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 ?
7501	2^338090+33277	101776	Stefano Morozzi	02/2022
7502	2^338091-105601	101776	Stefano Morozzi	02/2022
7503	2^338091-32127	101776	Stefano Morozzi	03/2022
7504	2^338092+12873	101776	Stefano Morozzi	04/2022
7505	2^338091-58485	101776	Stefano Morozzi	04/2022
7506	2^338086+177643	101775	Stefano Morozzi	12/2021
7507	2^338089+82905	101775	Stefano Morozzi	02/2022
7508	2^338088+87565	101775	Stefano Morozzi	04/2022
7509	2^338088-166205	101775	Stefano Morozzi	01/2023
7510	2^338089-140053	101775	Stefano Morozzi	01/2023
7511	2^338085-3301	101774	Stefano Morozzi	01/2022
7512	2^338084+108691	101774	Stefano Morozzi	03/2022
7513	2^338083+164369	101774	Stefano Morozzi	05/2022
7514	2^338080+107521	101773	Stefano Morozzi	02/2022
7515	2^338080-156917	101773	Stefano Morozzi	03/2022
7516	2^338076+62311	101772	Stefano Morozzi	04/2022
7517	2^338079+161745	101772	Stefano Morozzi	04/2022
7518	2^338078-60075	101772	Stefano Morozzi	06/2022
7519	2^338079+167079	101772	Stefano Morozzi	09/2022
7520	2^338076+122535	101772	Stefano Morozzi	11/2022
7521	2^338077+95619	101772	Stefano Morozzi	11/2022
7522	2^338078+20539	101772	Stefano Morozzi	11/2022
7523	2^338076-36813	101772	Stefano Morozzi	12/2022
7524	2^338078-64911	101772	Stefano Morozzi	01/2023
7525	2^338073-77971	101771	Stefano Morozzi	01/2022
7526	2^338074+55579	101771	Stefano Morozzi	01/2022
7527	2^338073-81813	101771	Stefano Morozzi	03/2022
7528	2^338073+138645	101771	Stefano Morozzi	05/2022
7529	2^338075+148043	101771	Stefano Morozzi	11/2022
7530	2^338070-152607	101770	Stefano Morozzi	01/2022
7531	2^338070+138787	101770	Stefano Morozzi	05/2022
7532	2^338071+165249	101770	Stefano Morozzi	06/2022
7533	2^338070+70359	101770	Stefano Morozzi	11/2022
7534	2^338071+98573	101770	Stefano Morozzi	11/2022
7535	2^338069+79365	101769	Stefano Morozzi	01/2022
7536	2^338069+107571	101769	Stefano Morozzi	02/2022
7537	2^338068+73035	101769	Stefano Morozzi	11/2022
7538	2^338064+100087	101768	Stefano Morozzi	11/2021
7539	2^338064-83793	101768	Stefano Morozzi	04/2022
7540	2^338064+193701	101768	Stefano Morozzi	09/2022
7541	2^338060-151047	101767	Stefano Morozzi	12/2021
7542	2^338060-130805	101767	Stefano Morozzi	02/2022
7543	2^338060-136593	101767	Stefano Morozzi	12/2022
7544	2^338062-15725	101767	Stefano Morozzi	01/2023
7545	2^338058-76415	101766	Stefano Morozzi	12/2021
7546	2^338057+83865	101766	Stefano Morozzi	03/2022
7547	2^338057+86997	101766	Stefano Morozzi	04/2022
7548	2^338058+188589	101766	Stefano Morozzi	05/2022
7549	2^338058+68089	101766	Stefano Morozzi	09/2022
7550	2^338059+121803	101766	Stefano Morozzi	11/2022
7551	2^338057-39021	101766	Stefano Morozzi	01/2023
7552	2^338056+50605	101765	Stefano Morozzi	11/2021
7553	2^338053+53231	101765	Stefano Morozzi	01/2022
7554	2^338054-180497	101765	Stefano Morozzi	02/2022
7555	2^338053+59891	101765	Stefano Morozzi	03/2022
7556	2^338056+33987	101765	Stefano Morozzi	03/2022
7557	2^338055-157779	101765	Stefano Morozzi	03/2022
7558	2^338056+90307	101765	Stefano Morozzi	06/2022
7559	2^338052-55373	101764	Stefano Morozzi	02/2022
7560	2^338050-138281	101764	Stefano Morozzi	12/2022
7561	2^338048+31185	101763	Stefano Morozzi	01/2022
7562	2^338047+31935	101763	Stefano Morozzi	02/2022
7563	2^338047+108011	101763	Stefano Morozzi	02/2022
7564	2^338049+56777	101763	Stefano Morozzi	02/2022
7565	2^338049-7531	101763	Stefano Morozzi	03/2022
7566	2^338048-304019	101763	Harrison Mesh	06/2022
7567	2^338049+191291	101763	Stefano Morozzi	06/2022
7568	2^338047-187699	101763	Stefano Morozzi	12/2022
7569	2^338047-66405	101763	Stefano Morozzi	01/2023
7570	2^338046-25841	101762	Stefano Morozzi	12/2021
7571	2^338046-2285	101762	Stefano Morozzi	12/2021
7572	2^338046-177851	101762	Stefano Morozzi	01/2022
7573	2^338043+84045	101762	Stefano Morozzi	03/2022
7574	2^338046-57573	101762	Stefano Morozzi	03/2022
7575	2^338044-8177	101762	Stefano Morozzi	04/2022
7576	2^338045-58443	101762	Stefano Morozzi	04/2022
7577	2^338044+193497	101762	Stefano Morozzi	09/2022
7578	2^338043+45701	101762	Stefano Morozzi	11/2022
7579	2^338044-114197	101762	Stefano Morozzi	01/2023
7580	2^338042+194973	101761	Stefano Morozzi	11/2022
7581	2^338040-164483	101761	Stefano Morozzi	01/2023
7582	2^338038-57887	101760	Stefano Morozzi	04/2022
7583	2^338037+139169	101760	Stefano Morozzi	05/2022
7584	2^338037+188595	101760	Stefano Morozzi	05/2022
7585	2^338038-187241	101760	Stefano Morozzi	12/2022
7586	2^338034+125653	101759	Stefano Morozzi	11/2021
7587	2^338034-25211	101759	Stefano Morozzi	12/2021
7588	2^338033-154099	101759	Stefano Morozzi	02/2022
7589	2^338034-31803	101759	Stefano Morozzi	03/2022
7590	2^338033+162311	101759	Stefano Morozzi	04/2022
7591	2^338033-83071	101759	Stefano Morozzi	04/2022
7592	2^338035-158095	101759	Stefano Morozzi	04/2022
7593	2^338036-34193	101759	Stefano Morozzi	04/2022
7594	2^338036+42873	101759	Stefano Morozzi	09/2022
7595	2^338036+93373	101759	Stefano Morozzi	09/2022
7596	2^338035+146129	101759	Stefano Morozzi	11/2022
7597	2^338036+23983	101759	Stefano Morozzi	11/2022
7598	2^338036+170433	101759	Stefano Morozzi	11/2022
7599	2^338031+79989	101758	Stefano Morozzi	01/2022
7600	2^338032+158073	101758	Stefano Morozzi	02/2022
7601	2^338030-54371	101758	Stefano Morozzi	02/2022
7602	2^338032-180747	101758	Stefano Morozzi	02/2022
7603	2^338029-27909	101757	Stefano Morozzi	01/2022
7604	2^338027+70475	101757	Stefano Morozzi	11/2022
7605	2^338028-38705	101757	Stefano Morozzi	12/2022
7606	2^338028-140459	101757	Stefano Morozzi	01/2023
7607	2^338024-128495	101756	Stefano Morozzi	01/2022
7608	2^338025+34785	101756	Stefano Morozzi	03/2022
7609	2^338025-181765	101756	Stefano Morozzi	03/2022
7610	2^338024+63765	101756	Stefano Morozzi	05/2022
7611	2^338023-160621	101756	Stefano Morozzi	06/2022
7612	2^338026+117553	101756	Stefano Morozzi	09/2022
7613	2^338020-52437	101755	Stefano Morozzi	12/2021
7614	2^338021+160241	101755	Stefano Morozzi	03/2022
7615	2^338022+185845	101755	Stefano Morozzi	03/2022
7616	2^338021+189587	101755	Stefano Morozzi	05/2022
7617	2^338021-85891	101755	Stefano Morozzi	06/2022
7618	2^338020-87797	101755	Stefano Morozzi	12/2022
7619	2^338018-102741	101754	Stefano Morozzi	01/2022
7620	2^338018+29937	101754	Stefano Morozzi	01/2022
7621	2^338017-29505	101754	Stefano Morozzi	02/2022
7622	2^338018-30873	101754	Stefano Morozzi	02/2022
7623	2^338018-157013	101754	Stefano Morozzi	03/2022
7624	2^338019+168929	101754	Stefano Morozzi	09/2022
7625	2^338017+172721	101754	Stefano Morozzi	11/2022
7626	2^338018-136131	101754	Stefano Morozzi	12/2022
7627	2^338016+50797	101753	Stefano Morozzi	11/2021
7628	2^338016+26707	101753	Stefano Morozzi	12/2021
7629	2^338014+104677	101753	Stefano Morozzi	01/2022
7630	2^338013+145091	101753	Stefano Morozzi	11/2022
7631	2^338016-16335	101753	Stefano Morozzi	01/2023
7634	2^338010-19833	101752	Enzo Doria	06/2013
7632	2^338011+28665	101752	Stefano Morozzi	01/2022
7633	2^338010+89505	101752	Stefano Morozzi	05/2022
7635	2^338007+58985	101751	Stefano Morozzi	03/2022
7636	2^338008+109741	101751	Stefano Morozzi	03/2022
7637	2^338009+9527	101751	Stefano Morozzi	03/2022
7638	2^338007+14511	101751	Stefano Morozzi	05/2022
7639	2^338008+67957	101751	Stefano Morozzi	09/2022
7640	2^338009-11935	101751	Stefano Morozzi	12/2022
7641	2^338007-14199	101751	Stefano Morozzi	01/2023
7642	2^338005-75829	101750	Stefano Morozzi	12/2021
7643	2^338006-125055	101750	Stefano Morozzi	12/2021
7644	2^338006+5013	101750	Stefano Morozzi	01/2022
7645	2^338003+40269	101750	Stefano Morozzi	06/2022
7646	2^338006+166495	101750	Stefano Morozzi	06/2022
7647	2^338003-188551	101750	Stefano Morozzi	12/2022
7648	2^338000+25113	101749	Stefano Morozzi	12/2021
7650	3^213215-76	101730	Lelio R Paula	09/2016
7649	23907^17998+17998^23907	101730	Hans Havermann	01/2019
7651	10^101728+154953	101729	Patrick De Geest	02/2020
7654	2^337930+63	101728	Lelio R Paula	07/2011
7652	10^101728-987654321	101728	Robert Price	12/2019
7653	10^101728-60741	101728	Patrick De Geest	02/2020
7655	2^337920+1869661	101725	Enzo Doria	05/2016
7656	2^337922+100280245065	101725	Paul Bourdelais	10/2021
7657	24116^16509+16509^24116	101715	Hans Havermann	01/2019
7658	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
7659	2^337859-19645	101706	Enzo Doria	05/2013
7660	2^337754+1869169	101675	Enzo Doria	05/2016
7661	3*10^101657-37	101658	Robert Price	07/2018
7662	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
7663	11^97605-24	101646	Lelio R Paula	10/2016
7664	(83*10^101636+133)/9	101637	Robert Price	08/2021
7665	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
7666	8^112539-112539	101633	Robert Price	01/2014
7667	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
7668	(11*10^101613+61)/9	101614	Tyler Busby	01/2023
7669	25694^9003+9003^25694	101605	Hans Havermann	12/2018
7670	2^337515-19869	101603	Enzo Doria	06/2013
7671	2^337473+719	101590	Lelio R Paula	08/2011
7672	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
7673	2^337452-108815	101584	Enzo Doria	03/2014
7674	2^337453+1185	101584	Lelio R Paula	09/2016
7675	(41*10^101583+319)/9	101584	Robert Price	06/2021
7676	2^337410-113561	101571	Enzo Doria	08/2014
7677	2^337387+855	101564	Lelio R Paula	09/2016
7678	2^337367-17295	101558	Lelio R Paula	09/2016
7679	2^337342-109035	101551	Enzo Doria	04/2014
7680	23703^19238+19238^23703	101548	Hans Havermann	12/2018
7681	(26*10^101537-167)/3	101538	Robert Price	10/2019
7682	2^337267-19	101528	Lelio R Paula	07/2011
7683	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
7684	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
7685	2^337222-340871	101514	Harrison Mesh	06/2022
7686	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
7687	2^337183-19989	101503	Enzo Doria	06/2013
7688	2^337149+72425	101492	Enzo Doria	04/2016
7689	24041^16642+16642^24041	101483	Hans Havermann	12/2018
7690	33982^969+969^33982	101482	Hans Havermann	12/2018
7691	2^337101-20241	101478	Enzo Doria	06/2013
7692	2^337035-20001	101458	Enzo Doria	06/2013
7693	(7*10^101456+89)/3	101457	Robert Price	08/2020
7694	2^337017-16995	101453	Lelio R Paula	09/2016
7695	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
7696	2^336979-115315	101441	Enzo Doria	06/2015
7697	2^336970-20885	101439	Enzo Doria	06/2013
7698	2^336958+79	101435	Lelio R Paula	10/2009
7699	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
7700	2^336942+169	101430	Lelio R Paula	10/2009
7701	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
7702	4*10^101415-89	101416	Robert Price	11/2018
7703	(14*10^101410-89)/3	101411	Robert Price	05/2020
7704	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
7705	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
7706	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
7707	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
7708	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
7709	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
7710	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
7711	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
7712	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
7713	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
7714	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
7715	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
7716	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
7717	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
7718	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
7719	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
7720	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
7721	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
7722	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
7723	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
7724	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
7725	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
7726	24097^16150+16150^24097	101405	Hans Havermann	12/2018
7727	2^336842+94065	101400	Lelio R Paula	09/2016
7728	(7*10^101395-1)/3	101396	Robert Price	08/2022
7729	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
7730	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
7731	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
7732	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
7733	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
7734	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
7735	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
7736	10^101369+203811	101370	Patrick De Geest	11/2016
7737	10^101369-99	101369	Lelio R Paula	09/2016
7738	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
7739	2^336701-113563	101358	Enzo Doria	08/2014
7740	89717!4-512	101351	Robert Price	11/2019
7741	2^336644-109023	101340	Enzo Doria	04/2014
7742	2^336601-21081	101327	Enzo Doria	06/2013
7743	20^77869+63	101310	Lelio R Paula	09/2016
7744	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
7746	6^130179-137	101299	Lelio R Paula	10/2016
7745	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
7747	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
7748	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
7749	2^336369-19753	101258	Enzo Doria	05/2013
7750	23842^17653+17653^23842	101253	Hans Havermann	11/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)