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	2^970670+383059	292201	Enzo Doria	12/2016
1502	2^970141-100363	292042	Enzo Doria	02/2014
1503	2^969945+1874717	291983	Enzo Doria	06/2016
1504	2^969384+1880701	291814	Enzo Doria	10/2016
1505	(13*10^291721-43)/3	291722	Robert Price	08/2023
1506	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1507	10^(2145126+1)-210^145126-1	290253	Robert Price	03/2025
1508	3*2^963892+5	290161	Jon Grantham	07/2023
1509	(151*10^289877-1)/3	289879	Robert Price	07/2023
1510	2^962194+60139	289650	Enzo Doria	02/2016
1511	2^961409+44267	289413	Enzo Doria	04/2025
1512	2^959307-1861507	288781	Enzo Doria	11/2015
1513	(17*10^288692+31)/3	288693	Robert Price	04/2023
1514	14^251797-3	288592	Paul Bourdelais	12/2020
1515	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1516	(2*10^288371-23)/3	288371	Robert Price	10/2022
1517	(31*10^288238-1)/3	288240	Robert Price	02/2023
1518	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
1519	2^957372+283531	288198	Enzo Doria	02/2017
1520	2^957192-1864049	288144	Enzo Doria	01/2016
1521	(95774^58081-1)/(95774^241-1)	288116	Ryan Propper	11/2023
1522	2^956446+1875199	287919	Enzo Doria	06/2016
1523	2^956283+219143	287870	Enzo Doria	02/2024
1524	7*10^287854+39	287855	Robert Price	01/2023
1525	2^956082+28309	287810	Enzo Doria	02/2024
1526	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
1527	2^955178+1883587	287538	Enzo Doria	12/2016
1528	2^954127-954127^2	287221	Henri Lifchitz	01/2021
1529	2^954001+1875257	287183	Enzo Doria	07/2016
1530	2*10^287175-49	287176	Robert Price	05/2023
1531	(22*10^287085-19)/3	287086	Robert Price	07/2023
1532	2^953667+38573	287083	Enzo Doria	11/2024
1533	2^953488+22411	287029	Enzo Doria	09/2023
1534	(23891^65536+1)/2	286932	Serge Batalov	03/2018
1535	5*3^601336-2^601336	286911	Jon Grantham	08/2023
1536	2^952268+1878601	286662	Enzo Doria	09/2016
1537	2^950801+81557	286220	Enzo Doria	08/2016
1538	2^949403+217523	285799	Enzo Doria	01/2024
1539	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
1540	(19*10^285615+53)/9	285616	Rytis Slatkevicius	12/2024
1541	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
1542	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
1543	2^948510+782569	285530	Enzo Doria	10/2016
1544	2^948374-114137	285490	Enzo Doria	01/2015
1545	2^947739+1872923	285298	Enzo Doria	06/2016
1546	2^946274+218407	284857	Enzo Doria	03/2024
1547	7*10^284751+9	284752	Robert Price	04/2023
1548	2^944561-21	284342	Stefano Morozzi	07/2022
1549	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
1550	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
1551	2^942533+82067	283731	Enzo Doria	09/2016
1552	2^941469+39	283411	Jon Grantham	08/2023
1553	(10^283342-31)/3	283342	Robert Price	03/2023
1554	2^940950+1874989	283255	Enzo Doria	06/2016
1555	2^940426-2786141	283097	Enzo Doria	11/2015
1556	2^940155+226973	283015	Enzo Doria	09/2024
1557	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
1558	2^939881-114115	282933	Enzo Doria	12/2014
1559	(14*10^282673-143)/3	282674	Robert Price	05/2023
1560	10^282493+632551	282494	Patrick De Geest	02/2017
1562	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
1561	10^282493-132327	282493	Patrick De Geest	02/2017
1563	3^591827-2^591827	282374	Mike Oakes	08/2009
1564	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
1565	2^936716-1835519	281980	Enzo Doria	04/2015
1566	2^936588+79411	281942	Enzo Doria	06/2016
1567	2^936047+1877423	281779	Enzo Doria	08/2016
1568	2^935713+1869377	281678	Enzo Doria	05/2016
1569	2^933082+1877059	280886	Enzo Doria	08/2016
1570	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1571	2^932443+225893	280694	Enzo Doria	08/2024
1572	2^932064+26521	280580	Enzo Doria	12/2023
1573	2^931976+25	280553	Stefano Morozzi	05/2021
1574	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1575	(10^279978+11)/3	279978	Serge Batalov	07/2015
1576	2^929524-1864829	279815	Enzo Doria	01/2016
1577	2^929329+22697	279756	Enzo Doria	09/2023
1578	2^929152+60181	279703	Enzo Doria	02/2016
1579	2^928621-2787883	279543	Enzo Doria	11/2015
1580	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1581	3*10^279271+77	279272	Robert Price	06/2024
1582	2^927429+1882277	279184	Enzo Doria	12/2016
1583	2^926766-11	278985	Stefano Morozzi	07/2022
1584	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1585	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1586	(166*10^278633-7)/3	278635	Robert Price	02/2023
1587	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1588	2^925330-1301	278553	Yves Minet	06/2015
1589	(299*10^278546+1)/3	278548	Robert Price	01/2023
1590	2^925299+216053	278543	Enzo Doria	11/2023
1592	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1591	(79^146749-1)/6395645198026062186	278457	Paul Vanderveen	06/2025
1593	(266*10^278325+1)/3	278327	Robert Price	01/2023
1594	2^923261-69175	277930	Enzo Doria	11/2015
1595	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1596	2^922301+57	277641	Stefano Morozzi	05/2021
1597	7*10^277478-39	277479	Robert Price	07/2023
1598	((((((((((((((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
1599	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1600	2^920318+2792299	277044	Enzo Doria	02/2016
1601	(16*10^276537-31)/3	276538	Robert Price	03/2023
1602	2^918596-2786939	276525	Enzo Doria	11/2015
1603	2^917910+28369	276319	Enzo Doria	01/2024
1604	2^917328+228571	276144	Enzo Doria	11/2024
1605	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1606	2^916639+60563	275936	Enzo Doria	04/2016
1607	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1608	2^916385-2786383	275860	Enzo Doria	11/2015
1609	2^915928+82081	275722	Enzo Doria	09/2016
1610	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1611	2^915576-114137	275616	Enzo Doria	01/2015
1612	2^914828+1876741	275391	Enzo Doria	07/2016
1613	2^914757-2203	275370	Yves Minet	12/2015
1614	7*10^275157-27	275158	Robert Price	11/2022
1615	2^912744+20011	274764	Enzo Doria	06/2023
1616	2^911900+1871245	274510	Enzo Doria	05/2016
1617	(16*10^274251-91)/3	274252	Robert Price	11/2022
1618	2^910999+9	274239	Stefano Morozzi	05/2021
1619	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
1620	2^910490+283429	274085	Enzo Doria	01/2017
1621	7*10^273983+39	273984	Robert Price	01/2023
1622	2^909988-1862249	273934	Enzo Doria	12/2015
1623	2^909901+378567	273908	Boyan Hu	08/2024
1624	2^909297+1879157	273726	Enzo Doria	08/2016
1625	2^909257-1864423	273714	Enzo Doria	01/2016
1626	2^909254+31309	273713	Enzo Doria	03/2024
1627	2^908739-7	273558	Stefano Morozzi	07/2022
1628	2^908579-1861747	273510	Enzo Doria	12/2015
1629	3*2^908005-5	273338	Jon Grantham	07/2023
1630	2^907635-2791597	273226	Enzo Doria	01/2016
1631	2^907059+211193	273052	Enzo Doria	08/2023
1632	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1633	2^906594-113201	272912	Enzo Doria	08/2014
1634	9*10^272800+91	272801	Robert Price	05/2023
1635	2*10^272710-49	272711	Robert Price	05/2023
1636	2*10^272403-91	272404	Robert Price	02/2023
1637	2^904773+1872167	272364	Enzo Doria	06/2016
1638	6^349903+5	272278	Paul Bourdelais	02/2021
1639	2^904149-1862473	272176	Enzo Doria	12/2015
1640	2^902926+227839	271808	Enzo Doria	10/2024
1641	(7*10^271757-61)/9	271757	Erik Branger	03/2012
1642	2^902497+1880117	271679	Enzo Doria	09/2016
1643	2^901858+77689	271487	Enzo Doria	06/2016
1644	2^901372+1875301	271341	Enzo Doria	06/2016
1645	2^901146+219049	271272	Enzo Doria	02/2024
1646	(8*10^271039-77)/3	271040	Robert Price	04/2023
1647	2^899999+1144031	270927	Norman Luhn	09/2023
1648	2*10^270802-91	270803	Robert Price	02/2023
1649	23*10^270799-7	270801	Robert Price	10/2022
1650	2^899121-115033	270663	Enzo Doria	07/2015
1651	2^898900+883021	270596	Enzo Doria	12/2016
1652	2^898762-251511	270555	Enzo Doria	12/2013
1653	2^898589+47	270503	Lelio R Paula	03/2016
1654	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1655	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1656	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1657	2^897867-3217	270285	Yves Minet	12/2016
1658	2^897849-115273	270280	Enzo Doria	07/2015
1659	2^897367+26289	270135	Enzo Doria	03/2024
1660	2^896616-114179	269909	Enzo Doria	12/2014
1661	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1662	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1663	(22*10^269517-19)/3	269518	Robert Price	07/2023
1664	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1665	2^894928+583561	269401	Enzo Doria	04/2017
1666	2^894673-39343	269324	Enzo Doria	08/2015
1667	2^893836+23221	269072	Enzo Doria	10/2023
1668	2^892718+29539	268735	Enzo Doria	03/2024
1669	2^892660+213901	268718	Enzo Doria	10/2023
1670	F(1285607)	268676	Henri Lifchitz	11/2008
1671	2^892234+22189	268590	Enzo Doria	09/2023
1672	2^892151+24863	268565	Enzo Doria	11/2023
1673	2^892112+187663	268553	Enzo Doria	08/2016
1674	(266*10^268407-17)/3	268409	Robert Price	02/2023
1675	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1676	2^890957-69583	268205	Enzo Doria	12/2015
1677	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1678	2^890122-351401	267954	Enzo Doria	07/2015
1679	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1680	2^888852+229051	267572	Enzo Doria	11/2024
1681	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1682	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1683	(485^99523-1)/484	267291	Michael Stocker	05/2020
1684	2^886324+77791	266811	Enzo Doria	06/2016
1685	7*10^266731+87	266732	Robert Price	11/2022
1686	2^886040+213901	266725	Enzo Doria	10/2023
1687	2^885242+217909	266485	Enzo Doria	01/2024
1688	2^884738+26809	266333	Enzo Doria	12/2023
1689	2^884714+1880527	266326	Enzo Doria	10/2016
1690	7*10^266024-47	266025	Robert Price	08/2023
1691	11^255426+255426^11	265999	Serge Batalov	05/2014
1692	2^883462-343421	265949	Enzo Doria	07/2015
1693	2^883442+1875019	265943	Enzo Doria	06/2016
1694	2^883333-291583	265910	Enzo Doria	07/2015
1695	2^883132+30421	265850	Enzo Doria	03/2024
1696	10^265566+3593037	265567	Paul Bourdelais	08/2023
1697	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1698	(16*10^265052-91)/3	265053	Robert Price	11/2022
1699	2^880411+1882673	265031	Enzo Doria	12/2016
1700	2^880101+228917	264937	Enzo Doria	11/2024
1701	(14*10^264791-11)/3	264792	Robert Price	08/2022
1702	2^879530-2788031	264765	Enzo Doria	12/2015
1703	2^879292+25171	264694	Enzo Doria	11/2023
1704	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1705	2^878118+2793079	264340	Enzo Doria	02/2016
1706	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1707	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1708	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1709	(19*10^263971+131)/3	263972	Robert Price	08/2023
1710	2^876202-17	263764	Stefano Morozzi	07/2022
1711	(14*10^263720-11)/3	263721	Robert Price	08/2022
1712	2^875748-461129	263627	Enzo Doria	07/2015
1713	2^875518-15	263558	Stefano Morozzi	07/2022
1714	(29*10^263523-17)/3	263524	Robert Price	01/2023
1715	2^875181-2789923	263456	Enzo Doria	12/2015
1716	2^875101-350083	263432	Enzo Doria	08/2015
1717	2^874684+1883587	263307	Enzo Doria	01/2017
1718	2^874616+1872211	263286	Enzo Doria	05/2016
1719	2^874566+30049	263271	Enzo Doria	03/2024
1720	3^551491+16	263129	Robert Price	04/2020
1721	2^874073+2792957	263123	Enzo Doria	02/2016
1722	(7*10^263006-19)/3	263007	Robert Price	10/2023
1723	2^873628+1878751	262989	Enzo Doria	08/2016
1724	2^873497+20837	262949	Enzo Doria	08/2023
1725	2^873288-269	262886	Yves Minet	01/2015
1726	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1727	(28*10^262655-43)/3	262656	Robert Price	04/2023
1728	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1729	2^871991-4207	262496	Yves Minet	03/2021
1730	(23*10^262324+7)/3	262325	Robert Price	05/2023
1731	2^871146-3173	262242	Yves Minet	07/2016
1732	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1733	2^869601-163	261776	Yves Minet	01/2015
1734	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1735	2^869326+282859	261694	Enzo Doria	11/2016
1736	2^869035-114181	261606	Enzo Doria	12/2014
1737	2^868817+26777	261540	Enzo Doria	12/2023
1738	3^547850+9000004	261391	Enzo Doria	10/2023
1739	Phi(156793,2^7)	261261	Henri Lifchitz	10/2025
1740	4*10^261248+91	261249	Robert Price	11/2022
1741	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1742	2^866908+34891	260966	Enzo Doria	07/2024
1743	2^865715+80303	260607	Enzo Doria	07/2016
1744	2^865474+23209	260534	Enzo Doria	10/2023
1745	2^865238+214759	260463	Enzo Doria	11/2023
1746	2^865048+1882411	260406	Enzo Doria	12/2016
1747	2^864899-113871	260361	Enzo Doria	10/2014
1748	(16*10^260256-91)/3	260257	Robert Price	11/2022
1749	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1750	2^864298-2788421	260180	Enzo Doria	12/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301998 PRPs in the top)