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) !!!

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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 (> 30000)	Who ?	When ?
1501	2^475160-2797859	143038	Enzo Doria	04/2016
1502	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1503	2^475027-461437	142998	Enzo Doria	07/2015
1504	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1505	(8*10^142932+43)/3	142933	Robert Price	06/2018
1506	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1507	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1508	2^474417-59923	142814	Enzo Doria	10/2015
1509	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1510	2^474053+2897	142705	Lelio R Paula	08/2012
1511	(10^142699+359)/9	142699	Serge Batalov	12/2014
1512	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1513	2^473740-1856639	142610	Enzo Doria	09/2015
1514	2^473617-114223	142573	Enzo Doria	12/2014
1515	2^473257+1873217	142465	Enzo Doria	06/2016
1516	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1517	(10^142425+359)/9	142425	Serge Batalov	12/2014
1518	2^473101+773027	142418	Enzo Doria	05/2016
1519	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1520	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1521	2^472634-109511	142278	Enzo Doria	04/2014
1522	(48^84589+1)/49	142213	Robert Price	01/2014
1523	2^472258+7	142164	Lelio R Paula	08/2015
1524	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1525	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1526	2^471792+1880881	142024	Enzo Doria	11/2016
1527	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1528	(4*10^141926-79)/3	141927	Robert Price	02/2018
1529	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1530	4*5^202913-9	141831	Lelio R Paula	04/2015
1531	2*7^167812-3	141818	Lelio R Paula	12/2014
1532	2^471043+35	141799	Robert Price	11/2015
1533	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1534	2^470692+76771	141693	Enzo Doria	05/2016
1535	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1536	2^470305-459373	141576	Enzo Doria	05/2015
1537	2^470183+72623	141540	Enzo Doria	04/2016
1538	2^470173-16465	141537	Enzo Doria	04/2013
1539	2^469974-1841	141477	Enzo Doria	05/2014
1540	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1541	2*10^141448+63	141449	Robert Price	05/2018
1542	2^469824+43	141432	Lelio R Paula	09/2017
1543	2*10^141407-27	141408	Robert Price	05/2018
1544	2^469630-59711	141373	Enzo Doria	10/2015
1545	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1546	197^61601+2	141342	Lelio R Paula	08/2017
1547	2^469372-112949	141296	Enzo Doria	07/2014
1549	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1548	143^65536+106^65536	141253	Serge Batalov	03/2018
1550	2^469198+782569	141243	Enzo Doria	10/2016
1551	2^469076-2786939	141206	Enzo Doria	11/2015
1552	2^468804+1874941	141125	Enzo Doria	06/2016
1553	2^468787+81353	141119	Enzo Doria	08/2016
1554	2^468595-350407	141062	Enzo Doria	06/2015
1555	2^468564+87855	141052	Lelio R Paula	01/2016
1556	2^468551-21987	141048	Enzo Doria	07/2013
1557	2^468523-7	141040	Lelio R Paula	08/2015
1558	2^468405+87855	141004	Lelio R Paula	01/2016
1559	2^467978-113051	140876	Enzo Doria	07/2014
1560	2^467780-344429	140816	Enzo Doria	07/2015
1561	2^467605-1855603	140764	Enzo Doria	09/2015
1562	5*10^140744-7	140745	Robert Price	09/2015
1563	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1564	2^467401-1850023	140702	Enzo Doria	08/2015
1565	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1566	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1567	2^467166-1854941	140631	Enzo Doria	09/2015
1568	2^466866-1840571	140541	Enzo Doria	06/2015
1569	2^466829-459523	140530	Enzo Doria	05/2015
1570	2^466692-113213	140489	Enzo Doria	07/2014
1571	153^64265-2	140400	Lelio R Paula	11/2017
1572	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1573	2^466181-112735	140335	Enzo Doria	07/2014
1574	(5*10^140281-119)/3	140282	Robert Price	03/2018
1575	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1576	2^465803-114817	140221	Enzo Doria	05/2015
1577	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1578	2^465503-112735	140131	Enzo Doria	07/2014
1579	6^179964+179964^6-1	140040	Robert Price	04/2014
1580	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1581	2^465072-344789	140001	Enzo Doria	07/2015
1582	2^464864-17	139939	Lelio R Paula	09/2017
1583	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1584	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1585	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1586	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
1587	2^463633-2788423	139568	Enzo Doria	11/2015
1588	2^463271-109501	139459	Enzo Doria	04/2014
1589	(5*10^139457+79)/3	139458	Robert Price	03/2018
1590	2^463237-99	139449	Lelio R Paula	09/2017
1591	(7*10^139417-547)/9	139417	Robert Price	01/2018
1592	(10^139398+191)/3	139398	Robert Price	02/2018
1593	2^463019+79463	139383	Enzo Doria	06/2016
1594	3^292129-112756	139381	Enzo Doria	07/2014
1595	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1596	2^462855-1865707	139334	Enzo Doria	02/2016
1597	2^462786-292043	139313	Enzo Doria	08/2015
1598	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1599	2^462238-935	139148	Yves Minet	02/2014
1600	2^461228+1870441	138844	Enzo Doria	05/2016
1601	2^461204-113675	138837	Enzo Doria	08/2014
1602	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1603	(17*10^138812-521)/9	138813	Robert Price	04/2018
1604	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1605	2^460567-113541	138645	Enzo Doria	08/2014
1606	7*10^138604+3	138605	Robert Price	08/2015
1607	2^460330+69	138574	Lelio R Paula	09/2017
1608	2^460078-69581	138498	Enzo Doria	12/2015
1609	2^459768+1531	138404	Lelio R Paula	06/2012
1610	2^459343-113611	138277	Enzo Doria	08/2014
1611	2^459199+1874393	138233	Enzo Doria	06/2016
1612	2^459063-345307	138192	Enzo Doria	06/2015
1613	2*10^138162-43	138163	Robert Price	04/2018
1614	2^458927-112747	138151	Enzo Doria	06/2014
1615	2^458927-69217	138151	Enzo Doria	11/2015
1616	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1617	2^458465+2^32+1	138012	T. D. Noe	06/2007
1618	2^458321-113053	137969	Enzo Doria	07/2014
1619	2^458298+79459	137962	Enzo Doria	06/2016
1620	2^458248-21815	137947	Enzo Doria	07/2013
1621	2^458194+1876549	137931	Enzo Doria	07/2016
1622	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1623	2^457937+57	137853	Lelio R Paula	09/2017
1624	(8*10^137845+13)/3	137846	Robert Price	06/2018
1625	2^457822+105	137819	Donovan Johnson	06/2006
1626	2^457754-113711	137798	Enzo Doria	09/2014
1627	11^132315-360	137792	Enzo Doria	09/2012
1628	2^457347-37	137676	Lelio R Paula	09/2017
1629	2^457322-2786393	137668	Enzo Doria	10/2015
1630	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
1631	2^457240-59939	137643	Enzo Doria	10/2015
1632	2^457120-21575	137607	Enzo Doria	07/2013
1633	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1634	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1635	2^456796-113513	137510	Enzo Doria	08/2014
1636	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1637	2^456503-114361	137422	Enzo Doria	01/2015
1638	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1639	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1640	2^455922+76249	137247	Enzo Doria	05/2016
1641	14^119741-119741^14	137239	Serge Batalov	04/2016
1642	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1644	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1643	124^65536+57^65536	137195	Serge Batalov	03/2018
1645	2^455689+72677	137177	Enzo Doria	04/2016
1646	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1647	(37^87421-1)/36	137093	Robert Price	03/2012
1648	2^455323-57	137066	Lelio R Paula	09/2017
1649	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1650	2^455025-112723	136977	Enzo Doria	06/2014
1651	2^454675-1777	136871	Yves Minet	10/2011
1652	3*10^136829+29	136830	Robert Price	05/2018
1653	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1654	2^454348-53	136773	Lelio R Paula	09/2017
1655	31^91680-2	136729	Lelio R Paula	05/2017
1656	2^454199-113697	136728	Enzo Doria	09/2014
1657	2^453935-2791357	136649	Enzo Doria	01/2016
1658	2^453906-69131	136640	Enzo Doria	11/2015
1659	2^453791+1873913	136605	Enzo Doria	06/2016
1660	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1661	2^453503-2788297	136519	Enzo Doria	11/2015
1662	2^453267-113827	136447	Enzo Doria	09/2014
1663	2^453102+1877629	136398	Enzo Doria	08/2016
1664	L(651821)	136223	Henri Lifchitz	09/2008
1665	2^452460+77701	136205	Enzo Doria	05/2016
1666	2^452440-114755	136199	Enzo Doria	04/2015
1667	2*10^136057-43	136058	Robert Price	04/2018
1668	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1669	2^451947-22165	136050	Enzo Doria	07/2013
1670	2^451787-21805	136002	Enzo Doria	07/2013
1671	2^451734-112817	135986	Enzo Doria	06/2014
1672	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1673	2^451705-21879	135977	Enzo Doria	07/2013
1674	2^451560-112349	135934	Enzo Doria	06/2014
1675	2^451530+45	135925	Lelio R Paula	08/2017
1676	2^451450-21743	135900	Enzo Doria	07/2013
1677	2^450805+65	135706	Lelio R Paula	08/2017
1678	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1679	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1680	2^449944-113247	135447	Enzo Doria	07/2014
1681	2^449770-113247	135395	Enzo Doria	07/2014
1682	2^449637-21471	135355	Enzo Doria	07/2013
1683	2^449571-75	135335	Lelio R Paula	08/2017
1684	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1685	(13*10^135279+437)/9	135280	Robert Price	04/2018
1686	2^449330-35	135262	Lelio R Paula	08/2017
1687	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1688	2^449049-115309	135178	Enzo Doria	07/2015
1689	(10^135174+191)/3	135174	Robert Price	02/2018
1690	2^449030-15	135172	Lelio R Paula	08/2017
1691	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1692	2^448762-351401	135091	Enzo Doria	07/2015
1693	2*10^135083-43	135084	Robert Price	04/2018
1694	(10^135011+719)/9	135011	Serge Batalov	12/2014
1695	2^448386-2786261	134978	Enzo Doria	03/2016
1696	2^448113-113949	134896	Enzo Doria	11/2014
1697	2^447888-2786639	134828	Enzo Doria	03/2016
1698	2^447870-396765	134823	Enzo Doria	07/2013
1699	2^447766-21791	134791	Enzo Doria	07/2013
1700	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1701	2^447552-1019	134727	Yves Minet	02/2014
1702	(2*10^134720-41)/3	134720	Robert Price	02/2018
1703	2^447437-113569	134692	Enzo Doria	08/2014
1704	2^447426-65	134689	Lelio R Paula	08/2017
1705	2^447357-2797573	134668	Enzo Doria	04/2016
1706	2^447278+93	134645	Lelio R Paula	08/2017
1707	2^447094-113193	134589	Enzo Doria	07/2014
1708	3^282041-9934	134568	Enzo Doria	05/2014
1709	2^447019-109039	134567	Enzo Doria	04/2014
1710	2^446990-22041	134558	Enzo Doria	07/2013
1711	123^64370+122	134528	Karsten Bonath	04/2018
1712	2^446782-39701	134495	Enzo Doria	09/2015
1713	2^446494-16485	134409	Enzo Doria	04/2013
1714	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1715	2^446441+65	134393	Lelio R Paula	08/2017
1716	(10^134385+719)/9	134385	Serge Batalov	12/2014
1717	(2*10^134364+529)/9	134364	Robert Price	01/2018
1718	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
1719	(2^446022-7)/339	134264	Lelio R Paula	07/2015
1720	63^74568+2	134174	Lelio R Paula	06/2017
1721	2^445671-22071	134161	Enzo Doria	07/2013
1722	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
1723	2^445515-113859	134114	Enzo Doria	10/2014
1724	2^445328-216917	134058	Enzo Doria	05/2014
1725	2^445202+1874899	134020	Enzo Doria	06/2016
1726	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
1727	2*10^133955+51	133956	Robert Price	05/2018
1728	2^444964-113639	133948	Enzo Doria	08/2014
1729	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
1730	2^444784-113859	133894	Enzo Doria	10/2014
1731	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
1732	62^74521-61^74521	133571	Robert Price	05/2013
1733	2^443198-1867301	133416	Enzo Doria	03/2016
1734	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
1735	2^442799+1874633	133296	Enzo Doria	06/2016
1736	L(637751)	133283	Henri Lifchitz	09/2008
1737	109^65410-2	133269	Lelio R Paula	10/2017
1738	2^442688-113489	133263	Enzo Doria	08/2014
1739	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
1740	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
1741	2^442437-1849993	133187	Enzo Doria	08/2015
1742	2^442430-2791721	133185	Enzo Doria	03/2016
1743	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
1744	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
1745	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
1746	2^441781-2787883	132990	Enzo Doria	03/2016
1747	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
1748	2^441618+37	132941	Lelio R Paula	08/2017
1749	2^441521-113575	132912	Enzo Doria	08/2014
1750	2^441396-65	132874	Lelio R Paula	08/2017

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