PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)


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(2^489280-7)/6381147285Lelio R Paula09/2015
15022^489125+80357147242Enzo Doria06/2016
15032^488648-112799147098Enzo Doria07/2014
15042^488627-350317147092Enzo Doria06/2015
1505(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
15062^488280-2165146987Yves Minet07/2014
15072^488278+45146987Lelio R Paula12/2017
15082^487927-39146881Lelio R Paula12/2017
1509(7*10^146860-13)/3146861Robert Price07/2018
15102^487726-1863341146821Enzo Doria12/2015
15112^487121-39523146639Enzo Doria09/2015
1512(7*2^486967+1)/39146591Lelio R Paula09/2015
15132^486893-79146570Yves Minet09/2017
15142^486840+1879141146554Enzo Doria08/2016
15152^486774-87146534Lelio R Paula12/2017
151696^73877-95^73877146445Robert Price10/2015
1517(52^85259+1)/53146304Paul Bourdelais09/2017
1518179^64935+2146290Lelio R Paula10/2017
15192^485531-114621146160Enzo Doria05/2015
1520(2^485461-9)/4249146135Lelio R Paula09/2015
15212^485389+81887146117Enzo Doria08/2016
1522(10^146063+71)/9146063Serge Batalov07/2015
1523(2^485119+7)/2745146032Lelio R Paula09/2015
1524(22*10^146029+257)/9146030Robert Price06/2018
15252^484743+1872923145923Enzo Doria05/2016
15262^484341+1879157145802Enzo Doria08/2016
15272^484271-51145781Lelio R Paula11/2017
152870^78989-69^78989145743Robert Price01/2014
152951^85334+2145714Robert Price07/2015
15302^483886-1857101145665Enzo Doria10/2015
15312^483563-1863457145567Enzo Doria12/2015
15322^483516-1861409145553Enzo Doria11/2015
15332^483384-115019145514Enzo Doria06/2015
15342^483302-3221145489Lelio R Paula12/2012
15352^483046+1874029145412Enzo Doria06/2016
15362^482991-2789317145395Enzo Doria12/2015
15372^482978-2789711145391Enzo Doria12/2015
15382^482966-2789711145388Enzo Doria12/2015
15392^482817-1858843145343Enzo Doria10/2015
15402^482751-113635145323Enzo Doria08/2014
15412^482705-459763145309Enzo Doria05/2015
1542(4^241306+11)/3145281Robert Price03/2017
1543(19*2^482534+1)/7145258Lelio R Paula09/2015
154453^84239-52^84239145252Robert Price01/2013
1545(2^482333+5)/9287145193Lelio R Paula09/2015
15462^482087+72623145123Enzo Doria04/2016
15472^482016-286565145102Enzo Doria07/2015
15482^481840+15145049Robert Price09/2015
15492^481801-481801145037Henri Lifchitz03/2005
15502^481775+1869083145029Enzo Doria05/2016
155129^99167+2145022Ray Chandler08/2011
15522^481663+1875653144996Enzo Doria07/2016
15532^481149-459073144841Enzo Doria05/2015
15542^481045-113215144809Enzo Doria07/2014
15552^480859-113695144753Enzo Doria09/2014
15562^480766-2787191144725Enzo Doria11/2015
1557(21*27^101106-151)/26144720Curtis Bright05/2015
15582^480678+1874239144699Enzo Doria06/2016
1559(8*10^144683+1)/9144683Serge Batalov05/2010
1560L(692147)144651Henri Lifchitz10/2008
15612^480417+35144620Robert Price11/2015
15622^480296-59879144584Enzo Doria10/2015
15632^479844+3144448Donovan Johnson06/2006
1564(27*2^479642+1)/733144386Lelio R Paula08/2015
1565(21*2^479605-1)/11144376Lelio R Paula09/2015
15662^479348-2792219144299Enzo Doria02/2016
15673^302389-6242144277Enzo Doria05/2014
15682*10^144220-3144221Robert Price07/2015
15692^478904-109109144165Enzo Doria04/2014
15702^478337-115333143994Enzo Doria07/2015
1571(7*2^478330-1)/3143993Lelio R Paula08/2015
157288^74047-87^74047143984Robert Price05/2015
1573(19*10^143963+467)/9143964Robert Price02/2018
1574(71^77761+1)/72143954Paul Bourdelais09/2017
15752^478088+27143919Robert Price11/2015
15762^477475-22071143735Enzo Doria07/2013
15772^477417-22123143717Enzo Doria07/2013
15782^477359-3577143700Yves Minet03/2017
15792^476936-396765143573Enzo Doria07/2013
15802^476888-2791229143558Enzo Doria01/2016
15812^476868-1859939143552Enzo Doria11/2015
15822^476558-113627143459Enzo Doria08/2014
15832^476478-45143435Lelio R Paula11/2017
1584(2^475854+9)/73143245Lelio R Paula08/2015
15852^475813-113239143234Enzo Doria07/2014
15862^475624-114059143178Enzo Doria11/2014
1587(11*2^475553-7)/15143156Renaud Lifchitz03/2011
15882^475480-2786129143134Enzo Doria10/2015
15892^475299-111937143080Enzo Doria05/2014
15902^475160-2797859143038Enzo Doria04/2016
1591(2^475069+3)/395143008Lelio R Paula08/2015
15922^475027-461437142998Enzo Doria07/2015
1593(2^474958+78557)/3142977Lelio R Paula07/2015
1594(8*10^142932+43)/3142933Robert Price06/2018
1595(54^82471-1)/53142871Paul Bourdelais09/2017
1596(11*2^474432-1)/95142818Lelio R Paula09/2015
15972^474417-59923142814Enzo Doria10/2015
15984*10^142810-21142811Robert Price09/2018
1599(3*2^474166+1)/7142738Lelio R Paula08/2015
16002^474053+2897142705Lelio R Paula08/2012
1601(10^142699+359)/9142699Serge Batalov12/2014
1602898^48311-897^48311142676Jean-Louis Charton12/2012
16032^473740-1856639142610Enzo Doria09/2015
16042^473617-114223142573Enzo Doria12/2014
16052^473257+1873217142465Enzo Doria06/2016
1606(19*2^473242+1)/11142461Lelio R Paula09/2015
1607(14*10^142440+61)/3142441Robert Price12/2018
1608(10^142425+359)/9142425Serge Batalov12/2014
16092^473101+773027142418Enzo Doria05/2016
1610(13*2^472838-1)/3142340Lelio R Paula09/2015
1611(17*2^472789-1)/187347142320Lelio R Paula09/2015
16122^472634-109511142278Enzo Doria04/2014
1613(48^84589+1)/49142213Robert Price01/2014
16142^472258+7142164Lelio R Paula08/2015
1615tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
1616(11*2^471913-1)/21142060Lelio R Paula09/2015
16172^471792+1880881142024Enzo Doria11/2016
1618(31*2^471580-1)/135141960Lelio R Paula08/2015
1619(4*10^141926-79)/3141927Robert Price02/2018
1620(904*19^110984-1)/3141924Curtis Bright05/2015
1621(14*10^141853+37)/3141854Robert Price12/2018
1622(41*10^141836-59)/9141837Robert Price10/2018
16234*5^202913-9141831Lelio R Paula04/2015
16242*7^167812-3141818Lelio R Paula12/2014
16252^471043+35141799Robert Price11/2015
1626(11*2^470956-1)/7945141770Lelio R Paula08/2015
1627(11*10^141718-131)/3141719Robert Price09/2018
16282^470692+76771141693Enzo Doria05/2016
1629(21*2^470391+1)/533141601Lelio R Paula09/2015
16302^470305-459373141576Enzo Doria05/2015
16312^470183+72623141540Enzo Doria04/2016
16322^470173-16465141537Enzo Doria04/2013
16332^469974-1841141477Enzo Doria05/2014
1634(23*2^469939+1)/25141466Lelio R Paula08/2015
16352*10^141448+63141449Robert Price05/2018
16362^469824+43141432Lelio R Paula09/2017
16372*10^141407-27141408Robert Price05/2018
16382^469630-59711141373Enzo Doria10/2015
1639(25*10^141366-331)/9141367Robert Price08/2018
1640(2^469564-3)/611141351Lelio R Paula08/2015
1641197^61601+2141342Lelio R Paula08/2017
16422^469372-112949141296Enzo Doria07/2014
1644143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
1643143^65536+106^65536141253Serge Batalov03/2018
16452^469198+782569141243Enzo Doria10/2016
16462^469076-2786939141206Enzo Doria11/2015
16472^468804+1874941141125Enzo Doria06/2016
16482^468787+81353141119Enzo Doria08/2016
16492^468595-350407141062Enzo Doria06/2015
16502^468564+87855141052Lelio R Paula01/2016
16512^468551-21987141048Enzo Doria07/2013
16522^468523-7141040Lelio R Paula08/2015
16532^468405+87855141004Lelio R Paula01/2016
16542^467978-113051140876Enzo Doria07/2014
16552^467780-344429140816Enzo Doria07/2015
16562^467605-1855603140764Enzo Doria09/2015
16575*10^140744-7140745Robert Price09/2015
1658(5^201359-1)/4140744Paul Bourdelais12/2008
16592^467401-1850023140702Enzo Doria08/2015
1660(2^467270+78557)/23247140658Lelio R Paula07/2015
1661(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
16622^467166-1854941140631Enzo Doria09/2015
16632^466866-1840571140541Enzo Doria06/2015
16642^466829-459523140530Enzo Doria05/2015
16652^466692-113213140489Enzo Doria07/2014
1666153^64265-2140400Lelio R Paula11/2017
1667(112*10^140357-1)/3140359Serge Batalov12/2014
16682^466181-112735140335Enzo Doria07/2014
1669(5*10^140281-119)/3140282Robert Price03/2018
1670(27*2^465872+1)/691140241Lelio R Paula08/2015
16712^465803-114817140221Enzo Doria05/2015
1672floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
16732^465503-112735140131Enzo Doria07/2014
16746^179964+179964^6-1140040Robert Price04/2014
1675(29*2^465077-1)/9140003Lelio R Paula08/2015
16762^465072-344789140001Enzo Doria07/2015
16772^464864-17139939Lelio R Paula09/2017
1678(17^113621+1)/18139804Paul Bourdelais09/2011
1679(13*10^139782+191)/3139783Robert Price11/2018
1680(19*2^464312-1)/3139773Lelio R Paula08/2015
16813*10^139722+13139723Robert Price07/2018
1682(31*2^463970+1)/5139670Lelio R Paula08/2015
1683(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
16842^463633-2788423139568Enzo Doria11/2015
16852^463271-109501139459Enzo Doria04/2014
1686(5*10^139457+79)/3139458Robert Price03/2018
16872^463237-99139449Lelio R Paula09/2017
1688(7*10^139417-547)/9139417Robert Price01/2018
1689(10^139398+191)/3139398Robert Price02/2018
16902^463019+79463139383Enzo Doria06/2016
16913^292129-112756139381Enzo Doria07/2014
1692(15*2^462951+1)/527139361Lelio R Paula08/2015
16932^462855-1865707139334Enzo Doria02/2016
16942^462786-292043139313Enzo Doria08/2015
1695(26*10^139289+1)/9139290Serge Batalov05/2010
16962^462238-935139148Yves Minet02/2014
16972^461228+1870441138844Enzo Doria05/2016
16982^461204-113675138837Enzo Doria08/2014
1699(2^461139-7)/47138815Lelio R Paula08/2015
1700(17*10^138812-521)/9138813Robert Price04/2018
17013*10^138811-11138812Robert Price07/2018
1702(17*2^460963+1)/124051613138757Lelio R Paula08/2015
1703(43*10^138648+101)/9138649Robert Price11/2018
17042^460567-113541138645Enzo Doria08/2014
17057*10^138604+3138605Robert Price08/2015
17062^460330+69138574Lelio R Paula09/2017
17072^460078-69581138498Enzo Doria12/2015
17082^459768+1531138404Lelio R Paula06/2012
17092^459343-113611138277Enzo Doria08/2014
17102^459199+1874393138233Enzo Doria06/2016
17112^459063-345307138192Enzo Doria06/2015
17122*10^138162-43138163Robert Price04/2018
17132^458927-112747138151Enzo Doria06/2014
17142^458927-69217138151Enzo Doria11/2015
1715555555*2^458524+1513138036Darren Bedwell08/2009
17162^458465+2^32+1138012T. D. Noe06/2007
17172^458321-113053137969Enzo Doria07/2014
17182^458298+79459137962Enzo Doria06/2016
17192^458248-21815137947Enzo Doria07/2013
17202^458194+1876549137931Enzo Doria07/2016
1721(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
17222^457937+57137853Lelio R Paula09/2017
1723(8*10^137845+13)/3137846Robert Price06/2018
17242^457822+105137819Donovan Johnson06/2006
17252^457754-113711137798Enzo Doria09/2014
172611^132315-360137792Enzo Doria09/2012
17272^457347-37137676Lelio R Paula09/2017
17282^457322-2786393137668Enzo Doria10/2015
1729gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
17302^457240-59939137643Enzo Doria10/2015
17312^457120-21575137607Enzo Doria07/2013
1732(11*2^456978+1)/15137564Lelio R Paula07/2015
1733(7*25^98399+10613)/12137556Curtis Bright05/2015
17342^456796-113513137510Enzo Doria08/2014
1735(7*2^456655+1)/39137467Lelio R Paula07/2015
17362^456503-114361137422Enzo Doria01/2015
1737(11*2^456387+1)/19137386Lelio R Paula07/2015
1738(71*10^137250+1)/9137251Serge Batalov05/2010
17392^455922+76249137247Enzo Doria05/2016
174014^119741-119741^14137239Serge Batalov04/2016
1741(19*2^455760+1)/3455137196Lelio R Paula07/2015
1743124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
1742124^65536+57^65536137195Serge Batalov03/2018
17442^455689+72677137177Enzo Doria04/2016
1745(17948!)^2+Prime(17948)137118Robert Price08/2014
1746(37^87421-1)/36137093Robert Price03/2012
17472^455323-57137066Lelio R Paula09/2017
1748(73*17^111333-9)/16136991Curtis Bright05/2015
17492^455025-112723136977Enzo Doria06/2014
17502^454675-1777136871Yves Minet10/2011


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!