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	2^1003046+60529	301947	Enzo Doria	04/2016
1502	83278^4209+4209^83278	301815	Hans Havermann	09/2021
1503	64431^48250+48250^64431	301763	Hans Havermann	09/2021
1504	67237^30714+30714^67237	301716	Hans Havermann	09/2021
1505	2^1002144+235861	301676	Enzo Doria	05/2025
1506	64641^46288+46288^64641	301581	Hans Havermann	09/2021
1507	71513^16482+16482^71513	301572	Hans Havermann	10/2021
1508	72017^15396+15396^72017	301565	Hans Havermann	09/2021
1509	65534^39927+39927^65534	301540	Hans Havermann	10/2021
1510	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
1511	63169^59152+59152^63169	301441	Hans Havermann	09/2021
1512	75055^10348+10348^75055	301336	Hans Havermann	09/2021
1513	2^1000647+1881353	301225	Enzo Doria	11/2016
1514	83686^3961+3961^83686	301086	Hans Havermann	10/2021
1515	68529^24742+24742^68529	301078	Hans Havermann	09/2021
1516	65207^41416+41416^65207	301072	Hans Havermann	10/2021
1518	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
1517	2^999999+77151	301030	Norman Luhn	09/2023
1519	90762^2071+2071^90762	300984	Hans Havermann	06/2021
1520	63909^51142+51142^63909	300934	Hans Havermann	08/2021
1521	2^999646+1874029	300924	Enzo Doria	06/2016
1522	66280^34607+34607^66280	300856	Hans Havermann	06/2021
1523	65534^38925+38925^65534	300817	Hans Havermann	07/2021
1524	63296^56517+56517^63296	300794	Hans Havermann	06/2021
1525	110610^523+523^110610	300694	Hans Havermann	06/2021
1526	66428^33609+33609^66428	300684	Hans Havermann	06/2021
1527	74247^11210+11210^74247	300672	Hans Havermann	06/2021
1528	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
1529	10^300476+3	300477	Ed Trice	10/2012
1530	10^300476-530913	300476	Patrick De Geest	03/2016
1531	66703^31960+31960^66703	300471	Hans Havermann	06/2021
1532	63722^51915+51915^63722	300468	Hans Havermann	06/2021
1533	2^998053+1879667	300444	Enzo Doria	09/2016
1534	77018^7959+7959^77018	300437	Hans Havermann	07/2021
1535	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
1536	2^997689+217787	300335	Enzo Doria	01/2024
1537	69478^20987+20987^69478	300281	Hans Havermann	07/2021
1538	64088^48393+48393^64088	300239	Hans Havermann	07/2021
1539	2^997369+237917	300238	Enzo Doria	06/2025
1540	64605^44146+44146^64605	300084	Hans Havermann	08/2021
1541	2^996845+29027	300081	Enzo Doria	02/2024
1542	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
1543	67594^27465+27465^67594	300035	Hans Havermann	06/2021
1544	10^300000+287389	300001	Patrick De Geest	10/2019
1545	10^300000-83657	300000	Patrick De Geest	10/2019
1546	70599^17756+17756^70599	300000	Hans Havermann	06/2021
1547	numbpart(72526161452)	299999	Serge Batalov	04/2017
1548	2^996182-114431	299881	Enzo Doria	02/2015
1549	3*2^996126+5	299865	Jon Grantham	07/2023
1550	2^996034-17	299837	Stefano Morozzi	07/2022
1551	2^995793+36587	299764	Enzo Doria	09/2024
1552	(19*10^299640+77)/3	299641	Robert Price	03/2023
1553	2^995214-2788361	299590	Enzo Doria	12/2015
1554	2^994791-114319	299462	Enzo Doria	01/2015
1555	2^994490-1863791	299372	Enzo Doria	01/2016
1556	2^993322+1885729	299020	Enzo Doria	03/2017
1557	2^993227+230033	298992	Enzo Doria	12/2024
1558	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
1559	2^992711-2788807	298836	Enzo Doria	12/2015
1560	2^992525-114199	298780	Enzo Doria	12/2014
1561	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
1562	2^992329+1884707	298721	Enzo Doria	02/2017
1563	2^992292+229801	298710	Enzo Doria	12/2024
1564	2^992052+215491	298638	Enzo Doria	11/2023
1565	2^991968-23	298613	Stefano Morozzi	07/2022
1566	2^991715-19	298536	Stefano Morozzi	07/2022
1567	2^991387+237383	298438	Enzo Doria	06/2025
1568	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
1569	2^989562+25	297888	Stefano Morozzi	05/2021
1570	2^988580+214051	297593	Enzo Doria	10/2023
1571	2^988537+218837	297580	Enzo Doria	03/2024
1572	(19*10^297497+77)/3	297498	Robert Price	03/2023
1573	(2*10^297488-23)/3	297488	Robert Price	10/2022
1574	2^988148+48271	297463	Enzo Doria	07/2025
1575	2^987033+46427	297127	Enzo Doria	05/2025
1576	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
1577	2^985217-114553	296580	Enzo Doria	03/2015
1578	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
1579	2^984650+21529	296410	Enzo Doria	08/2023
1580	2^984131-1828009	296253	Enzo Doria	01/2015
1581	2^983620+60451	296100	Phil Moore	03/2008
1582	2^982721-2683	295829	Yves Minet	02/2016
1583	(23*10^295581+7)/3	295582	Robert Price	05/2023
1584	2^981298-2788421	295401	Enzo Doria	12/2015
1585	2^981163-2790967	295360	Enzo Doria	12/2015
1586	2^981016-15	295316	Stefano Morozzi	07/2022
1587	8*10^295160-13	295161	Robert Price	08/2023
1588	2^979594+1865839	294888	Enzo Doria	02/2016
1589	2^979502+221029	294860	Enzo Doria	03/2024
1590	2*10^294527-91	294528	Robert Price	02/2023
1591	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
1592	10^294475+49	294476	Robert Price	02/2023
1593	2^977896+234601	294377	Enzo Doria	04/2025
1594	(11*10^294308+91)/3	294309	Robert Price	03/2023
1595	2^976760+1885021	294035	Enzo Doria	02/2017
1596	3*2^976518+5	293962	Jon Grantham	07/2023
1597	2^975798+218599	293745	Enzo Doria	01/2024
1598	2^974441+1878407	293336	Enzo Doria	08/2016
1599	2^974180+1876831	293258	Enzo Doria	07/2016
1600	2^974170+453319	293255	Enzo Doria	01/2017
1601	(211^126023-1)/210	292911	Anonymous	05/2024
1602	2^972744-114419	292826	Enzo Doria	03/2015
1603	11^281143+6	292781	Paul Bourdelais	03/2021
1604	(4*10^292619-91)/3	292620	Robert Price	12/2022
1605	E(69468)/13247122135	292549	Sergey Batalov	10/2023
1606	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
1607	3*10^292344-97	292345	Robert Price	01/2023
1608	2^970911+1873373	292274	Enzo Doria	07/2016
1609	2^970670+383059	292201	Enzo Doria	12/2016
1610	2^970141-100363	292042	Enzo Doria	02/2014
1611	2^969945+1874717	291983	Enzo Doria	06/2016
1612	2^969384+1880701	291814	Enzo Doria	10/2016
1613	(13*10^291721-43)/3	291722	Robert Price	08/2023
1614	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1615	10^(2145126+1)-210^145126-1	290253	Robert Price	03/2025
1616	3*2^963892+5	290161	Jon Grantham	07/2023
1617	(151*10^289877-1)/3	289879	Robert Price	07/2023
1618	2^962194+60139	289650	Enzo Doria	02/2016
1619	2^961409+44267	289413	Enzo Doria	04/2025
1620	2^959307-1861507	288781	Enzo Doria	11/2015
1621	(17*10^288692+31)/3	288693	Robert Price	04/2023
1622	14^251797-3	288592	Paul Bourdelais	12/2020
1623	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1624	(2*10^288371-23)/3	288371	Robert Price	10/2022
1625	(31*10^288238-1)/3	288240	Robert Price	02/2023
1626	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
1627	2^957372+283531	288198	Enzo Doria	02/2017
1628	2^957192-1864049	288144	Enzo Doria	01/2016
1629	(95774^58081-1)/(95774^241-1)	288116	Ryan Propper	11/2023
1630	2^956446+1875199	287919	Enzo Doria	06/2016
1631	2^956283+219143	287870	Enzo Doria	02/2024
1632	7*10^287854+39	287855	Robert Price	01/2023
1633	2^956082+28309	287810	Enzo Doria	02/2024
1634	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
1635	2^955178+1883587	287538	Enzo Doria	12/2016
1636	2^954127-954127^2	287221	Henri Lifchitz	01/2021
1637	2^954001+1875257	287183	Enzo Doria	07/2016
1638	2*10^287175-49	287176	Robert Price	05/2023
1639	(22*10^287085-19)/3	287086	Robert Price	07/2023
1640	2^953667+38573	287083	Enzo Doria	11/2024
1641	2^953488+22411	287029	Enzo Doria	09/2023
1642	(23891^65536+1)/2	286932	Serge Batalov	03/2018
1643	5*3^601336-2^601336	286911	Jon Grantham	08/2023
1644	2^952268+1878601	286662	Enzo Doria	09/2016
1645	2^950801+81557	286220	Enzo Doria	08/2016
1646	2^949403+217523	285799	Enzo Doria	01/2024
1647	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
1648	(19*10^285615+53)/9	285616	Rytis Slatkevicius	12/2024
1649	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
1650	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
1651	2^948510+782569	285530	Enzo Doria	10/2016
1652	2^948374-114137	285490	Enzo Doria	01/2015
1653	2^947739+1872923	285298	Enzo Doria	06/2016
1654	2^946274+218407	284857	Enzo Doria	03/2024
1655	7*10^284751+9	284752	Robert Price	04/2023
1656	2^944561-21	284342	Stefano Morozzi	07/2022
1657	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
1658	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
1659	2^942533+82067	283731	Enzo Doria	09/2016
1660	2^941469+39	283411	Jon Grantham	08/2023
1661	(10^283342-31)/3	283342	Robert Price	03/2023
1662	2^940950+1874989	283255	Enzo Doria	06/2016
1663	2^940426-2786141	283097	Enzo Doria	11/2015
1664	2^940155+226973	283015	Enzo Doria	09/2024
1665	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
1666	2^939881-114115	282933	Enzo Doria	12/2014
1667	(14*10^282673-143)/3	282674	Robert Price	05/2023
1668	10^282493+632551	282494	Patrick De Geest	02/2017
1670	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
1669	10^282493-132327	282493	Patrick De Geest	02/2017
1671	3^591827-2^591827	282374	Mike Oakes	08/2009
1672	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
1673	2^936716-1835519	281980	Enzo Doria	04/2015
1674	2^936588+79411	281942	Enzo Doria	06/2016
1675	2^936047+1877423	281779	Enzo Doria	08/2016
1676	2^935713+1869377	281678	Enzo Doria	05/2016
1677	2^933082+1877059	280886	Enzo Doria	08/2016
1678	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1679	2^932443+225893	280694	Enzo Doria	08/2024
1680	2^932064+26521	280580	Enzo Doria	12/2023
1681	2^931976+25	280553	Stefano Morozzi	05/2021
1682	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1683	(10^279978+11)/3	279978	Serge Batalov	07/2015
1684	2^929524-1864829	279815	Enzo Doria	01/2016
1685	2^929329+22697	279756	Enzo Doria	09/2023
1686	2^929152+60181	279703	Enzo Doria	02/2016
1687	2^928621-2787883	279543	Enzo Doria	11/2015
1688	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1689	3*10^279271+77	279272	Robert Price	06/2024
1690	2^927429+1882277	279184	Enzo Doria	12/2016
1691	2^926766-11	278985	Stefano Morozzi	07/2022
1692	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1693	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1694	(5347*26^197061-297)/25	278839	Eric Chen	12/2025
1695	(166*10^278633-7)/3	278635	Robert Price	02/2023
1696	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1697	2^925330-1301	278553	Yves Minet	06/2015
1698	(299*10^278546+1)/3	278548	Robert Price	01/2023
1699	2^925299+216053	278543	Enzo Doria	11/2023
1701	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1700	(79^146749-1)/6395645198026062186	278457	Paul Vanderveen	06/2025
1702	(266*10^278325+1)/3	278327	Robert Price	01/2023
1703	2^923261-69175	277930	Enzo Doria	11/2015
1704	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1705	2^922301+57	277641	Stefano Morozzi	05/2021
1706	7*10^277478-39	277479	Robert Price	07/2023
1707	((((((((((((((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
1708	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1709	2^920318+2792299	277044	Enzo Doria	02/2016
1710	(16*10^276537-31)/3	276538	Robert Price	03/2023
1711	2^918596-2786939	276525	Enzo Doria	11/2015
1712	2^917910+28369	276319	Enzo Doria	01/2024
1713	2^917328+228571	276144	Enzo Doria	11/2024
1714	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1715	2^916639+60563	275936	Enzo Doria	04/2016
1716	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1717	2^916385-2786383	275860	Enzo Doria	11/2015
1718	2^915928+82081	275722	Enzo Doria	09/2016
1719	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1720	2^915576-114137	275616	Enzo Doria	01/2015
1721	2^914828+1876741	275391	Enzo Doria	07/2016
1722	2^914757-2203	275370	Yves Minet	12/2015
1723	7*10^275157-27	275158	Robert Price	11/2022
1724	2^912744+20011	274764	Enzo Doria	06/2023
1725	2^911900+1871245	274510	Enzo Doria	05/2016
1726	(16*10^274251-91)/3	274252	Robert Price	11/2022
1727	2^910999+9	274239	Stefano Morozzi	05/2021
1728	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
1729	2^910490+283429	274085	Enzo Doria	01/2017
1730	7*10^273983+39	273984	Robert Price	01/2023
1731	2^909988-1862249	273934	Enzo Doria	12/2015
1732	2^909901+378567	273908	Boyan Hu	08/2024
1733	2^909297+1879157	273726	Enzo Doria	08/2016
1734	2^909257-1864423	273714	Enzo Doria	01/2016
1735	2^909254+31309	273713	Enzo Doria	03/2024
1736	2^908739-7	273558	Stefano Morozzi	07/2022
1737	2^908579-1861747	273510	Enzo Doria	12/2015
1738	3*2^908005-5	273338	Jon Grantham	07/2023
1739	2^907635-2791597	273226	Enzo Doria	01/2016
1740	2^907059+211193	273052	Enzo Doria	08/2023
1741	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1742	2^906594-113201	272912	Enzo Doria	08/2014
1743	9*10^272800+91	272801	Robert Price	05/2023
1744	2*10^272710-49	272711	Robert Price	05/2023
1745	2*10^272403-91	272404	Robert Price	02/2023
1746	2^904773+1872167	272364	Enzo Doria	06/2016
1747	6^349903+5	272278	Paul Bourdelais	02/2021
1748	2^904149-1862473	272176	Enzo Doria	12/2015
1749	2^902926+227839	271808	Enzo Doria	10/2024
1750	(7*10^271757-61)/9	271757	Erik Branger	03/2012

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303025 PRPs in the top)