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 (> 30000)	Who ?	When ?
1501	2^452460+77701	136205	Enzo Doria	05/2016
1502	2^452440-114755	136199	Enzo Doria	04/2015
1503	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1504	2^451947-22165	136050	Enzo Doria	07/2013
1505	2^451787-21805	136002	Enzo Doria	07/2013
1506	2^451734-112817	135986	Enzo Doria	06/2014
1507	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1508	2^451705-21879	135977	Enzo Doria	07/2013
1509	2^451560-112349	135934	Enzo Doria	06/2014
1510	2^451530+45	135925	Lelio R Paula	08/2017
1511	2^451450-21743	135900	Enzo Doria	07/2013
1512	2^450805+65	135706	Lelio R Paula	08/2017
1513	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1514	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1515	2^449944-113247	135447	Enzo Doria	07/2014
1516	2^449770-113247	135395	Enzo Doria	07/2014
1517	2^449637-21471	135355	Enzo Doria	07/2013
1518	2^449571-75	135335	Lelio R Paula	08/2017
1519	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1520	2^449330-35	135262	Lelio R Paula	08/2017
1521	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1522	2^449049-115309	135178	Enzo Doria	07/2015
1523	2^449030-15	135172	Lelio R Paula	08/2017
1524	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1525	2^448762-351401	135091	Enzo Doria	07/2015
1526	(10^135011+719)/9	135011	Serge Batalov	12/2014
1527	2^448386-2786261	134978	Enzo Doria	03/2016
1528	2^448113-113949	134896	Enzo Doria	11/2014
1529	2^447888-2786639	134828	Enzo Doria	03/2016
1530	2^447870-396765	134823	Enzo Doria	07/2013
1531	2^447766-21791	134791	Enzo Doria	07/2013
1532	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1533	2^447552-1019	134727	Yves Minet	02/2014
1534	2^447437-113569	134692	Enzo Doria	08/2014
1535	2^447426-65	134689	Lelio R Paula	08/2017
1536	2^447357-2797573	134668	Enzo Doria	04/2016
1537	2^447278+93	134645	Lelio R Paula	08/2017
1538	2^447094-113193	134589	Enzo Doria	07/2014
1539	3^282041-9934	134568	Enzo Doria	05/2014
1540	2^447019-109039	134567	Enzo Doria	04/2014
1541	2^446990-22041	134558	Enzo Doria	07/2013
1542	2^446782-39701	134495	Enzo Doria	09/2015
1543	2^446494-16485	134409	Enzo Doria	04/2013
1544	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1545	2^446441+65	134393	Lelio R Paula	08/2017
1546	(10^134385+719)/9	134385	Serge Batalov	12/2014
1547	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
1548	(2^446022-7)/339	134264	Lelio R Paula	07/2015
1549	63^74568+2	134174	Lelio R Paula	06/2017
1550	2^445671-22071	134161	Enzo Doria	07/2013
1551	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
1552	2^445515-113859	134114	Enzo Doria	10/2014
1553	2^445328-216917	134058	Enzo Doria	05/2014
1554	2^445202+1874899	134020	Enzo Doria	06/2016
1555	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
1556	2^444964-113639	133948	Enzo Doria	08/2014
1557	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
1558	2^444784-113859	133894	Enzo Doria	10/2014
1559	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
1560	62^74521-61^74521	133571	Robert Price	05/2013
1561	2^443198-1867301	133416	Enzo Doria	03/2016
1562	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
1563	2^442799+1874633	133296	Enzo Doria	06/2016
1564	L(637751)	133283	Henri Lifchitz	09/2008
1565	2^442688-113489	133263	Enzo Doria	08/2014
1566	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
1567	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
1568	2^442437-1849993	133187	Enzo Doria	08/2015
1569	2^442430-2791721	133185	Enzo Doria	03/2016
1570	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
1571	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
1572	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
1573	2^441781-2787883	132990	Enzo Doria	03/2016
1574	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
1575	2^441618+37	132941	Lelio R Paula	08/2017
1576	2^441521-113575	132912	Enzo Doria	08/2014
1577	2^441396-65	132874	Lelio R Paula	08/2017
1578	2^441330+1871959	132854	Enzo Doria	05/2016
1579	2^441063+383	132774	Lelio R Paula	06/2012
1580	2^440846+1870909	132708	Enzo Doria	05/2016
1581	2^440656-113489	132651	Enzo Doria	08/2014
1582	numbpart(14180123587)	132646	Serge Batalov	04/2017
1583	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
1584	(38^83891+1)/39	132529	Robert Price	09/2013
1585	2^439931-21	132433	Lelio R Paula	08/2017
1586	47^79201-46^79201	132432	Robert Price	10/2012
1587	2^439897-113653	132423	Enzo Doria	08/2014
1588	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
1589	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
1590	2^439576-113247	132326	Enzo Doria	07/2014
1591	2^439497-29143	132302	Enzo Doria	07/2015
1592	2^439409-114193	132276	Enzo Doria	12/2014
1593	9*10^132148-7	132149	Robert Price	09/2015
1594	2^438845+1870217	132106	Enzo Doria	05/2016
1595	2^438789+87855	132089	Lelio R Paula	01/2016
1596	2^438774-2786411	132085	Enzo Doria	03/2016
1597	2^438755-1848205	132079	Enzo Doria	07/2015
1598	2^438739-112087	132074	Enzo Doria	06/2014
1599	L(631181)	131910	Henri Lifchitz	09/2008
1600	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
1601	2^438079-1863877	131875	Enzo Doria	03/2016
1602	(2^438067+5)/329	131869	Lelio R Paula	06/2015
1603	2^437908-113855	131824	Enzo Doria	09/2014
1604	2^437884-286349	131817	Enzo Doria	07/2015
1605	3^276062-112292	131716	Enzo Doria	07/2014
1606	2^437343+75953	131654	Enzo Doria	04/2016
1607	35^85243-34^85243	131621	Robert Price	05/2012
1608	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
1609	2^436451+1884713	131385	Enzo Doria	03/2017
1610	2^436365+35	131359	Robert Price	11/2015
1611	2^436300+1866871	131340	Enzo Doria	03/2016
1612	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
1613	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
1615	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
1614	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
1616	2^435773+1875557	131181	Enzo Doria	06/2016
1617	2^435612-2789939	131133	Enzo Doria	12/2015
1618	66^72047-65^72047	131093	Robert Price	09/2013
1619	2^435468+75631	131089	Enzo Doria	04/2016
1620	37^83588-2	131083	Lelio R Paula	08/2015
1621	(4^217720+11)/3	131081	Robert Price	02/2017
1622	2^435202-113193	131009	Enzo Doria	07/2014
1623	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
1624	2^434835-111937	130899	Enzo Doria	05/2014
1625	2^434685+72257	130854	Enzo Doria	04/2016
1626	2^434539-29317	130810	Enzo Doria	07/2015
1627	2^434469-114259	130789	Enzo Doria	01/2015
1628	2^434246+33	130722	Robert Price	11/2015
1629	2^433911-91	130621	Lelio R Paula	06/2017
1630	2^433744-114419	130570	Enzo Doria	02/2015
1632	2^433708+1869451	130560	Enzo Doria	05/2016
1631	2^433710+93	130560	Lelio R Paula	06/2017
1633	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
1634	4*10^130480+9	130481	Robert Price	05/2015
1635	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
1636	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
1637	2^433023-113497	130353	Enzo Doria	08/2014
1638	2^433002+1179379	130347	Enzo Doria	06/2016
1639	2^432974+19	130339	Robert Price	08/2015
1640	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
1641	2^432217+41	130111	Lelio R Paula	06/2017
1642	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
1643	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
1644	97^65480-2	130094	Lelio R Paula	05/2017
1645	2^432117-113215	130081	Enzo Doria	07/2014
1646	2^431804+72511	129986	Enzo Doria	04/2016
1647	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
1648	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
1649	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
1650	2^430807+1869563	129686	Enzo Doria	05/2016
1651	2^430721-21429	129660	Enzo Doria	07/2013
1652	2^430415-276271	129568	Enzo Doria	07/2015
1653	2^430142-2791721	129486	Enzo Doria	03/2016
1654	2^429568-21017	129313	Enzo Doria	07/2013
1655	2^429194-112685	129201	Enzo Doria	06/2014
1656	2^429145-2780449	129186	Enzo Doria	04/2016
1657	2^428892-113453	129110	Enzo Doria	07/2014
1658	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
1659	2^428727-113959	129060	Enzo Doria	10/2014
1660	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
1661	(10^129051-31)/3	129051	Serge Batalov	12/2014
1662	2^428564+71161	129011	Enzo Doria	04/2016
1663	2^428502-113285	128992	Enzo Doria	07/2014
1664	2^428421-21373	128968	Enzo Doria	06/2013
1665	L(616787)	128901	Henri Lifchitz	09/2008
1666	91^65772-2	128851	Lelio R Paula	05/2017
1667	2^428022+43	128848	Lelio R Paula	05/2017
1668	2^427999-459397	128841	Enzo Doria	05/2015
1669	2^427993+76847	128839	Enzo Doria	05/2016
1670	2^427824-1851507	128788	Enzo Doria	08/2015
1671	2^427807-21469	128783	Enzo Doria	07/2013
1672	11^123594-240	128710	Enzo Doria	09/2012
1673	2^427504-21503	128692	Enzo Doria	07/2013
1674	2^427420+91	128667	Lelio R Paula	05/2017
1675	2^427269-113635	128621	Enzo Doria	08/2014
1676	2^427130+1877569	128579	Enzo Doria	08/2016
1677	2^427016-115349	128545	Enzo Doria	07/2015
1678	2^426889-112879	128507	Enzo Doria	06/2014
1679	2^426804+1869931	128481	Enzo Doria	05/2016
1680	2^426750+77635	128465	Enzo Doria	05/2016
1681	2^426425-91	128367	Lelio R Paula	05/2017
1682	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
1683	2^426352+74971	128345	Enzo Doria	04/2016
1684	2^426300-1863689	128330	Enzo Doria	03/2016
1685	2^426293+1881017	128327	Enzo Doria	11/2016
1686	2^426043+35	128252	Robert Price	11/2015
1687	2^425808-459959	128181	Enzo Doria	06/2015
1688	2^425627-113605	128127	Enzo Doria	08/2014
1689	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
1690	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
1691	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
1692	2^425205+4911	128000	Marek Hubal	02/2017
1693	2^425118-113663	127974	Enzo Doria	08/2014
1694	2^425061+1869761	127957	Enzo Doria	05/2016
1695	2^424918-21141	127914	Enzo Doria	07/2013
1696	2^424864-29489	127897	Enzo Doria	08/2015
1697	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
1698	2^424632-2786639	127827	Enzo Doria	03/2016
1699	2^424577-113755	127811	Enzo Doria	09/2014
1700	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
1701	11^122629-720	127705	Enzo Doria	11/2012
1702	2^423696-21429	127546	Enzo Doria	07/2013
1703	2^423664-1864559	127536	Enzo Doria	03/2016
1704	3^267267-4	127519	Henri Lifchitz	10/2014
1705	(19^99689+5^99689)/24	127477	Robert Price	09/2013
1706	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
1707	2^423328-21537	127435	Enzo Doria	07/2013
1708	(2^423165-7)/25	127384	Lelio R Paula	05/2015
1709	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
1710	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
1711	2^422515-114997	127190	Enzo Doria	06/2015
1712	5*10^127179-3	127180	Robert Price	07/2015
1713	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
1714	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
1715	2^421860-113285	126993	Enzo Doria	07/2014
1716	(2^421827-7)/11	126982	Lelio R Paula	05/2015
1717	11^121910-840	126957	Enzo Doria	12/2012
1718	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
1719	331^50339-10004	126846	Enzo Doria	07/2012
1720	2^421363-2790757	126843	Enzo Doria	03/2016
1721	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
1722	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
1723	2^421161-286183	126783	Enzo Doria	06/2015
1724	2^420939-113935	126716	Enzo Doria	10/2014
1725	2^420741-113659	126656	Enzo Doria	08/2014
1726	2^420694-21	126642	Lelio R Paula	05/2017
1727	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
1728	2^420424-59189	126561	Enzo Doria	10/2015
1729	2^420126+71893	126471	Enzo Doria	04/2016
1730	2^419866+1877059	126393	Enzo Doria	07/2016
1731	F(604711)	126377	Henri Lifchitz	02/2005
1732	2^419757+72707	126360	Enzo Doria	04/2016
1733	2^419720-21569	126349	Enzo Doria	07/2013
1734	2^419637+29	126324	Henri Lifchitz	02/2006
1735	2^419612+1876741	126316	Enzo Doria	07/2016
1736	2^419520+2793271	126289	Enzo Doria	03/2016
1737	(2^419447-5)/369	126264	Lelio R Paula	05/2014
1738	2^419328-1859939	126231	Enzo Doria	03/2016
1739	2^419282-1851507	126217	Enzo Doria	08/2015
1740	2^419251+1866143	126208	Enzo Doria	03/2016
1741	11^121185+2	126202	Robert Price	05/2014
1742	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
1743	2^418851+23	126087	Robert Price	09/2015
1744	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
1745	2^418829+167	126081	Lelio R Paula	01/2012
1746	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
1747	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
1748	2^418319-109501	125927	Enzo Doria	04/2014
1749	2^418316-112373	125926	Enzo Doria	06/2014
1750	2^417968+1869811	125821	Enzo Doria	06/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)