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 ?
1501	65207^41416+41416^65207	301072	Hans Havermann	10/2021
1503	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
1502	2^999999+77151	301030	Norman Luhn	09/2023
1504	90762^2071+2071^90762	300984	Hans Havermann	06/2021
1505	63909^51142+51142^63909	300934	Hans Havermann	08/2021
1506	2^999646+1874029	300924	Enzo Doria	06/2016
1507	66280^34607+34607^66280	300856	Hans Havermann	06/2021
1508	65534^38925+38925^65534	300817	Hans Havermann	07/2021
1509	63296^56517+56517^63296	300794	Hans Havermann	06/2021
1510	110610^523+523^110610	300694	Hans Havermann	06/2021
1511	66428^33609+33609^66428	300684	Hans Havermann	06/2021
1512	74247^11210+11210^74247	300672	Hans Havermann	06/2021
1513	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
1514	10^300476+3	300477	Ed Trice	10/2012
1515	10^300476-530913	300476	Patrick De Geest	03/2016
1516	66703^31960+31960^66703	300471	Hans Havermann	06/2021
1517	63722^51915+51915^63722	300468	Hans Havermann	06/2021
1518	2^998053+1879667	300444	Enzo Doria	09/2016
1519	77018^7959+7959^77018	300437	Hans Havermann	07/2021
1520	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
1521	2^997689+217787	300335	Enzo Doria	01/2024
1522	69478^20987+20987^69478	300281	Hans Havermann	07/2021
1523	64088^48393+48393^64088	300239	Hans Havermann	07/2021
1524	2^997369+237917	300238	Enzo Doria	06/2025
1525	64605^44146+44146^64605	300084	Hans Havermann	08/2021
1526	2^996845+29027	300081	Enzo Doria	02/2024
1527	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
1528	67594^27465+27465^67594	300035	Hans Havermann	06/2021
1529	10^300000+287389	300001	Patrick De Geest	10/2019
1530	10^300000-83657	300000	Patrick De Geest	10/2019
1531	70599^17756+17756^70599	300000	Hans Havermann	06/2021
1532	numbpart(72526161452)	299999	Serge Batalov	04/2017
1533	2^996182-114431	299881	Enzo Doria	02/2015
1534	3*2^996126+5	299865	Jon Grantham	07/2023
1535	2^996034-17	299837	Stefano Morozzi	07/2022
1536	2^995793+36587	299764	Enzo Doria	09/2024
1537	(19*10^299640+77)/3	299641	Robert Price	03/2023
1538	2^995214-2788361	299590	Enzo Doria	12/2015
1539	2^994791-114319	299462	Enzo Doria	01/2015
1540	2^994490-1863791	299372	Enzo Doria	01/2016
1541	2^993322+1885729	299020	Enzo Doria	03/2017
1542	2^993227+230033	298992	Enzo Doria	12/2024
1543	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
1544	2^992711-2788807	298836	Enzo Doria	12/2015
1545	2^992525-114199	298780	Enzo Doria	12/2014
1546	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
1547	2^992329+1884707	298721	Enzo Doria	02/2017
1548	2^992292+229801	298710	Enzo Doria	12/2024
1549	2^992052+215491	298638	Enzo Doria	11/2023
1550	2^991968-23	298613	Stefano Morozzi	07/2022
1551	2^991715-19	298536	Stefano Morozzi	07/2022
1552	2^991387+237383	298438	Enzo Doria	06/2025
1553	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
1554	2^989562+25	297888	Stefano Morozzi	05/2021
1555	2^988580+214051	297593	Enzo Doria	10/2023
1556	2^988537+218837	297580	Enzo Doria	03/2024
1557	(19*10^297497+77)/3	297498	Robert Price	03/2023
1558	(2*10^297488-23)/3	297488	Robert Price	10/2022
1559	2^988148+48271	297463	Enzo Doria	07/2025
1560	2^987033+46427	297127	Enzo Doria	05/2025
1561	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
1562	2^985217-114553	296580	Enzo Doria	03/2015
1563	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
1564	2^984650+21529	296410	Enzo Doria	08/2023
1565	2^984131-1828009	296253	Enzo Doria	01/2015
1566	2^983620+60451	296100	Phil Moore	03/2008
1567	2^982721-2683	295829	Yves Minet	02/2016
1568	(23*10^295581+7)/3	295582	Robert Price	05/2023
1569	2^981298-2788421	295401	Enzo Doria	12/2015
1570	2^981163-2790967	295360	Enzo Doria	12/2015
1571	2^981016-15	295316	Stefano Morozzi	07/2022
1572	8*10^295160-13	295161	Robert Price	08/2023
1573	2^979594+1865839	294888	Enzo Doria	02/2016
1574	2^979502+221029	294860	Enzo Doria	03/2024
1575	2*10^294527-91	294528	Robert Price	02/2023
1576	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
1577	10^294475+49	294476	Robert Price	02/2023
1578	2^977896+234601	294377	Enzo Doria	04/2025
1579	(11*10^294308+91)/3	294309	Robert Price	03/2023
1580	2^976760+1885021	294035	Enzo Doria	02/2017
1581	3*2^976518+5	293962	Jon Grantham	07/2023
1582	2^975798+218599	293745	Enzo Doria	01/2024
1583	2^974441+1878407	293336	Enzo Doria	08/2016
1584	2^974180+1876831	293258	Enzo Doria	07/2016
1585	2^974170+453319	293255	Enzo Doria	01/2017
1586	(211^126023-1)/210	292911	Anonymous	05/2024
1587	2^972744-114419	292826	Enzo Doria	03/2015
1588	11^281143+6	292781	Paul Bourdelais	03/2021
1589	(4*10^292619-91)/3	292620	Robert Price	12/2022
1590	E(69468)/13247122135	292549	Sergey Batalov	10/2023
1591	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
1592	3*10^292344-97	292345	Robert Price	01/2023
1593	2^970911+1873373	292274	Enzo Doria	07/2016
1594	2^970670+383059	292201	Enzo Doria	12/2016
1595	2^970141-100363	292042	Enzo Doria	02/2014
1596	2^969945+1874717	291983	Enzo Doria	06/2016
1597	2^969384+1880701	291814	Enzo Doria	10/2016
1598	(13*10^291721-43)/3	291722	Robert Price	08/2023
1599	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1600	10^(2145126+1)-210^145126-1	290253	Robert Price	03/2025
1601	3*2^963892+5	290161	Jon Grantham	07/2023
1602	(151*10^289877-1)/3	289879	Robert Price	07/2023
1603	2^962194+60139	289650	Enzo Doria	02/2016
1604	2^961409+44267	289413	Enzo Doria	04/2025
1605	2^959307-1861507	288781	Enzo Doria	11/2015
1606	(17*10^288692+31)/3	288693	Robert Price	04/2023
1607	14^251797-3	288592	Paul Bourdelais	12/2020
1608	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1609	(2*10^288371-23)/3	288371	Robert Price	10/2022
1610	(31*10^288238-1)/3	288240	Robert Price	02/2023
1611	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
1612	2^957372+283531	288198	Enzo Doria	02/2017
1613	2^957192-1864049	288144	Enzo Doria	01/2016
1614	(95774^58081-1)/(95774^241-1)	288116	Ryan Propper	11/2023
1615	2^956446+1875199	287919	Enzo Doria	06/2016
1616	2^956283+219143	287870	Enzo Doria	02/2024
1617	7*10^287854+39	287855	Robert Price	01/2023
1618	2^956082+28309	287810	Enzo Doria	02/2024
1619	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
1620	2^955178+1883587	287538	Enzo Doria	12/2016
1621	2^954127-954127^2	287221	Henri Lifchitz	01/2021
1622	2^954001+1875257	287183	Enzo Doria	07/2016
1623	2*10^287175-49	287176	Robert Price	05/2023
1624	(22*10^287085-19)/3	287086	Robert Price	07/2023
1625	2^953667+38573	287083	Enzo Doria	11/2024
1626	2^953488+22411	287029	Enzo Doria	09/2023
1627	(23891^65536+1)/2	286932	Serge Batalov	03/2018
1628	5*3^601336-2^601336	286911	Jon Grantham	08/2023
1629	2^952268+1878601	286662	Enzo Doria	09/2016
1630	2^950801+81557	286220	Enzo Doria	08/2016
1631	2^949403+217523	285799	Enzo Doria	01/2024
1632	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
1633	(19*10^285615+53)/9	285616	Rytis Slatkevicius	12/2024
1634	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
1635	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
1636	2^948510+782569	285530	Enzo Doria	10/2016
1637	2^948374-114137	285490	Enzo Doria	01/2015
1638	2^947739+1872923	285298	Enzo Doria	06/2016
1639	2^946274+218407	284857	Enzo Doria	03/2024
1640	7*10^284751+9	284752	Robert Price	04/2023
1641	2^944561-21	284342	Stefano Morozzi	07/2022
1642	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
1643	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
1644	2^942533+82067	283731	Enzo Doria	09/2016
1645	2^941469+39	283411	Jon Grantham	08/2023
1646	(10^283342-31)/3	283342	Robert Price	03/2023
1647	2^940950+1874989	283255	Enzo Doria	06/2016
1648	2^940426-2786141	283097	Enzo Doria	11/2015
1649	2^940155+226973	283015	Enzo Doria	09/2024
1650	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
1651	2^939881-114115	282933	Enzo Doria	12/2014
1652	(14*10^282673-143)/3	282674	Robert Price	05/2023
1653	10^282493+632551	282494	Patrick De Geest	02/2017
1655	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
1654	10^282493-132327	282493	Patrick De Geest	02/2017
1656	3^591827-2^591827	282374	Mike Oakes	08/2009
1657	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
1658	2^936716-1835519	281980	Enzo Doria	04/2015
1659	2^936588+79411	281942	Enzo Doria	06/2016
1660	2^936047+1877423	281779	Enzo Doria	08/2016
1661	2^935713+1869377	281678	Enzo Doria	05/2016
1662	2^933082+1877059	280886	Enzo Doria	08/2016
1663	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1664	2^932443+225893	280694	Enzo Doria	08/2024
1665	2^932064+26521	280580	Enzo Doria	12/2023
1666	2^931976+25	280553	Stefano Morozzi	05/2021
1667	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1668	(10^279978+11)/3	279978	Serge Batalov	07/2015
1669	2^929524-1864829	279815	Enzo Doria	01/2016
1670	2^929329+22697	279756	Enzo Doria	09/2023
1671	2^929152+60181	279703	Enzo Doria	02/2016
1672	2^928621-2787883	279543	Enzo Doria	11/2015
1673	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1674	3*10^279271+77	279272	Robert Price	06/2024
1675	2^927429+1882277	279184	Enzo Doria	12/2016
1676	2^926766-11	278985	Stefano Morozzi	07/2022
1677	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1678	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1679	(5347*26^197061-297)/25	278839	Eric Chen	12/2025
1680	(166*10^278633-7)/3	278635	Robert Price	02/2023
1681	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1682	2^925330-1301	278553	Yves Minet	06/2015
1683	(299*10^278546+1)/3	278548	Robert Price	01/2023
1684	2^925299+216053	278543	Enzo Doria	11/2023
1686	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1685	(79^146749-1)/6395645198026062186	278457	Paul Vanderveen	06/2025
1687	(266*10^278325+1)/3	278327	Robert Price	01/2023
1688	2^923261-69175	277930	Enzo Doria	11/2015
1689	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1690	2^922301+57	277641	Stefano Morozzi	05/2021
1691	7*10^277478-39	277479	Robert Price	07/2023
1692	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
1693	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1694	2^920318+2792299	277044	Enzo Doria	02/2016
1695	(16*10^276537-31)/3	276538	Robert Price	03/2023
1696	2^918596-2786939	276525	Enzo Doria	11/2015
1697	2^917910+28369	276319	Enzo Doria	01/2024
1698	2^917328+228571	276144	Enzo Doria	11/2024
1699	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1700	2^916639+60563	275936	Enzo Doria	04/2016
1701	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1702	2^916385-2786383	275860	Enzo Doria	11/2015
1703	2^915928+82081	275722	Enzo Doria	09/2016
1704	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1705	2^915576-114137	275616	Enzo Doria	01/2015
1706	2^914828+1876741	275391	Enzo Doria	07/2016
1707	2^914757-2203	275370	Yves Minet	12/2015
1708	7*10^275157-27	275158	Robert Price	11/2022
1709	2^912744+20011	274764	Enzo Doria	06/2023
1710	2^911900+1871245	274510	Enzo Doria	05/2016
1711	(16*10^274251-91)/3	274252	Robert Price	11/2022
1712	2^910999+9	274239	Stefano Morozzi	05/2021
1713	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
1714	2^910490+283429	274085	Enzo Doria	01/2017
1715	7*10^273983+39	273984	Robert Price	01/2023
1716	2^909988-1862249	273934	Enzo Doria	12/2015
1717	2^909901+378567	273908	Boyan Hu	08/2024
1718	2^909297+1879157	273726	Enzo Doria	08/2016
1719	2^909257-1864423	273714	Enzo Doria	01/2016
1720	2^909254+31309	273713	Enzo Doria	03/2024
1721	2^908739-7	273558	Stefano Morozzi	07/2022
1722	2^908579-1861747	273510	Enzo Doria	12/2015
1723	3*2^908005-5	273338	Jon Grantham	07/2023
1724	2^907635-2791597	273226	Enzo Doria	01/2016
1725	2^907059+211193	273052	Enzo Doria	08/2023
1726	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1727	2^906594-113201	272912	Enzo Doria	08/2014
1728	9*10^272800+91	272801	Robert Price	05/2023
1729	2*10^272710-49	272711	Robert Price	05/2023
1730	2*10^272403-91	272404	Robert Price	02/2023
1731	2^904773+1872167	272364	Enzo Doria	06/2016
1732	6^349903+5	272278	Paul Bourdelais	02/2021
1733	2^904149-1862473	272176	Enzo Doria	12/2015
1734	2^902926+227839	271808	Enzo Doria	10/2024
1735	(7*10^271757-61)/9	271757	Erik Branger	03/2012
1736	2^902497+1880117	271679	Enzo Doria	09/2016
1737	2^901858+77689	271487	Enzo Doria	06/2016
1738	2^901372+1875301	271341	Enzo Doria	06/2016
1739	2^901146+219049	271272	Enzo Doria	02/2024
1740	(8*10^271039-77)/3	271040	Robert Price	04/2023
1741	2^899999+1144031	270927	Norman Luhn	09/2023
1742	2*10^270802-91	270803	Robert Price	02/2023
1743	23*10^270799-7	270801	Robert Price	10/2022
1744	2^899121-115033	270663	Enzo Doria	07/2015
1745	2^898900+883021	270596	Enzo Doria	12/2016
1746	2^898762-251511	270555	Enzo Doria	12/2013
1747	2^898589+47	270503	Lelio R Paula	03/2016
1748	(939628*10^270345-93962791)/9	270351	Danilo Nitsche	03/2026
1749	1447184*10^270344-14471839	270351	Danilo Nitsche	03/2026
1750	269048*10^270344-2690479	270350	Danilo Nitsche	02/2026

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302984 PRPs in the top)