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	2^933082+1877059	280886	Enzo Doria	08/2016
1502	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1503	2^932443+225893	280694	Enzo Doria	08/2024
1504	2^932064+26521	280580	Enzo Doria	12/2023
1505	2^931976+25	280553	Stefano Morozzi	05/2021
1506	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1507	(10^279978+11)/3	279978	Serge Batalov	07/2015
1508	2^929524-1864829	279815	Enzo Doria	01/2016
1509	2^929329+22697	279756	Enzo Doria	09/2023
1510	2^929152+60181	279703	Enzo Doria	02/2016
1511	2^928621-2787883	279543	Enzo Doria	11/2015
1512	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1513	3*10^279271+77	279272	Robert Price	06/2024
1514	2^927429+1882277	279184	Enzo Doria	12/2016
1515	2^926766-11	278985	Stefano Morozzi	07/2022
1516	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1517	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1518	(166*10^278633-7)/3	278635	Robert Price	02/2023
1519	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1520	2^925330-1301	278553	Yves Minet	06/2015
1521	(299*10^278546+1)/3	278548	Robert Price	01/2023
1522	2^925299+216053	278543	Enzo Doria	11/2023
1524	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1523	(79^146749-1)/6395645198026062186	278457	Paul Vanderveen	06/2025
1525	(266*10^278325+1)/3	278327	Robert Price	01/2023
1526	2^923261-69175	277930	Enzo Doria	11/2015
1527	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1528	2^922301+57	277641	Stefano Morozzi	05/2021
1529	7*10^277478-39	277479	Robert Price	07/2023
1530	((((((((((((((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
1531	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1532	2^920318+2792299	277044	Enzo Doria	02/2016
1533	(16*10^276537-31)/3	276538	Robert Price	03/2023
1534	2^918596-2786939	276525	Enzo Doria	11/2015
1535	2^917910+28369	276319	Enzo Doria	01/2024
1536	2^917328+228571	276144	Enzo Doria	11/2024
1537	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1538	2^916639+60563	275936	Enzo Doria	04/2016
1539	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1540	2^916385-2786383	275860	Enzo Doria	11/2015
1541	2^915928+82081	275722	Enzo Doria	09/2016
1542	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1543	2^915576-114137	275616	Enzo Doria	01/2015
1544	2^914828+1876741	275391	Enzo Doria	07/2016
1545	2^914757-2203	275370	Yves Minet	12/2015
1546	7*10^275157-27	275158	Robert Price	11/2022
1547	2^912744+20011	274764	Enzo Doria	06/2023
1548	2^911900+1871245	274510	Enzo Doria	05/2016
1549	(16*10^274251-91)/3	274252	Robert Price	11/2022
1550	2^910999+9	274239	Stefano Morozzi	05/2021
1551	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
1552	2^910490+283429	274085	Enzo Doria	01/2017
1553	7*10^273983+39	273984	Robert Price	01/2023
1554	2^909988-1862249	273934	Enzo Doria	12/2015
1555	2^909901+378567	273908	Boyan Hu	08/2024
1556	2^909297+1879157	273726	Enzo Doria	08/2016
1557	2^909257-1864423	273714	Enzo Doria	01/2016
1558	2^909254+31309	273713	Enzo Doria	03/2024
1559	2^908739-7	273558	Stefano Morozzi	07/2022
1560	2^908579-1861747	273510	Enzo Doria	12/2015
1561	3*2^908005-5	273338	Jon Grantham	07/2023
1562	2^907635-2791597	273226	Enzo Doria	01/2016
1563	2^907059+211193	273052	Enzo Doria	08/2023
1564	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1565	2^906594-113201	272912	Enzo Doria	08/2014
1566	9*10^272800+91	272801	Robert Price	05/2023
1567	2*10^272710-49	272711	Robert Price	05/2023
1568	2*10^272403-91	272404	Robert Price	02/2023
1569	2^904773+1872167	272364	Enzo Doria	06/2016
1570	6^349903+5	272278	Paul Bourdelais	02/2021
1571	2^904149-1862473	272176	Enzo Doria	12/2015
1572	2^902926+227839	271808	Enzo Doria	10/2024
1573	(7*10^271757-61)/9	271757	Erik Branger	03/2012
1574	2^902497+1880117	271679	Enzo Doria	09/2016
1575	2^901858+77689	271487	Enzo Doria	06/2016
1576	2^901372+1875301	271341	Enzo Doria	06/2016
1577	2^901146+219049	271272	Enzo Doria	02/2024
1578	(8*10^271039-77)/3	271040	Robert Price	04/2023
1579	2^899999+1144031	270927	Norman Luhn	09/2023
1580	2*10^270802-91	270803	Robert Price	02/2023
1581	23*10^270799-7	270801	Robert Price	10/2022
1582	2^899121-115033	270663	Enzo Doria	07/2015
1583	2^898900+883021	270596	Enzo Doria	12/2016
1584	2^898762-251511	270555	Enzo Doria	12/2013
1585	2^898589+47	270503	Lelio R Paula	03/2016
1586	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1587	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1588	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1589	2^897867-3217	270285	Yves Minet	12/2016
1590	2^897849-115273	270280	Enzo Doria	07/2015
1591	2^897367+26289	270135	Enzo Doria	03/2024
1592	2^896616-114179	269909	Enzo Doria	12/2014
1593	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1594	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1595	(22*10^269517-19)/3	269518	Robert Price	07/2023
1596	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1597	2^894928+583561	269401	Enzo Doria	04/2017
1598	2^894673-39343	269324	Enzo Doria	08/2015
1599	2^893836+23221	269072	Enzo Doria	10/2023
1600	2^892718+29539	268735	Enzo Doria	03/2024
1601	2^892660+213901	268718	Enzo Doria	10/2023
1602	F(1285607)	268676	Henri Lifchitz	11/2008
1603	2^892234+22189	268590	Enzo Doria	09/2023
1604	2^892151+24863	268565	Enzo Doria	11/2023
1605	2^892112+187663	268553	Enzo Doria	08/2016
1606	(266*10^268407-17)/3	268409	Robert Price	02/2023
1607	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1608	2^890957-69583	268205	Enzo Doria	12/2015
1609	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1610	2^890122-351401	267954	Enzo Doria	07/2015
1611	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1612	2^888852+229051	267572	Enzo Doria	11/2024
1613	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1614	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1615	(485^99523-1)/484	267291	Michael Stocker	05/2020
1616	2^886324+77791	266811	Enzo Doria	06/2016
1617	7*10^266731+87	266732	Robert Price	11/2022
1618	2^886040+213901	266725	Enzo Doria	10/2023
1619	2^885242+217909	266485	Enzo Doria	01/2024
1620	2^884738+26809	266333	Enzo Doria	12/2023
1621	2^884714+1880527	266326	Enzo Doria	10/2016
1622	7*10^266024-47	266025	Robert Price	08/2023
1623	11^255426+255426^11	265999	Serge Batalov	05/2014
1624	2^883462-343421	265949	Enzo Doria	07/2015
1625	2^883442+1875019	265943	Enzo Doria	06/2016
1626	2^883333-291583	265910	Enzo Doria	07/2015
1627	2^883132+30421	265850	Enzo Doria	03/2024
1628	10^265566+3593037	265567	Paul Bourdelais	08/2023
1629	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1630	(16*10^265052-91)/3	265053	Robert Price	11/2022
1631	2^880411+1882673	265031	Enzo Doria	12/2016
1632	2^880101+228917	264937	Enzo Doria	11/2024
1633	(14*10^264791-11)/3	264792	Robert Price	08/2022
1634	2^879530-2788031	264765	Enzo Doria	12/2015
1635	2^879292+25171	264694	Enzo Doria	11/2023
1636	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1637	2^878118+2793079	264340	Enzo Doria	02/2016
1638	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1639	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1640	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1641	(19*10^263971+131)/3	263972	Robert Price	08/2023
1642	2^876202-17	263764	Stefano Morozzi	07/2022
1643	(14*10^263720-11)/3	263721	Robert Price	08/2022
1644	2^875748-461129	263627	Enzo Doria	07/2015
1645	2^875518-15	263558	Stefano Morozzi	07/2022
1646	(29*10^263523-17)/3	263524	Robert Price	01/2023
1647	2^875181-2789923	263456	Enzo Doria	12/2015
1648	2^875101-350083	263432	Enzo Doria	08/2015
1649	2^874684+1883587	263307	Enzo Doria	01/2017
1650	2^874616+1872211	263286	Enzo Doria	05/2016
1651	2^874566+30049	263271	Enzo Doria	03/2024
1652	3^551491+16	263129	Robert Price	04/2020
1653	2^874073+2792957	263123	Enzo Doria	02/2016
1654	(7*10^263006-19)/3	263007	Robert Price	10/2023
1655	2^873628+1878751	262989	Enzo Doria	08/2016
1656	2^873497+20837	262949	Enzo Doria	08/2023
1657	2^873288-269	262886	Yves Minet	01/2015
1658	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1659	(28*10^262655-43)/3	262656	Robert Price	04/2023
1660	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1661	2^871991-4207	262496	Yves Minet	03/2021
1662	(23*10^262324+7)/3	262325	Robert Price	05/2023
1663	2^871146-3173	262242	Yves Minet	07/2016
1664	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1665	2^869601-163	261776	Yves Minet	01/2015
1666	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1667	2^869326+282859	261694	Enzo Doria	11/2016
1668	2^869035-114181	261606	Enzo Doria	12/2014
1669	2^868817+26777	261540	Enzo Doria	12/2023
1670	3^547850+9000004	261391	Enzo Doria	10/2023
1671	4*10^261248+91	261249	Robert Price	11/2022
1672	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1673	2^866908+34891	260966	Enzo Doria	07/2024
1674	2^865715+80303	260607	Enzo Doria	07/2016
1675	2^865474+23209	260534	Enzo Doria	10/2023
1676	2^865238+214759	260463	Enzo Doria	11/2023
1677	2^865048+1882411	260406	Enzo Doria	12/2016
1678	2^864899-113871	260361	Enzo Doria	10/2014
1679	(16*10^260256-91)/3	260257	Robert Price	11/2022
1680	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1681	2^864298-2788421	260180	Enzo Doria	12/2015
1682	2^864039-2791357	260102	Enzo Doria	01/2016
1683	2^863621-113833	259976	Enzo Doria	10/2014
1684	10^259945-11	259945	Mischa Rodermond	04/2023
1685	2^863433+34877	259920	Enzo Doria	07/2024
1686	(28*10^259897+113)/3	259898	Robert Price	06/2023
1687	2^862837+75767	259740	Enzo Doria	05/2016
1688	2^862637-31	259680	Jorge Menendez	05/2019
1689	2^862088+1874941	259515	Enzo Doria	06/2016
1690	2^861987-134557	259484	Hans Havermann	10/2018
1691	(14*10^259431-143)/3	259432	Robert Price	05/2023
1692	2^861516-1854029	259343	Enzo Doria	09/2015
1693	2^860975-1853977	259180	Enzo Doria	09/2015
1694	3^543128+16	259138	Robert Price	04/2020
1695	2^860625-1858843	259074	Enzo Doria	10/2015
1696	2^860110+77689	258919	Enzo Doria	05/2016
1697	2^859600+1880371	258766	Enzo Doria	10/2016
1698	2^859433+494711	258716	Makoto Morimoto	10/2013
1700	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1699	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1701	(13*10^258710-43)/3	258711	Robert Price	08/2023
1702	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1703	2^859240+1875271	258658	Enzo Doria	06/2016
1704	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1705	2^858812+30421	258529	Enzo Doria	03/2024
1706	(23*10^258494-47)/3	258495	Robert Price	09/2023
1707	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1708	2^857608+105	258166	Stefano Morozzi	05/2021
1709	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1710	2^857016-633113	257988	Enzo Doria	12/2013
1711	2^855732-113969	257602	Enzo Doria	10/2014
1712	(5*10^257431+91)/3	257432	Robert Price	08/2023
1713	2^853682-3911	256984	Enzo Doria	05/2014
1714	11^246668-90	256879	Enzo Doria	12/2012
1715	2^853181+30287	256834	Enzo Doria	03/2024
1716	5*2^852698+3	256689	Jon Grantham	07/2023
1717	(23*10^256654+7)/3	256655	Robert Price	05/2023
1718	2^851904-113939	256449	Enzo Doria	10/2014
1719	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1720	11^246167-90	256357	Enzo Doria	12/2012
1721	(85*10^256301-1)/3	256303	Robert Price	12/2022
1722	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1723	2^850700-569049	256087	Enzo Doria	11/2013
1724	2^850675+153	256079	Stefano Morozzi	05/2021
1725	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1726	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1727	(14*10^255805-83)/3	255806	Robert Price	11/2022
1728	2^849316+25861	255670	Enzo Doria	12/2023
1729	2^849177-114025	255628	Enzo Doria	12/2014
1730	2*10^255442-21	255443	Robert Price	08/2023
1731	2^848502-3173	255425	Yves Minet	07/2016
1732	2^848178-140291	255328	Enzo Doria	01/2014
1733	7*10^255167+87	255168	Robert Price	11/2022
1734	2^847622-2441	255160	Yves Minet	02/2016
1735	2^847291+182843	255061	Enzo Doria	11/2016
1736	2^847174+1879429	255025	Enzo Doria	09/2016
1737	2^846881+215837	254937	Enzo Doria	12/2023
1738	24*29^174239+13361	254809	Curtis Bright	04/2015
1739	22*10^254639+7	254641	Robert Price	10/2022
1740	2^845633-933075	254561	Paul Bourdelais	11/2021
1741	2^845610-1868591	254554	Enzo Doria	04/2016
1742	2^845484+81931	254517	Enzo Doria	08/2016
1743	2^845402-114761	254492	Enzo Doria	05/2015
1744	98*10^254173-9	254175	Robert Price	05/2023
1745	2^844334-2792441	254170	Enzo Doria	02/2016
1746	2*10^254162+69	254163	Robert Price	08/2023
1747	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1748	11^243796-90	253888	Enzo Doria	12/2012
1749	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1750	30^171733-29^171733	253671	Jean-Louis Charton	10/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301901 PRPs in the top)