9500	2^338299+85611	101839	Stefano Morozzi	03/2022

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Probable Primes Top 10000

(300560 PRPs in the top)