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 ?
9501	2^338700-184565	101959	Stefano Morozzi	04/2022
9502	2^338700+189777	101959	Stefano Morozzi	05/2022
9503	2^338698+41779	101959	Stefano Morozzi	09/2022
9504	2^338699+148533	101959	Stefano Morozzi	11/2022
9505	2^338700+97381	101959	Stefano Morozzi	11/2022
9506	2^338698-142181	101959	Stefano Morozzi	02/2023
9507	2^338696+181671	101958	Stefano Morozzi	02/2022
9508	2^338697+146651	101958	Stefano Morozzi	11/2022
9509	2^338695-116977	101958	Stefano Morozzi	02/2023
9510	2^338692+106297	101957	Stefano Morozzi	01/2022
9511	2^338692+33195	101957	Stefano Morozzi	02/2022
9512	2^338692+110505	101957	Stefano Morozzi	03/2022
9513	2^338692+190093	101957	Stefano Morozzi	05/2022
9514	2^338692+173343	101957	Stefano Morozzi	11/2022
9515	2^338693+144975	101957	Stefano Morozzi	11/2022
9516	2^338692+149281	101957	Stefano Morozzi	02/2023
9517	2^338688+82203	101956	Stefano Morozzi	02/2022
9518	2^338689+82365	101956	Stefano Morozzi	02/2022
9519	2^338688-92159	101956	Stefano Morozzi	02/2023
9520	2^338686-81303	101955	Stefano Morozzi	03/2022
9521	2^338687+40461	101955	Stefano Morozzi	06/2022
9522	2^338687+65283	101955	Stefano Morozzi	06/2022
9528	2^338682-19865	101954	Enzo Doria	06/2013
9529	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
9523	(8*10^101954-269)/9	101954	Robert Price	09/2021
9524	2^338683+50303	101954	Stefano Morozzi	11/2021
9525	2^338682-107205	101954	Stefano Morozzi	03/2022
9526	2^338682+13839	101954	Stefano Morozzi	05/2022
9527	2^338683-42837	101954	Stefano Morozzi	02/2023
9530	2^338678-180005	101953	Stefano Morozzi	02/2022
9531	2^338680+15855	101953	Stefano Morozzi	06/2022
9532	2^338678+93175	101953	Stefano Morozzi	09/2022
9533	2^338680+99217	101953	Stefano Morozzi	02/2023
9534	2^338674-175967	101952	Stefano Morozzi	12/2021
9535	2^338677-177373	101952	Stefano Morozzi	12/2021
9536	2^338677+102999	101952	Stefano Morozzi	01/2022
9537	2^338676+33381	101952	Stefano Morozzi	03/2022
9538	2^338677-82699	101952	Stefano Morozzi	03/2022
9539	2^338676-34299	101952	Stefano Morozzi	04/2022
9540	2^338675+188445	101952	Stefano Morozzi	05/2022
9541	2^338676+165271	101952	Stefano Morozzi	06/2022
9542	2^338674-187551	101952	Stefano Morozzi	12/2022
9543	2^338676-42243	101952	Stefano Morozzi	02/2023
9544	2^338671-55041	101951	Stefano Morozzi	02/2022
9545	2^338673-80203	101951	Stefano Morozzi	02/2022
9546	2^338672-182063	101951	Stefano Morozzi	03/2022
9547	2^338672+36667	101951	Stefano Morozzi	04/2022
9548	2^338668+2583	101950	Stefano Morozzi	12/2021
9549	2^338670-157001	101950	Stefano Morozzi	03/2022
9550	2^338669-8353	101950	Stefano Morozzi	04/2022
9551	2^338670+40635	101950	Stefano Morozzi	06/2022
9559	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
9552	2^338665+1577	101949	Stefano Morozzi	12/2021
9553	2^338665-51133	101949	Stefano Morozzi	12/2021
9554	2^338664+4345	101949	Stefano Morozzi	01/2022
9555	2^338666-128943	101949	Stefano Morozzi	01/2022
9556	2^338664+131535	101949	Stefano Morozzi	01/2022
9557	2^338667+14943	101949	Stefano Morozzi	05/2022
9558	2^338665+166637	101949	Stefano Morozzi	09/2022
9560	2^338662+31587	101948	Stefano Morozzi	02/2022
9561	2^338663-58375	101948	Stefano Morozzi	04/2022
9562	2^338663-107869	101948	Stefano Morozzi	04/2022
9563	2^338663+90435	101948	Stefano Morozzi	06/2022
9564	2^338661+70457	101948	Stefano Morozzi	11/2022
9565	2^338662+70519	101948	Stefano Morozzi	11/2022
9566	2^338663-39447	101948	Stefano Morozzi	01/2023
9567	2^338658-159191	101947	Stefano Morozzi	04/2022
9568	2^338659-159687	101947	Stefano Morozzi	04/2022
9569	2^338659+15543	101947	Stefano Morozzi	05/2022
9570	2^338658+44395	101947	Stefano Morozzi	09/2022
9571	2^338658+192537	101947	Stefano Morozzi	09/2022
9572	2^338659-90531	101947	Stefano Morozzi	01/2023
9573	2^338659-114759	101947	Stefano Morozzi	01/2023
9574	2^338659+124079	101947	Stefano Morozzi	02/2023
9575	2^338654+51027	101946	Stefano Morozzi	12/2021
9576	2^338656-152115	101946	Stefano Morozzi	12/2021
9577	2^338654+32415	101946	Stefano Morozzi	02/2022
9578	2^338654+39799	101946	Stefano Morozzi	05/2022
9579	2^338655+144579	101946	Stefano Morozzi	09/2022
9580	2^338657+97509	101946	Stefano Morozzi	11/2022
9581	2^338653+126629	101945	Stefano Morozzi	12/2021
9582	2^338653+33279	101945	Stefano Morozzi	02/2022
9583	2^338652-107097	101945	Stefano Morozzi	03/2022
9584	2^338653+94475	101945	Stefano Morozzi	09/2022
9585	2^338651+194073	101945	Stefano Morozzi	09/2022
9586	2^338652-89157	101945	Stefano Morozzi	01/2023
9587	2^338649-154663	101944	Stefano Morozzi	02/2022
9588	2^338650+61399	101944	Stefano Morozzi	04/2022
9589	2^338650-35655	101944	Stefano Morozzi	06/2022
9590	2^338650+169623	101944	Stefano Morozzi	09/2022
9591	2^338649-40743	101944	Stefano Morozzi	01/2023
9592	2^338645+150311	101943	Stefano Morozzi	11/2021
9593	2^338645+28481	101943	Stefano Morozzi	01/2022
9594	2^338647-77895	101943	Stefano Morozzi	01/2022
9595	2^338647-84607	101943	Stefano Morozzi	04/2022
9596	2^338647+164523	101943	Stefano Morozzi	05/2022
9597	2^338645+64845	101943	Stefano Morozzi	05/2022
9598	2^338644-35969	101943	Stefano Morozzi	12/2022
9599	2^338645-15715	101943	Stefano Morozzi	01/2023
9600	2^338641-152541	101942	Stefano Morozzi	12/2021
9601	2^338643-56487	101942	Stefano Morozzi	03/2022
9602	2^338642-186525	101942	Stefano Morozzi	12/2022
9603	2^338643-41715	101942	Stefano Morozzi	02/2023
9604	2^338638+100575	101941	Stefano Morozzi	12/2021
9605	2^338639-127461	101941	Stefano Morozzi	12/2021
9606	2^338640+187657	101941	Stefano Morozzi	04/2022
9607	2^338640+44431	101941	Stefano Morozzi	09/2022
9608	2^338635+1961	101940	Stefano Morozzi	12/2021
9609	2^338637+102125	101940	Stefano Morozzi	12/2021
9610	2^338636-135329	101940	Stefano Morozzi	06/2022
9611	2^338635+199485	101940	Stefano Morozzi	02/2023
9616	28594^3673+3673^28594	101939	Hans Havermann	02/2019
9612	2^338631+110741	101939	Stefano Morozzi	03/2022
9613	2^338631+112119	101939	Stefano Morozzi	04/2022
9614	2^338634-83097	101939	Stefano Morozzi	04/2022
9615	2^338633+139701	101939	Stefano Morozzi	05/2022
9617	2^338630-150341	101938	Stefano Morozzi	12/2021
9618	2^338630+12867	101938	Stefano Morozzi	04/2022
9619	2^338629+42147	101938	Stefano Morozzi	09/2022
9620	2^338628+121083	101938	Stefano Morozzi	11/2022
9621	2^338630+147235	101938	Stefano Morozzi	11/2022
9622	2^338628-37679	101938	Stefano Morozzi	12/2022
9623	2^338629-41383	101938	Stefano Morozzi	01/2023
9624	2^338628-91877	101938	Stefano Morozzi	02/2023
9625	2^338626-105875	101937	Stefano Morozzi	02/2022
9626	2^338625-111729	101937	Stefano Morozzi	12/2022
9627	2^338627+49299	101937	Stefano Morozzi	02/2023
9628	2^338621+33069	101936	Stefano Morozzi	02/2022
9629	2^338623-106405	101936	Stefano Morozzi	03/2022
9630	2^338621+61751	101936	Stefano Morozzi	04/2022
9631	2^338623-86577	101936	Stefano Morozzi	12/2022
9632	2^338620-150735	101935	Stefano Morozzi	12/2021
9633	2^338619-27765	101935	Stefano Morozzi	01/2022
9634	2^338619-77959	101935	Stefano Morozzi	01/2022
9635	2^338619-186367	101935	Stefano Morozzi	12/2022
9636	2^338618-64905	101935	Stefano Morozzi	01/2023
9637	2^338615+151655	101934	Stefano Morozzi	12/2021
9638	2^338616+5047	101934	Stefano Morozzi	01/2022
9639	2^338616+39705	101934	Stefano Morozzi	05/2022
9640	2^338617+149321	101934	Stefano Morozzi	02/2023
9641	2^338611+76659	101933	Stefano Morozzi	12/2021
9642	2^338613-109791	101933	Stefano Morozzi	04/2022
9643	2^338612+119583	101933	Stefano Morozzi	09/2022
9644	2^338611-140397	101933	Stefano Morozzi	01/2023
9645	2^338614-39653	101933	Stefano Morozzi	01/2023
9646	2^338609+130139	101932	Stefano Morozzi	01/2022
9647	2^338609+131327	101932	Stefano Morozzi	01/2022
9648	2^338608-155453	101932	Stefano Morozzi	02/2022
9649	2^338609+161721	101932	Stefano Morozzi	04/2022
9650	2^338609-10405	101932	Stefano Morozzi	06/2022
9651	2^338608+94017	101932	Stefano Morozzi	09/2022
9652	2^338610+170515	101932	Stefano Morozzi	11/2022
9653	2^338607+30611	101931	Stefano Morozzi	01/2022
9654	2^338607+106695	101931	Stefano Morozzi	02/2022
9655	2^338606-32291	101931	Stefano Morozzi	03/2022
9656	2^338606+15195	101931	Stefano Morozzi	05/2022
9657	2^338605+197789	101931	Stefano Morozzi	11/2022
9658	2^338607-90621	101931	Stefano Morozzi	01/2023
9659	2^338603-1195	101930	Stefano Morozzi	12/2021
9660	2^338601+108867	101930	Stefano Morozzi	03/2022
9661	2^338603+34311	101930	Stefano Morozzi	03/2022
9662	2^338598+57127	101929	Stefano Morozzi	02/2022
9663	2^338598+162645	101929	Stefano Morozzi	04/2022
9664	2^338599+43445	101929	Stefano Morozzi	09/2022
9665	2^338599+19485	101929	Stefano Morozzi	09/2022
9666	2^338598+46195	101929	Stefano Morozzi	11/2022
9667	2^338600-36393	101929	Stefano Morozzi	12/2022
9668	2^338596-1739	101928	Stefano Morozzi	12/2021
9669	2^338595-78687	101928	Stefano Morozzi	01/2022
9670	2^338595+181683	101928	Stefano Morozzi	02/2022
9671	2^338597-106045	101928	Stefano Morozzi	02/2022
9672	2^338595+119565	101928	Stefano Morozzi	09/2022
9673	2^338595+19623	101928	Stefano Morozzi	09/2022
9674	2^338595+21711	101928	Stefano Morozzi	11/2022
9675	2^338596-111129	101928	Stefano Morozzi	12/2022
9676	2^338591+53769	101927	Stefano Morozzi	01/2022
9677	2^338593+156989	101927	Stefano Morozzi	02/2022
9678	2^338592+36157	101927	Stefano Morozzi	03/2022
9679	2^338593+42099	101927	Stefano Morozzi	09/2022
9680	2^338591+46685	101927	Stefano Morozzi	11/2022
9681	2^338593+120437	101927	Stefano Morozzi	11/2022
9682	2^338591-165517	101927	Stefano Morozzi	01/2023
9683	2^338592-166107	101927	Stefano Morozzi	01/2023
9684	2^338592-189249	101927	Stefano Morozzi	01/2023
9685	2^338594-40493	101927	Stefano Morozzi	01/2023
9686	2^338590+182007	101926	Stefano Morozzi	02/2022
9687	2^338590+60747	101926	Stefano Morozzi	03/2022
9688	2^338588+62397	101926	Stefano Morozzi	04/2022
9689	2^338589-9685	101926	Stefano Morozzi	04/2022
9690	2^338588+73765	101926	Stefano Morozzi	02/2023
9691	2^338589-16915	101926	Stefano Morozzi	02/2023
9698	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
9692	2^338586+1153	101925	Stefano Morozzi	12/2021
9693	2^338587-51709	101925	Stefano Morozzi	12/2021
9694	2^338586+105303	101925	Stefano Morozzi	01/2022
9695	2^338585-131773	101925	Stefano Morozzi	03/2022
9696	2^338587+168039	101925	Stefano Morozzi	09/2022
9697	2^338585-140719	101925	Stefano Morozzi	01/2023
9699	2^338584+100771	101924	Stefano Morozzi	11/2021
9700	2^338581-150415	101924	Stefano Morozzi	12/2021
9701	2^338581-2349	101924	Stefano Morozzi	12/2021
9702	2^338582+42933	101924	Stefano Morozzi	09/2022
9703	2^338584+93267	101924	Stefano Morozzi	09/2022
9704	2^338582-86697	101924	Stefano Morozzi	12/2022
9705	2^338582-138035	101924	Stefano Morozzi	12/2022
9706	2^338584-115569	101924	Stefano Morozzi	01/2023
9707	2^338581-92793	101924	Stefano Morozzi	02/2023
9708	2^338578+67593	101923	Stefano Morozzi	09/2022
9709	2^338580+142201	101923	Stefano Morozzi	09/2022
9710	2^338579-14635	101923	Stefano Morozzi	01/2023
9711	2^338579-164985	101923	Stefano Morozzi	01/2023
9712	2^338575-28815	101922	Stefano Morozzi	01/2022
9713	2^338575-33645	101922	Stefano Morozzi	04/2022
9714	2^338577-92239	101922	Stefano Morozzi	02/2023
9715	2^338573-156693	101921	Stefano Morozzi	03/2022
9716	2^338572+193305	101921	Stefano Morozzi	09/2022
9717	2^338573+173751	101921	Stefano Morozzi	02/2023
9718	2^338574+73707	101921	Stefano Morozzi	02/2023
9723	2^338568+37	101920	Lelio R Paula	07/2011
9719	2^338570-53933	101920	Stefano Morozzi	02/2022
9720	2^338569+87201	101920	Stefano Morozzi	04/2022
9721	2^338570-36897	101920	Stefano Morozzi	12/2022
9722	2^338570-61157	101920	Stefano Morozzi	12/2022
9724	2^338567-9619	101919	Stefano Morozzi	04/2022
9725	2^338565-141589	101919	Stefano Morozzi	01/2023
9726	2^338565+148821	101919	Stefano Morozzi	02/2023
9727	2^338564-56763	101918	Stefano Morozzi	03/2022
9728	2^338561+112007	101918	Stefano Morozzi	04/2022
9729	2^338561-9315	101918	Stefano Morozzi	04/2022
9730	2^338564+41965	101918	Stefano Morozzi	09/2022
9731	2^338561+121139	101918	Stefano Morozzi	11/2022
9732	2^338562+21799	101918	Stefano Morozzi	11/2022
9740	2^338559-1858777	101917	Enzo Doria	04/2016
9733	2^338558+4825	101917	Stefano Morozzi	01/2022
9734	2^338559-127935	101917	Stefano Morozzi	01/2022
9735	2^338560+154891	101917	Stefano Morozzi	01/2022
9736	2^338559+131885	101917	Stefano Morozzi	02/2022
9737	2^338558+93735	101917	Stefano Morozzi	09/2022
9738	2^338559-90957	101917	Stefano Morozzi	01/2023
9739	2^338559-190761	101917	Stefano Morozzi	01/2023
9741	2^338555+189981	101916	Stefano Morozzi	05/2022
9742	2^338553-125383	101915	Stefano Morozzi	12/2021
9743	2^338554-82821	101915	Stefano Morozzi	03/2022
9744	2^338548+76923	101914	Stefano Morozzi	12/2021
9745	2^338549+158517	101914	Stefano Morozzi	03/2022
9746	2^338549+85397	101914	Stefano Morozzi	03/2022
9747	2^338548+138121	101914	Stefano Morozzi	05/2022
9748	2^338550-110301	101914	Stefano Morozzi	06/2022
9749	2^338547+129321	101913	Stefano Morozzi	01/2022
9750	2^338547-153481	101913	Stefano Morozzi	01/2022

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Probable Primes Top 10000

(301737 PRPs in the top)