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 ?
9254	2^338682-19865	101954	Enzo Doria	06/2013
9255	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
9251	2^338682-107205	101954	Stefano Morozzi	03/2022
9252	2^338682+13839	101954	Stefano Morozzi	05/2022
9253	2^338683-42837	101954	Stefano Morozzi	02/2023
9256	2^338678-180005	101953	Stefano Morozzi	02/2022
9257	2^338680+15855	101953	Stefano Morozzi	06/2022
9258	2^338678+93175	101953	Stefano Morozzi	09/2022
9259	2^338680+99217	101953	Stefano Morozzi	02/2023
9260	2^338674-175967	101952	Stefano Morozzi	12/2021
9261	2^338677-177373	101952	Stefano Morozzi	12/2021
9262	2^338677+102999	101952	Stefano Morozzi	01/2022
9263	2^338676+33381	101952	Stefano Morozzi	03/2022
9264	2^338677-82699	101952	Stefano Morozzi	03/2022
9265	2^338676-34299	101952	Stefano Morozzi	04/2022
9266	2^338675+188445	101952	Stefano Morozzi	05/2022
9267	2^338676+165271	101952	Stefano Morozzi	06/2022
9268	2^338674-187551	101952	Stefano Morozzi	12/2022
9269	2^338676-42243	101952	Stefano Morozzi	02/2023
9270	2^338671-55041	101951	Stefano Morozzi	02/2022
9271	2^338673-80203	101951	Stefano Morozzi	02/2022
9272	2^338672-182063	101951	Stefano Morozzi	03/2022
9273	2^338672+36667	101951	Stefano Morozzi	04/2022
9274	2^338668+2583	101950	Stefano Morozzi	12/2021
9275	2^338670-157001	101950	Stefano Morozzi	03/2022
9276	2^338669-8353	101950	Stefano Morozzi	04/2022
9277	2^338670+40635	101950	Stefano Morozzi	06/2022
9285	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
9278	2^338665+1577	101949	Stefano Morozzi	12/2021
9279	2^338665-51133	101949	Stefano Morozzi	12/2021
9280	2^338664+4345	101949	Stefano Morozzi	01/2022
9281	2^338666-128943	101949	Stefano Morozzi	01/2022
9282	2^338664+131535	101949	Stefano Morozzi	01/2022
9283	2^338667+14943	101949	Stefano Morozzi	05/2022
9284	2^338665+166637	101949	Stefano Morozzi	09/2022
9286	2^338662+31587	101948	Stefano Morozzi	02/2022
9287	2^338663-58375	101948	Stefano Morozzi	04/2022
9288	2^338663-107869	101948	Stefano Morozzi	04/2022
9289	2^338663+90435	101948	Stefano Morozzi	06/2022
9290	2^338661+70457	101948	Stefano Morozzi	11/2022
9291	2^338662+70519	101948	Stefano Morozzi	11/2022
9292	2^338663-39447	101948	Stefano Morozzi	01/2023
9293	2^338658-159191	101947	Stefano Morozzi	04/2022
9294	2^338659-159687	101947	Stefano Morozzi	04/2022
9295	2^338659+15543	101947	Stefano Morozzi	05/2022
9296	2^338658+44395	101947	Stefano Morozzi	09/2022
9297	2^338658+192537	101947	Stefano Morozzi	09/2022
9298	2^338659-90531	101947	Stefano Morozzi	01/2023
9299	2^338659-114759	101947	Stefano Morozzi	01/2023
9300	2^338659+124079	101947	Stefano Morozzi	02/2023
9301	2^338654+51027	101946	Stefano Morozzi	12/2021
9302	2^338656-152115	101946	Stefano Morozzi	12/2021
9303	2^338654+32415	101946	Stefano Morozzi	02/2022
9304	2^338654+39799	101946	Stefano Morozzi	05/2022
9305	2^338655+144579	101946	Stefano Morozzi	09/2022
9306	2^338657+97509	101946	Stefano Morozzi	11/2022
9307	2^338653+126629	101945	Stefano Morozzi	12/2021
9308	2^338653+33279	101945	Stefano Morozzi	02/2022
9309	2^338652-107097	101945	Stefano Morozzi	03/2022
9310	2^338653+94475	101945	Stefano Morozzi	09/2022
9311	2^338651+194073	101945	Stefano Morozzi	09/2022
9312	2^338652-89157	101945	Stefano Morozzi	01/2023
9313	2^338649-154663	101944	Stefano Morozzi	02/2022
9314	2^338650+61399	101944	Stefano Morozzi	04/2022
9315	2^338650-35655	101944	Stefano Morozzi	06/2022
9316	2^338650+169623	101944	Stefano Morozzi	09/2022
9317	2^338649-40743	101944	Stefano Morozzi	01/2023
9318	2^338645+150311	101943	Stefano Morozzi	11/2021
9319	2^338645+28481	101943	Stefano Morozzi	01/2022
9320	2^338647-77895	101943	Stefano Morozzi	01/2022
9321	2^338647-84607	101943	Stefano Morozzi	04/2022
9322	2^338647+164523	101943	Stefano Morozzi	05/2022
9323	2^338645+64845	101943	Stefano Morozzi	05/2022
9324	2^338644-35969	101943	Stefano Morozzi	12/2022
9325	2^338645-15715	101943	Stefano Morozzi	01/2023
9326	2^338641-152541	101942	Stefano Morozzi	12/2021
9327	2^338643-56487	101942	Stefano Morozzi	03/2022
9328	2^338642-186525	101942	Stefano Morozzi	12/2022
9329	2^338643-41715	101942	Stefano Morozzi	02/2023
9330	2^338638+100575	101941	Stefano Morozzi	12/2021
9331	2^338639-127461	101941	Stefano Morozzi	12/2021
9332	2^338640+187657	101941	Stefano Morozzi	04/2022
9333	2^338640+44431	101941	Stefano Morozzi	09/2022
9334	2^338635+1961	101940	Stefano Morozzi	12/2021
9335	2^338637+102125	101940	Stefano Morozzi	12/2021
9336	2^338636-135329	101940	Stefano Morozzi	06/2022
9337	2^338635+199485	101940	Stefano Morozzi	02/2023
9342	28594^3673+3673^28594	101939	Hans Havermann	02/2019
9338	2^338631+110741	101939	Stefano Morozzi	03/2022
9339	2^338631+112119	101939	Stefano Morozzi	04/2022
9340	2^338634-83097	101939	Stefano Morozzi	04/2022
9341	2^338633+139701	101939	Stefano Morozzi	05/2022
9343	2^338630-150341	101938	Stefano Morozzi	12/2021
9344	2^338630+12867	101938	Stefano Morozzi	04/2022
9345	2^338629+42147	101938	Stefano Morozzi	09/2022
9346	2^338628+121083	101938	Stefano Morozzi	11/2022
9347	2^338630+147235	101938	Stefano Morozzi	11/2022
9348	2^338628-37679	101938	Stefano Morozzi	12/2022
9349	2^338629-41383	101938	Stefano Morozzi	01/2023
9350	2^338628-91877	101938	Stefano Morozzi	02/2023
9351	2^338626-105875	101937	Stefano Morozzi	02/2022
9352	2^338625-111729	101937	Stefano Morozzi	12/2022
9353	2^338627+49299	101937	Stefano Morozzi	02/2023
9354	2^338621+33069	101936	Stefano Morozzi	02/2022
9355	2^338623-106405	101936	Stefano Morozzi	03/2022
9356	2^338621+61751	101936	Stefano Morozzi	04/2022
9357	2^338623-86577	101936	Stefano Morozzi	12/2022
9358	2^338620-150735	101935	Stefano Morozzi	12/2021
9359	2^338619-27765	101935	Stefano Morozzi	01/2022
9360	2^338619-77959	101935	Stefano Morozzi	01/2022
9361	2^338619-186367	101935	Stefano Morozzi	12/2022
9362	2^338618-64905	101935	Stefano Morozzi	01/2023
9363	2^338615+151655	101934	Stefano Morozzi	12/2021
9364	2^338616+5047	101934	Stefano Morozzi	01/2022
9365	2^338616+39705	101934	Stefano Morozzi	05/2022
9366	2^338617+149321	101934	Stefano Morozzi	02/2023
9367	2^338611+76659	101933	Stefano Morozzi	12/2021
9368	2^338613-109791	101933	Stefano Morozzi	04/2022
9369	2^338612+119583	101933	Stefano Morozzi	09/2022
9370	2^338611-140397	101933	Stefano Morozzi	01/2023
9371	2^338614-39653	101933	Stefano Morozzi	01/2023
9372	2^338609+130139	101932	Stefano Morozzi	01/2022
9373	2^338609+131327	101932	Stefano Morozzi	01/2022
9374	2^338608-155453	101932	Stefano Morozzi	02/2022
9375	2^338609+161721	101932	Stefano Morozzi	04/2022
9376	2^338609-10405	101932	Stefano Morozzi	06/2022
9377	2^338608+94017	101932	Stefano Morozzi	09/2022
9378	2^338610+170515	101932	Stefano Morozzi	11/2022
9379	2^338607+30611	101931	Stefano Morozzi	01/2022
9380	2^338607+106695	101931	Stefano Morozzi	02/2022
9381	2^338606-32291	101931	Stefano Morozzi	03/2022
9382	2^338606+15195	101931	Stefano Morozzi	05/2022
9383	2^338605+197789	101931	Stefano Morozzi	11/2022
9384	2^338607-90621	101931	Stefano Morozzi	01/2023
9385	2^338603-1195	101930	Stefano Morozzi	12/2021
9386	2^338601+108867	101930	Stefano Morozzi	03/2022
9387	2^338603+34311	101930	Stefano Morozzi	03/2022
9388	2^338598+57127	101929	Stefano Morozzi	02/2022
9389	2^338598+162645	101929	Stefano Morozzi	04/2022
9390	2^338599+43445	101929	Stefano Morozzi	09/2022
9391	2^338599+19485	101929	Stefano Morozzi	09/2022
9392	2^338598+46195	101929	Stefano Morozzi	11/2022
9393	2^338600-36393	101929	Stefano Morozzi	12/2022
9394	2^338596-1739	101928	Stefano Morozzi	12/2021
9395	2^338595-78687	101928	Stefano Morozzi	01/2022
9396	2^338595+181683	101928	Stefano Morozzi	02/2022
9397	2^338597-106045	101928	Stefano Morozzi	02/2022
9398	2^338595+119565	101928	Stefano Morozzi	09/2022
9399	2^338595+19623	101928	Stefano Morozzi	09/2022
9400	2^338595+21711	101928	Stefano Morozzi	11/2022
9401	2^338596-111129	101928	Stefano Morozzi	12/2022
9402	2^338591+53769	101927	Stefano Morozzi	01/2022
9403	2^338593+156989	101927	Stefano Morozzi	02/2022
9404	2^338592+36157	101927	Stefano Morozzi	03/2022
9405	2^338593+42099	101927	Stefano Morozzi	09/2022
9406	2^338591+46685	101927	Stefano Morozzi	11/2022
9407	2^338593+120437	101927	Stefano Morozzi	11/2022
9408	2^338591-165517	101927	Stefano Morozzi	01/2023
9409	2^338592-166107	101927	Stefano Morozzi	01/2023
9410	2^338592-189249	101927	Stefano Morozzi	01/2023
9411	2^338594-40493	101927	Stefano Morozzi	01/2023
9412	2^338590+182007	101926	Stefano Morozzi	02/2022
9413	2^338590+60747	101926	Stefano Morozzi	03/2022
9414	2^338588+62397	101926	Stefano Morozzi	04/2022
9415	2^338589-9685	101926	Stefano Morozzi	04/2022
9416	2^338588+73765	101926	Stefano Morozzi	02/2023
9417	2^338589-16915	101926	Stefano Morozzi	02/2023
9424	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
9418	2^338586+1153	101925	Stefano Morozzi	12/2021
9419	2^338587-51709	101925	Stefano Morozzi	12/2021
9420	2^338586+105303	101925	Stefano Morozzi	01/2022
9421	2^338585-131773	101925	Stefano Morozzi	03/2022
9422	2^338587+168039	101925	Stefano Morozzi	09/2022
9423	2^338585-140719	101925	Stefano Morozzi	01/2023
9425	2^338584+100771	101924	Stefano Morozzi	11/2021
9426	2^338581-150415	101924	Stefano Morozzi	12/2021
9427	2^338581-2349	101924	Stefano Morozzi	12/2021
9428	2^338582+42933	101924	Stefano Morozzi	09/2022
9429	2^338584+93267	101924	Stefano Morozzi	09/2022
9430	2^338582-86697	101924	Stefano Morozzi	12/2022
9431	2^338582-138035	101924	Stefano Morozzi	12/2022
9432	2^338584-115569	101924	Stefano Morozzi	01/2023
9433	2^338581-92793	101924	Stefano Morozzi	02/2023
9434	2^338578+67593	101923	Stefano Morozzi	09/2022
9435	2^338580+142201	101923	Stefano Morozzi	09/2022
9436	2^338579-14635	101923	Stefano Morozzi	01/2023
9437	2^338579-164985	101923	Stefano Morozzi	01/2023
9438	2^338575-28815	101922	Stefano Morozzi	01/2022
9439	2^338575-33645	101922	Stefano Morozzi	04/2022
9440	2^338577-92239	101922	Stefano Morozzi	02/2023
9441	2^338573-156693	101921	Stefano Morozzi	03/2022
9442	2^338572+193305	101921	Stefano Morozzi	09/2022
9443	2^338573+173751	101921	Stefano Morozzi	02/2023
9444	2^338574+73707	101921	Stefano Morozzi	02/2023
9449	2^338568+37	101920	Lelio R Paula	07/2011
9445	2^338570-53933	101920	Stefano Morozzi	02/2022
9446	2^338569+87201	101920	Stefano Morozzi	04/2022
9447	2^338570-36897	101920	Stefano Morozzi	12/2022
9448	2^338570-61157	101920	Stefano Morozzi	12/2022
9450	2^338567-9619	101919	Stefano Morozzi	04/2022
9451	2^338565-141589	101919	Stefano Morozzi	01/2023
9452	2^338565+148821	101919	Stefano Morozzi	02/2023
9453	2^338564-56763	101918	Stefano Morozzi	03/2022
9454	2^338561+112007	101918	Stefano Morozzi	04/2022
9455	2^338561-9315	101918	Stefano Morozzi	04/2022
9456	2^338564+41965	101918	Stefano Morozzi	09/2022
9457	2^338561+121139	101918	Stefano Morozzi	11/2022
9458	2^338562+21799	101918	Stefano Morozzi	11/2022
9466	2^338559-1858777	101917	Enzo Doria	04/2016
9459	2^338558+4825	101917	Stefano Morozzi	01/2022
9460	2^338559-127935	101917	Stefano Morozzi	01/2022
9461	2^338560+154891	101917	Stefano Morozzi	01/2022
9462	2^338559+131885	101917	Stefano Morozzi	02/2022
9463	2^338558+93735	101917	Stefano Morozzi	09/2022
9464	2^338559-90957	101917	Stefano Morozzi	01/2023
9465	2^338559-190761	101917	Stefano Morozzi	01/2023
9467	2^338555+189981	101916	Stefano Morozzi	05/2022
9468	2^338553-125383	101915	Stefano Morozzi	12/2021
9469	2^338554-82821	101915	Stefano Morozzi	03/2022
9470	2^338548+76923	101914	Stefano Morozzi	12/2021
9471	2^338549+158517	101914	Stefano Morozzi	03/2022
9472	2^338549+85397	101914	Stefano Morozzi	03/2022
9473	2^338548+138121	101914	Stefano Morozzi	05/2022
9474	2^338550-110301	101914	Stefano Morozzi	06/2022
9475	2^338547+129321	101913	Stefano Morozzi	01/2022
9476	2^338547-153481	101913	Stefano Morozzi	01/2022
9477	2^338545-11059	101913	Stefano Morozzi	12/2022
9478	2^338544+107853	101912	Stefano Morozzi	02/2022
9479	2^338542+172813	101912	Stefano Morozzi	11/2022
9480	2^338544-12687	101912	Stefano Morozzi	12/2022
9481	2^338543-140677	101912	Stefano Morozzi	01/2023
9482	2^338541+152721	101911	Stefano Morozzi	01/2022
9483	2^338539+60825	101911	Stefano Morozzi	03/2022
9484	2^338539+160881	101911	Stefano Morozzi	03/2022
9485	2^338541-182523	101911	Stefano Morozzi	03/2022
9486	2^338540+87645	101911	Stefano Morozzi	04/2022
9487	2^338541+148305	101911	Stefano Morozzi	11/2022
9488	2^338541-163075	101911	Stefano Morozzi	12/2022
9489	2^338536-100785	101910	Stefano Morozzi	12/2021
9490	2^338535-51837	101910	Stefano Morozzi	12/2021
9491	2^338535-158745	101910	Stefano Morozzi	04/2022
9492	2^338536-189977	101910	Stefano Morozzi	01/2023
9493	2^338537-65623	101910	Stefano Morozzi	01/2023
9494	2^338532+39445	101909	Stefano Morozzi	05/2022
9495	2^338532+141415	101909	Stefano Morozzi	06/2022
9496	2^338532-136037	101909	Stefano Morozzi	06/2022
9497	2^338531+81081	101908	Stefano Morozzi	01/2022
9498	2^338530+59835	101908	Stefano Morozzi	03/2022
9499	2^338529+186551	101908	Stefano Morozzi	04/2022
9500	2^338531+61313	101908	Stefano Morozzi	04/2022

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Probable Primes Top 10000

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