PRP Records

Probable Primes Top 10000

(172213 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) !!!


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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 ?
97512^158337-1155*15833747665Henri Lifchitz01/2005
9752(656137^8192+1)/247653Lelio R Paula12/2014
97537^56386-247652Lelio R Paula06/2012
975411783^11062+11062^1178347649Anatoly F. Selevich04/2009
975655^27370-5447634Norbert Schneider08/2012
9755(653670^8192+1)/73728147634Lelio R Paula11/2014
97572^158227+70147632Lelio R Paula02/2013
97592^158222-46747630Yves Minet01/2012
975835^30847-1007847630Enzo Doria03/2013
97602^158216+64347628Lelio R Paula02/2013
9761(652648^8192+1)/4831918489747624Lelio R Paula11/2014
97622^158199-1515747623Enzo Doria04/2013
9763177^21182+247617Lelio R Paula05/2013
9764(7*2^158168-1)/8793947610Lelio R Paula01/2014
97657473^12290+12290^747347606Norbert Schneider03/2014
97662^158132-11480947603Enzo Doria05/2015
9767(11701^11701+6384)/547602Makoto Morimoto07/2016
97688345^12138+12138^834547599Norbert Schneider11/2013
976911^45703-78047595Enzo Doria11/2012
97702^158095+95347592Lelio R Paula02/2013
97715^68086-1715647591Enzo Doria02/2013
9772(11699^11699+1688)/166347591Makoto Morimoto06/2016
977312855^5032+5032^1285547586Hans Havermann02/2016
97745779^12648-12648^577947580Norbert Schneider12/2016
9775PIPrime(47577)47577Eric W. Weisstein05/2006
97765^68048-1808647564Enzo Doria02/2013
977714^41494+6747558Lelio R Paula11/2012
977824^34456-201547557Enzo Doria03/2013
9779(11689^11689+2459)/2^2/3^247547Makoto Morimoto06/2016
9780(635947^8192+1)/247542Lelio R Paula12/2014
97812^157921+65947539Lelio R Paula02/2013
9782(2^157929-5)/2546747537Lelio R Paula01/2012
9783(146^21961-1)/14547530Richard Fischer10/2016
97845552^12691-12691^555247521Norbert Schneider01/2017
978513233^3896+3896^1323347515Hans Havermann02/2016
97862^157838+90747514Lelio R Paula02/2013
9787(11*2^157828+1)/68747510Lelio R Paula01/2012
9788(11681^11681+2011)/2^2/3/11104947507Makoto Morimoto06/2016
978912^44020-4347506Lelio R Paula10/2012
9790(266*10^47499-11)/347501Robert Price09/2016
97913^99541+5647494Lelio R Paula04/2012
979235^30758-800447493Enzo Doria03/2013
97932^157753-382347489Yves Minet04/2009
9794(11677^11677+3717)/2/43/9697947488Makoto Morimoto07/2016
9795(625575^8192+1)/247483Lelio R Paula12/2014
979612913!-12913#+14748103/2005
979731^31835-3047478Theodore Burton12/2005
97982^157716+90147478Lelio R Paula01/2013
97992^157710+425747476Lelio R Paula03/2009
9800(623727^8192+1)/247473Lelio R Paula12/2014
9801(623697^8192+1)/247473Lelio R Paula12/2014
98027*2^157683-347469Henri Lifchitz06/2003
98035^67892-1550647455Enzo Doria02/2013
98042^157637-1360947454Enzo Doria04/2013
9805(17*10^47452-179)/947453Robert Price03/2017
9806(619901^8192+1)/13107447446Lelio R Paula12/2014
9807(618739^8192+1)/247444Lelio R Paula12/2014
9808(67*10^47439+17)/347441Robert Price02/2017
9809(27*2^157580+1)/4347437Lelio R Paula07/2012
98105146^12777-12777^514647422Norbert Schneider02/2017
98115^67839-7247418Lelio R Paula05/2012
9812(78557*2^157501+1)/3547416Lelio R Paula06/2014
98132^157502+7681947413Enzo Doria05/2016
98142^157497+841547412Lelio R Paula10/2011
981519^37074-1847409Theodore Burton11/2005
9816(2^157497+47)/37747409Lelio R Paula01/2012
98172*5^67826+347409Lelio R Paula09/2014
9818(11657^11657+656)/5347403Makoto Morimoto06/2016
98195762^12603-12603^576247395Norbert Schneider12/2016
98202^157410-40147386Yves Minet01/2012
98212^157401+80747383Lelio R Paula02/2013
9822(2^157457-1)/4612545359/35801252162615347376Anonymous07/2016
98234*6^60879-747374Lelio R Paula09/2014
9824Phi(72939,-10)47360Ray Chandler04/2009
98257^56039-6247359Lelio R Paula06/2012
98262^157315+95947357Lelio R Paula02/2013
9827(140009^9203+1)/14001047355Faysal YAtim02/2008
98282^157294+425747351Lelio R Paula03/2009
9829(15*2^157287-1)/747349Lelio R Paula01/2014
9830(78557*2^157254+1)/347343Lelio R Paula06/2014
98314*10^47340+3*7^4734047341Mike Oakes10/2010
983243^28976-247332Lelio R Paula08/2013
98332^157225-322347330Yves Minet12/2014
98352^157179+56347316Lelio R Paula02/2013
9834(lucasV(1,2,314396)+2)/(3*11*76283)47316Mike Oakes01/2017
98362^157171+186935347314Enzo Doria05/2016
9837(3^99172-8)/2051347313Lelio R Paula03/2012
98382^157166-1554547312Enzo Doria04/2013
98402^157159-306747310Yves Minet08/2009
98392^157158-11261347310Enzo Doria06/2014
98422^157156+25525547309Lelio R Paula03/2009
9841(11639^11639+11640^11640)/(328367027*24073627267)47309Walter Nissen09/2014
9843(32*10^47304-23)/947305Patrick De Geest05/2005
98456^60788+5347303Lelio R Paula06/2012
98448*7^55972+547303Lelio R Paula09/2014
9846(594651^8192+1)/147456247297Lelio R Paula11/2014
9847(594323^8192+1)/13107447296Lelio R Paula11/2014
98482^157110+35547295Lelio R Paula02/2013
9849(22*10^47292+161)/347293Robert Price02/2017
98502^157098+42747292Lelio R Paula02/2013
9851(11633^11633+4855)/2^3/3/11^2/13/19^2/1147147285Makoto Morimoto07/2016
98527*10^47280-947281Dmitry Domanov11/2010
9853(590189^8192+1)/247276Lelio R Paula11/2014
9854(3^99088-7)/1138809847270Lelio R Paula03/2012
98552^157024+1228547269Lelio R Paula03/2009
9856(2^156991-509203)/258219547253Lelio R Paula05/2012
9858(19*10^47237+11)/347238Erik Branger05/2013
9857(583841^8192+1)/247238Lelio R Paula11/2014
98592^156915-85194747237Paul Bourdelais11/2012
986035^30592-502247237Enzo Doria03/2013
9861(583621^8192+1)/247236Lelio R Paula11/2014
98627*2^156908-547235Lelio R Paula02/2014
9863(583583^8192+1)/29491447231Lelio R Paula11/2014
986411847^9694+9694^1184747229Anatoly F. Selevich07/2009
9865(11621^11621+3940)/3/7/13/79/1373/7229/17494347226Makoto Morimoto07/2016
986611708^10803+10803^1170847225Anatoly F. Selevich04/2010
98676330^12421+12421^633047218Norbert Schneider06/2014
9868(11617^11617+2342)/3^2/11/9026347218Makoto Morimoto06/2016
9869(2^156877+5)/35355616147217Lelio R Paula01/2012
9870(6^60667-61)/2547207Lelio R Paula05/2014
98712^156749+78947187Lelio R Paula02/2013
9872(574789^8192+1)/247182Lelio R Paula11/2014
9873(8*10^47178-77)/347179Robert Price05/2016
987424^34180-106347176Enzo Doria03/2013
987511^45298-936047174Enzo Doria02/2013
98762^156702+4347173Lelio R Paula08/2010
987720^36253-436347167Enzo Doria03/2013
98782^156682+1501547166Lelio R Paula10/2011
987919^36881+4247162Lelio R Paula11/2012
98802^156656-1554547159Enzo Doria04/2013
98812^156653+89747158Lelio R Paula02/2013
988235^30539-324447155Enzo Doria03/2013
9883(34*10^47158-7)/9/37/2785147153Makoto Morimoto04/2016
98846244^12423-12423^624447152Norbert Schneider03/2013
988511872^9355+9355^1187247145Anatoly F. Selevich10/2009
9886(31*10^47135+23)/947136Erik Branger05/2013
9887(11597^11597+2349)/2/7/21147131Makoto Morimoto06/2016
988810^47122+17313347123Patrick De Geest06/2016
989010^47122-2*10^1172-147122Serge Batalov01/2015
988910^47122-15260147122Patrick De Geest03/2016
98912^156525-13947119Lelio R Paula01/2011
98921934^14337+14337^193447118Norbert Schneider07/2013
98932^156487-11476947108Enzo Doria05/2015
9894(11593^11593+123)/2^2/29/79/5311347108Makoto Morimoto06/2016
9895Phi(117790,10)/47116147107Makoto Kamada05/2015
98962^156447+72547096Lelio R Paula02/2013
98972^156445+64547095Lelio R Paula02/2013
989810^47094+2520347095Patrick De Geest06/2016
989910^47094-2*10^9900-147094Serge Batalov01/2015
990010^47094-292147094Patrick De Geest03/2016
99012^156424+59147089Lelio R Paula02/2013
99022^156403+2947082Henri Lifchitz05/2005
9903(558261^8192+1)/247078Lelio R Paula11/2014
99042^156380+75147076Lelio R Paula01/2013
9905(557769^8192+1)/247075Lelio R Paula11/2014
99062^156376+8147074Henri Lifchitz08/2005
9907(11587^11587+4766)/3^4/41/563/15889/196668147073Makoto Morimoto07/2016
990813307^3442+3442^1330747065Hans Havermann01/2016
9909(555829^8192+1)/247063Lelio R Paula11/2014
991013563^2950+2950^1356347062Hans Havermann08/2015
99113^98634+447061Lelio R Paula03/2012
99122^156326-172147059Yves Minet09/2012
99135^67326-1421647059Enzo Doria03/2013
9914(555005^8192+1)/247057Lelio R Paula11/2014
9915(43*10^47051+11)/947052Erik Branger05/2013
99169*5^67308-847048Lelio R Paula09/2014
9917(553149^8192+1)/247046Lelio R Paula11/2014
99184*5^67298+947040Lelio R Paula09/2014
99192^156260-9347039Lelio R Paula08/2010
99202^156254+1947038Lelio R Paula08/2010
9921(22*10^47034+161)/347035Robert Price02/2017
99225^67290-2*3^6729047034Mike Oakes11/2009
992335^30460-502247033Enzo Doria03/2013
99242^156233-214547031Lelio R Paula03/2009
992510^47028+15707147029Patrick De Geest06/2016
992710^47028-2*10^8592-147028Serge Batalov01/2015
992810^47028-6443147028Patrick De Geest03/2016
992610^47027+22201947028Patrick De Geest06/2016
993010^47026+5147027Robert Price12/2010
992910^47027-15518347027Patrick De Geest03/2016
993110^47026-3955147026Patrick De Geest10/2011
9932277^19252-34447023Enzo Doria07/2012
99332^156186+1291547017Lelio R Paula10/2011
99342^156172-5939947013Gary Barnes08/2009
99356^60413-5^6041347011Predrag Minovic07/2004
993610^47006+38938347007Patrick De Geest06/2016
99392^156149+1291547006Lelio R Paula10/2011
993810^47006-2*10^5472-147006Serge Batalov01/2015
993710^47006-38809747006Patrick De Geest03/2016
994010^47000+4248347001Patrick De Geest01/2012
994110^47000-2552947000Patrick De Geest01/2012
994210^46999+1077147000Patrick De Geest01/2012
994310^46999-3287346999Patrick De Geest01/2012
9944(15*2^156117-1)/746997Lelio R Paula01/2014
99452^156111+45424546995Henri Lifchitz01/2007
9946(31*2^156104-1)/42784546988Lelio R Paula01/2014
99472^156073-4870346983Gary Barnes08/2009
9948(542497^8192+1)/246976Lelio R Paula11/2014
9949(9^49223+1)/1046970Paul Bourdelais10/2007
9950(229*10^46968-1)/346970Robert Price12/2016
99512^155996-9346960Lelio R Paula08/2010
9952(7*10^46957+179)/346958Robert Price04/2016
99532^155979-685546955Lelio R Paula11/2008
99542^155978-469146955Yves Minet07/2011
9955163^21224-21224^16346952Norbert Schneider10/2015
9956(23*2^155966-1)/9146950Lelio R Paula01/2014
99572^155958-14346949Lelio R Paula01/2011
996019862^231+231^1986246947Anatoly F. Selevich02/2007
9959(3^98415+2)/138186655346947Lelio R Paula03/2012
995812^43502-4146947Lelio R Paula10/2012
996135^30404-553446946Enzo Doria03/2013
9962Phi(93914,10)/32399203032146945Maksym Voznyy01/2010
9963(21181*2^155944+1)/1464147146941Lelio R Paula05/2014
9964(536981^8192+1)/246940Lelio R Paula11/2014
996513^42134+2446935Lelio R Paula10/2012
9966(535603^8192+1)/246931Lelio R Paula11/2014
9967(11551^11551+9088)/28146925Makoto Morimoto07/2016
996812776!-p(12776)46918Henri Lifchitz12/2005
996916725^638+638^1672546911Anatoly F. Selevich05/2006
9970(3^98324+7)/202446910Lelio R Paula03/2012
99712^155823-1509746908Enzo Doria04/2013
9972(11549^11549+2146)/3^2/5/11/13709/76303/688739346900Makoto Morimoto06/2016
99732^155794-344346899Yves Minet12/2016
99744*3^98285-546895Lelio R Paula03/2014
99755^67089+3846894Lelio R Paula05/2012
9976(33*2^155762+1)/746890Michael Porter10/2015
9977(530026^8192+1)/14745746889Lelio R Paula11/2014
9978(55*10^46885+53)/946886Erik Branger05/2013
9979(529461^8192+1)/13107446885Lelio R Paula11/2014
99805^67074-5446883Lelio R Paula05/2012
9981200^20373+20373^20046879Serge Batalov05/2014
99823^98251+2646878Lelio R Paula04/2012
998310^46877+579946878Patrick De Geest06/2016
998410^46877-2*10^12568-146877Serge Batalov01/2015
998510^46877-13566946877Patrick De Geest03/2016
99862^155702-40146871Yves Minet01/2012
9988(526974^8192+1)/6553746869Syoichiro Yamada05/2008
99877^55459+9446869Lelio R Paula06/2012
998912763!+12763!2+12763#+246864Joe McLean08/2007
999020^36015-114346857Enzo Doria03/2013
99912^155641-13946853Lelio R Paula01/2011
999211^44989-123046852Enzo Doria11/2012
999310^46851+753746852Patrick De Geest06/2016
999610^46851-2*10^68-146851Serge Batalov01/2015
999510^46851-3408346851Patrick De Geest03/2016
999410^46850+8619346851Patrick De Geest06/2016
999710^46850-2*10^12396-146850Serge Batalov01/2015
999810^46850-6799746850Patrick De Geest03/2016
999910^46847+6042746848Patrick De Geest06/2016
1000010^46847-400146847Patrick De Geest03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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