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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(61*10^101986+47)/9	101987	Robert Price	07/2022
9502	2^338787+53309	101986	Stefano Morozzi	01/2022
9503	2^338787-153817	101986	Stefano Morozzi	01/2022
9504	2^338789+56229	101986	Stefano Morozzi	01/2022
9505	2^338790+6429	101986	Stefano Morozzi	01/2022
9506	2^338788+131701	101986	Stefano Morozzi	02/2022
9507	2^338785+104639	101985	Stefano Morozzi	01/2022
9508	2^338784+37591	101985	Stefano Morozzi	04/2022
9509	2^338786-9831	101985	Stefano Morozzi	04/2022
9510	2^338783+109065	101984	Stefano Morozzi	03/2022
9511	2^338779+86711	101983	Stefano Morozzi	04/2022
9512	2^338778+113589	101983	Stefano Morozzi	05/2022
9513	2^338775-30369	101982	Stefano Morozzi	02/2022
9514	2^338774+159135	101982	Stefano Morozzi	03/2022
9515	2^338776+113001	101982	Stefano Morozzi	04/2022
9516	2^338774+117039	101982	Stefano Morozzi	09/2022
9517	2^338775+167109	101982	Stefano Morozzi	09/2022
9518	2^338774+147595	101982	Stefano Morozzi	11/2022
9519	2^338772+42733	101981	Stefano Morozzi	09/2022
9520	2^338771-138805	101981	Stefano Morozzi	12/2022
9521	2^338768-181007	101980	Stefano Morozzi	02/2022
9522	2^338768+108807	101980	Stefano Morozzi	03/2022
9523	2^338767+169155	101980	Stefano Morozzi	09/2022
9524	2^338769+95369	101980	Stefano Morozzi	11/2022
9525	2^338769+195965	101980	Stefano Morozzi	11/2022
9526	2^338770-12725	101980	Stefano Morozzi	12/2022
9527	2^338768-140843	101980	Stefano Morozzi	01/2023
9528	2^338764+138013	101979	Stefano Morozzi	04/2022
9529	2^338765-160323	101979	Stefano Morozzi	06/2022
9530	2^338765+124545	101979	Stefano Morozzi	02/2023
9536	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
9531	2^338761+103671	101978	Stefano Morozzi	01/2022
9532	2^338763-7651	101978	Stefano Morozzi	03/2022
9533	2^338763+65591	101978	Stefano Morozzi	06/2022
9534	2^338762-111875	101978	Stefano Morozzi	12/2022
9535	2^338762-192237	101978	Stefano Morozzi	02/2023
9537	2^338757-5151	101977	Stefano Morozzi	02/2022
9538	2^338760-79037	101977	Stefano Morozzi	02/2022
9539	2^338757-82143	101977	Stefano Morozzi	03/2022
9540	2^338757+137007	101977	Stefano Morozzi	04/2022
9541	2^338755+158531	101976	Stefano Morozzi	03/2022
9542	2^338755+74081	101976	Stefano Morozzi	02/2023
9543	2^338752-153353	101975	Stefano Morozzi	01/2022
9544	2^338751+8001	101975	Stefano Morozzi	02/2022
9545	2^338752+32977	101975	Stefano Morozzi	02/2022
9546	2^338753-79233	101975	Stefano Morozzi	02/2022
9547	2^338752-88157	101975	Stefano Morozzi	12/2022
9548	2^338750-175625	101974	Stefano Morozzi	12/2021
9549	2^338747-2731	101974	Stefano Morozzi	12/2021
9550	2^338750-29597	101974	Stefano Morozzi	02/2022
9551	2^338748+35095	101974	Stefano Morozzi	03/2022
9552	2^338747+137475	101974	Stefano Morozzi	04/2022
9553	2^338747+162005	101974	Stefano Morozzi	04/2022
9554	2^338750+162237	101974	Stefano Morozzi	04/2022
9555	2^338747-184365	101974	Stefano Morozzi	04/2022
9556	2^338748+64341	101974	Stefano Morozzi	05/2022
9557	2^338750+24445	101974	Stefano Morozzi	02/2023
9558	2^338746+59577	101973	Stefano Morozzi	03/2022
9559	2^338746+62055	101973	Stefano Morozzi	04/2022
9560	2^338744+194065	101973	Stefano Morozzi	09/2022
9561	2^338741+25359	101972	Stefano Morozzi	12/2021
9562	2^338743+176981	101972	Stefano Morozzi	12/2021
9563	2^338741+183029	101972	Stefano Morozzi	02/2022
9564	2^338743-130309	101972	Stefano Morozzi	02/2022
9565	2^338741+86349	101972	Stefano Morozzi	04/2022
9566	2^338741+111561	101972	Stefano Morozzi	04/2022
9567	2^338743+172301	101972	Stefano Morozzi	11/2022
9568	2^338741-189969	101972	Stefano Morozzi	01/2023
9569	2^338739+76959	101971	Stefano Morozzi	12/2021
9570	2^338739-105957	101971	Stefano Morozzi	02/2022
9571	2^338739+190149	101971	Stefano Morozzi	05/2022
9572	2^338738+64947	101971	Stefano Morozzi	05/2022
9573	2^338740+119947	101971	Stefano Morozzi	11/2022
9574	2^338740-186837	101971	Stefano Morozzi	12/2022
9575	2^338737+127547	101970	Stefano Morozzi	12/2021
9576	2^338737+128591	101970	Stefano Morozzi	01/2022
9577	2^338735-153165	101970	Stefano Morozzi	01/2022
9578	2^338734+13719	101970	Stefano Morozzi	05/2022
9579	2^338734-138225	101970	Stefano Morozzi	12/2022
9580	2^338735-186129	101970	Stefano Morozzi	12/2022
9586	25295^10744+10744^25295	101969	Hans Havermann	01/2019
9587	25712^9243+9243^25712	101969	Hans Havermann	01/2019
9581	2^338731-150895	101969	Stefano Morozzi	12/2021
9582	2^338731+54911	101969	Stefano Morozzi	01/2022
9583	2^338731+85863	101969	Stefano Morozzi	03/2022
9584	2^338732+185047	101969	Stefano Morozzi	03/2022
9585	2^338733+193791	101969	Stefano Morozzi	09/2022
9588	2^338729+69221	101968	Stefano Morozzi	09/2022
9589	2^338728+123355	101968	Stefano Morozzi	11/2022
9590	2^338730-87063	101968	Stefano Morozzi	12/2022
9591	2^338726+128199	101967	Stefano Morozzi	01/2022
9592	2^338727+127745	101967	Stefano Morozzi	01/2022
9593	2^338724+32971	101967	Stefano Morozzi	02/2022
9594	2^338727+189683	101967	Stefano Morozzi	05/2022
9595	2^338727+118293	101967	Stefano Morozzi	09/2022
9596	2^338723-76651	101966	Stefano Morozzi	12/2021
9597	2^338721+79037	101966	Stefano Morozzi	01/2022
9598	2^338723-132621	101966	Stefano Morozzi	03/2022
9599	2^338722+137313	101966	Stefano Morozzi	04/2022
9600	2^338722+162915	101966	Stefano Morozzi	04/2022
9601	2^338723+199161	101966	Stefano Morozzi	02/2023
9602	2^338718-126861	101965	Stefano Morozzi	12/2021
9603	2^338718-109127	101965	Stefano Morozzi	04/2022
9608	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
9604	2^338714+30835	101964	Stefano Morozzi	01/2022
9605	2^338714+156715	101964	Stefano Morozzi	02/2022
9606	2^338715+19923	101964	Stefano Morozzi	09/2022
9607	2^338716+173253	101964	Stefano Morozzi	11/2022
9609	2^338711+125399	101963	Stefano Morozzi	12/2021
9610	2^338713-30895	101963	Stefano Morozzi	02/2022
9611	2^338712-132545	101963	Stefano Morozzi	03/2022
9612	2^338713+87825	101963	Stefano Morozzi	04/2022
9613	2^338712+190333	101963	Stefano Morozzi	06/2022
9614	2^338709-154429	101962	Stefano Morozzi	02/2022
9615	2^338710+140545	101962	Stefano Morozzi	06/2022
9616	2^338706-102917	101961	Stefano Morozzi	01/2022
9617	2^338705+34727	101961	Stefano Morozzi	03/2022
9618	2^338706-165633	101961	Stefano Morozzi	01/2023
9619	2^338707-116115	101961	Stefano Morozzi	01/2023
9620	2^338698+104083	101959	Stefano Morozzi	01/2022
9621	2^338700-184565	101959	Stefano Morozzi	04/2022
9622	2^338700+189777	101959	Stefano Morozzi	05/2022
9623	2^338698+41779	101959	Stefano Morozzi	09/2022
9624	2^338699+148533	101959	Stefano Morozzi	11/2022
9625	2^338700+97381	101959	Stefano Morozzi	11/2022
9626	2^338698-142181	101959	Stefano Morozzi	02/2023
9627	2^338696+181671	101958	Stefano Morozzi	02/2022
9628	2^338697+146651	101958	Stefano Morozzi	11/2022
9629	2^338695-116977	101958	Stefano Morozzi	02/2023
9630	2^338692+106297	101957	Stefano Morozzi	01/2022
9631	2^338692+33195	101957	Stefano Morozzi	02/2022
9632	2^338692+110505	101957	Stefano Morozzi	03/2022
9633	2^338692+190093	101957	Stefano Morozzi	05/2022
9634	2^338692+173343	101957	Stefano Morozzi	11/2022
9635	2^338693+144975	101957	Stefano Morozzi	11/2022
9636	2^338692+149281	101957	Stefano Morozzi	02/2023
9637	2^338688+82203	101956	Stefano Morozzi	02/2022
9638	2^338689+82365	101956	Stefano Morozzi	02/2022
9639	2^338688-92159	101956	Stefano Morozzi	02/2023
9640	2^338686-81303	101955	Stefano Morozzi	03/2022
9641	2^338687+40461	101955	Stefano Morozzi	06/2022
9642	2^338687+65283	101955	Stefano Morozzi	06/2022
9648	2^338682-19865	101954	Enzo Doria	06/2013
9649	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
9643	(8*10^101954-269)/9	101954	Robert Price	09/2021
9644	2^338683+50303	101954	Stefano Morozzi	11/2021
9645	2^338682-107205	101954	Stefano Morozzi	03/2022
9646	2^338682+13839	101954	Stefano Morozzi	05/2022
9647	2^338683-42837	101954	Stefano Morozzi	02/2023
9650	2^338678-180005	101953	Stefano Morozzi	02/2022
9651	2^338680+15855	101953	Stefano Morozzi	06/2022
9652	2^338678+93175	101953	Stefano Morozzi	09/2022
9653	2^338680+99217	101953	Stefano Morozzi	02/2023
9654	2^338674-175967	101952	Stefano Morozzi	12/2021
9655	2^338677-177373	101952	Stefano Morozzi	12/2021
9656	2^338677+102999	101952	Stefano Morozzi	01/2022
9657	2^338676+33381	101952	Stefano Morozzi	03/2022
9658	2^338677-82699	101952	Stefano Morozzi	03/2022
9659	2^338676-34299	101952	Stefano Morozzi	04/2022
9660	2^338675+188445	101952	Stefano Morozzi	05/2022
9661	2^338676+165271	101952	Stefano Morozzi	06/2022
9662	2^338674-187551	101952	Stefano Morozzi	12/2022
9663	2^338676-42243	101952	Stefano Morozzi	02/2023
9664	2^338671-55041	101951	Stefano Morozzi	02/2022
9665	2^338673-80203	101951	Stefano Morozzi	02/2022
9666	2^338672-182063	101951	Stefano Morozzi	03/2022
9667	2^338672+36667	101951	Stefano Morozzi	04/2022
9668	2^338668+2583	101950	Stefano Morozzi	12/2021
9669	2^338670-157001	101950	Stefano Morozzi	03/2022
9670	2^338669-8353	101950	Stefano Morozzi	04/2022
9671	2^338670+40635	101950	Stefano Morozzi	06/2022
9679	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
9672	2^338665+1577	101949	Stefano Morozzi	12/2021
9673	2^338665-51133	101949	Stefano Morozzi	12/2021
9674	2^338664+4345	101949	Stefano Morozzi	01/2022
9675	2^338666-128943	101949	Stefano Morozzi	01/2022
9676	2^338664+131535	101949	Stefano Morozzi	01/2022
9677	2^338667+14943	101949	Stefano Morozzi	05/2022
9678	2^338665+166637	101949	Stefano Morozzi	09/2022
9680	2^338662+31587	101948	Stefano Morozzi	02/2022
9681	2^338663-58375	101948	Stefano Morozzi	04/2022
9682	2^338663-107869	101948	Stefano Morozzi	04/2022
9683	2^338663+90435	101948	Stefano Morozzi	06/2022
9684	2^338661+70457	101948	Stefano Morozzi	11/2022
9685	2^338662+70519	101948	Stefano Morozzi	11/2022
9686	2^338663-39447	101948	Stefano Morozzi	01/2023
9687	2^338658-159191	101947	Stefano Morozzi	04/2022
9688	2^338659-159687	101947	Stefano Morozzi	04/2022
9689	2^338659+15543	101947	Stefano Morozzi	05/2022
9690	2^338658+44395	101947	Stefano Morozzi	09/2022
9691	2^338658+192537	101947	Stefano Morozzi	09/2022
9692	2^338659-90531	101947	Stefano Morozzi	01/2023
9693	2^338659-114759	101947	Stefano Morozzi	01/2023
9694	2^338659+124079	101947	Stefano Morozzi	02/2023
9695	2^338654+51027	101946	Stefano Morozzi	12/2021
9696	2^338656-152115	101946	Stefano Morozzi	12/2021
9697	2^338654+32415	101946	Stefano Morozzi	02/2022
9698	2^338654+39799	101946	Stefano Morozzi	05/2022
9699	2^338655+144579	101946	Stefano Morozzi	09/2022
9700	2^338657+97509	101946	Stefano Morozzi	11/2022
9701	2^338653+126629	101945	Stefano Morozzi	12/2021
9702	2^338653+33279	101945	Stefano Morozzi	02/2022
9703	2^338652-107097	101945	Stefano Morozzi	03/2022
9704	2^338653+94475	101945	Stefano Morozzi	09/2022
9705	2^338651+194073	101945	Stefano Morozzi	09/2022
9706	2^338652-89157	101945	Stefano Morozzi	01/2023
9707	2^338649-154663	101944	Stefano Morozzi	02/2022
9708	2^338650+61399	101944	Stefano Morozzi	04/2022
9709	2^338650-35655	101944	Stefano Morozzi	06/2022
9710	2^338650+169623	101944	Stefano Morozzi	09/2022
9711	2^338649-40743	101944	Stefano Morozzi	01/2023
9712	2^338645+150311	101943	Stefano Morozzi	11/2021
9713	2^338645+28481	101943	Stefano Morozzi	01/2022
9714	2^338647-77895	101943	Stefano Morozzi	01/2022
9715	2^338647-84607	101943	Stefano Morozzi	04/2022
9716	2^338647+164523	101943	Stefano Morozzi	05/2022
9717	2^338645+64845	101943	Stefano Morozzi	05/2022
9718	2^338644-35969	101943	Stefano Morozzi	12/2022
9719	2^338645-15715	101943	Stefano Morozzi	01/2023
9720	2^338641-152541	101942	Stefano Morozzi	12/2021
9721	2^338643-56487	101942	Stefano Morozzi	03/2022
9722	2^338642-186525	101942	Stefano Morozzi	12/2022
9723	2^338643-41715	101942	Stefano Morozzi	02/2023
9724	2^338638+100575	101941	Stefano Morozzi	12/2021
9725	2^338639-127461	101941	Stefano Morozzi	12/2021
9726	2^338640+187657	101941	Stefano Morozzi	04/2022
9727	2^338640+44431	101941	Stefano Morozzi	09/2022
9728	2^338635+1961	101940	Stefano Morozzi	12/2021
9729	2^338637+102125	101940	Stefano Morozzi	12/2021
9730	2^338636-135329	101940	Stefano Morozzi	06/2022
9731	2^338635+199485	101940	Stefano Morozzi	02/2023
9736	28594^3673+3673^28594	101939	Hans Havermann	02/2019
9732	2^338631+110741	101939	Stefano Morozzi	03/2022
9733	2^338631+112119	101939	Stefano Morozzi	04/2022
9734	2^338634-83097	101939	Stefano Morozzi	04/2022
9735	2^338633+139701	101939	Stefano Morozzi	05/2022
9737	2^338630-150341	101938	Stefano Morozzi	12/2021
9738	2^338630+12867	101938	Stefano Morozzi	04/2022
9739	2^338629+42147	101938	Stefano Morozzi	09/2022
9740	2^338628+121083	101938	Stefano Morozzi	11/2022
9741	2^338630+147235	101938	Stefano Morozzi	11/2022
9742	2^338628-37679	101938	Stefano Morozzi	12/2022
9743	2^338629-41383	101938	Stefano Morozzi	01/2023
9744	2^338628-91877	101938	Stefano Morozzi	02/2023
9745	2^338626-105875	101937	Stefano Morozzi	02/2022
9746	2^338625-111729	101937	Stefano Morozzi	12/2022
9747	2^338627+49299	101937	Stefano Morozzi	02/2023
9748	2^338621+33069	101936	Stefano Morozzi	02/2022
9749	2^338623-106405	101936	Stefano Morozzi	03/2022
9750	2^338621+61751	101936	Stefano Morozzi	04/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301883 PRPs in the top)