PRP Records

Probable Primes Top 10000

(277054 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 (> 50000) Who ? When ?
9251(19*2^248099-1)/2974686Lelio R Paula01/2014
925220780^3927+3927^2078074685Hans Havermann12/2019
9253(86*10^74676-41)/974677Robert Price11/2015
9254(2^248065+3650)/274675Stefano Morozzi01/2020
9255(p(15711)#-4)/274672Robert Price09/2017
925610^74670+3174671Robert Price01/2011
925710^74670-12246374670Patrick De Geest05/2013
92582^248036-6974667Lelio R Paula03/2012
925911^71698-600074666Enzo Doria12/2012
9260(2^248032+406)/274665Stefano Morozzi01/2020
926158*(10^(3*24887)-1)/111-174661Robert Price10/2014
926214^65139-4574658Lelio R Paula01/2015
926317967^14288+14288^1796774653Hans Havermann11/2019
92646^95921-13374642Lelio R Paula01/2015
926511^71675+7874642Lelio R Paula02/2015
926617875^14986+14986^1787574641Hans Havermann12/2019
9267(2^247931+1458)/274635Stefano Morozzi01/2020
9268(166*10^74624-7)/374626Robert Price11/2020
926918^59449-9174625Lelio R Paula01/2015
9270(12696^18181-1)/1269574605Serge Batalov08/2020
92716^95864-1604374597Enzo Doria02/2013
92725*7^88261+674590Lelio R Paula10/2014
92739*5^106710+474589Lelio R Paula10/2014
9274(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
927521157^3352+3352^2115774585Hans Havermann12/2019
9276(265*10^74579+17)/374581Robert Price05/2016
927717798^15489+15489^1779874575Hans Havermann11/2019
9278(2^247759-1017)/331831171774574Lelio R Paula07/2012
92795^106682-2474568Lelio R Paula08/2014
9280(2^247686+1450)/274561Stefano Morozzi01/2020
9281474^27863+27863^47474556Norbert Schneider01/2017
9282(14*10^74540+79)/374541Robert Price11/2017
9283(2^247582+1630)/274530Stefano Morozzi01/2020
9284(35365^16384+1)/274524Lelio R Paula11/2011
9285(1705^23059-1)/170474518Serge Batalov08/2020
92863^156161+266074508Lelio R Paula01/2015
92882^247474-5869574498Lelio R Paula05/2013
9287(2^247476+886)/274498Stefano Morozzi01/2020
928911^71519-9074480Enzo Doria07/2012
9290(19*2^247419-1)/2320298374475Lelio R Paula01/2014
9292(2^247394-7)/374473Lelio R Paula06/2012
929118^59328+1774473Lelio R Paula01/2015
92932^247379-18174469Lelio R Paula03/2012
9294(15*2^247370-1)/47974465Lelio R Paula01/2014
929518860^8877+8877^1886074465Hans Havermann12/2019
929617355^17564-17564^1735574462Norbert Schneider11/2019
92972^247344+204774458Lelio R Paula05/2013
92982^247311-101774449Lelio R Paula05/2013
9299(2^247288+1938)/274441Stefano Morozzi01/2020
93002^247280+774439Lelio R Paula03/2012
9301(68*10^74434+13)/974435Ray Chandler11/2010
93023^156004-6274433Lelio R Paula01/2015
930321865^2536+2536^2186574432Hans Havermann11/2019
9304(2^247223+1050)/274422Stefano Morozzi01/2020
930536095!2-6474416Robert Price06/2015
930667699!4+1674409Robert Price09/2019
93072^247165-374405M. Frind & P. Underwood07/2002
93082^247150+3276974400Lelio R Paula05/2013
9309(2^247130+3858)/274394Stefano Morozzi01/2020
9310(2^247055+2426)/274371Stefano Morozzi01/2020
931112^68911+7374368Lelio R Paula01/2015
93122^246999+7490374355Enzo Doria04/2016
93132^246989-11064374352Enzo Doria05/2014
931410^74350+27943974351Patrick De Geest07/2017
9317(10^74350+11)/374350Robert Price11/2014
931510^74350-40000000174350Robert Price07/2017
931610^74350-71624174350Patrick De Geest07/2017
931867647!4-51274346Robert Price11/2019
931910^74335+1365974336Patrick De Geest05/2013
932010^74335-5374335Robert Price05/2011
932123360^1521+1521^2336074335Hans Havermann11/2019
9322(2^246914+3418)/274329Stefano Morozzi01/2020
93232^246906-121574327Lelio R Paula05/2013
9324(2^246879+1494)/274318Stefano Morozzi01/2020
93252^246848+11174309Lelio R Paula03/2012
9326(2^246842+2490)/274307Stefano Morozzi01/2020
93286^95490-1844374306Enzo Doria03/2013
9327(2^246840+2902)/274306Stefano Morozzi01/2020
932918^59188-236974298Enzo Doria03/2013
9330(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
93312^246744+4075574278Lelio R Paula05/2013
9332(29*10^74276+91)/374277Robert Price03/2016
933317222^17533-17533^1722274272Norbert Schneider11/2019
9334(2^246720+3606)/274270Stefano Morozzi01/2020
93356^95441+16374268Lelio R Paula01/2015
9336(40734^16111-1)/4073374267Anonymous11/2020
9337(14235^17881-1)/1423474263Serge Batalov08/2020
9338V(390863)74258Serge Batalov03/2015
933910^74254+9174255Robert Price03/2011
9341(19*10^74253-1)/974254Ray Chandler02/2012
934010^74254-13056974254Patrick De Geest05/2013
9342771^25718+25718^77174250Norbert Schneider10/2016
93432^246618+42774240Henri Lifchitz02/2005
934488*10^74234+374236Robert Price11/2016
93458*10^74234-4974235Robert Price04/2016
9346(19648^17291-1)/1964774232Serge Batalov08/2020
93472^246578+1228574228Lelio R Paula05/2013
9348(3^155569-5)/274225Lelio R Paula06/2012
934913^66628+4674220Lelio R Paula01/2015
9350(2^246534+3034)/274214Stefano Morozzi01/2020
9351(2^246486+798)/274200Stefano Morozzi01/2020
93522^246476-1729574197Lelio R Paula05/2013
9353(2^246465+446)/274194Stefano Morozzi01/2020
9354(61*10^74189-1)/374191Robert Price11/2017
9355(15185*2^246432-1)/1374187Lelio R Paula04/2015
93565*2^246413-374179Lelio R Paula05/2014
93572^246386-2863574170Lelio R Paula05/2013
9358(2^246371+3050)/274165Stefano Morozzi01/2020
93592^246334-11124574154Enzo Doria05/2014
93603*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
936115^63045+8274147Lelio R Paula01/2015
936219255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
9363(199^32251-1)/19874139Serge Batalov08/2020
9364(2^246277+2114)/274137Stefano Morozzi01/2020
93652^246268-11050774135Enzo Doria05/2014
93663^155328+266074111Lelio R Paula01/2015
93682^246148-278624974098Enzo Doria03/2016
936719740^5671+5671^1974074098Hans Havermann01/2020
9369(2^246135+3386)/274094Stefano Morozzi01/2020
9370(16*10^74092-19)/374093Robert Price03/2016
93712^246115-11076774088Enzo Doria05/2014
93727^87666-6874087Lelio R Paula08/2014
9373(2^246091+1938)/274081Stefano Morozzi01/2020
937510^74079+114514191974080Marisa Kirisame03/2015
937410^74079+621974080Patrick De Geest03/2016
937610^74079-28270774079Patrick De Geest03/2016
9377129^35098+274078Lelio R Paula05/2013
937822193^2176+2176^2219374073Hans Havermann12/2019
937917703^15278+15278^1770374071Hans Havermann12/2019
93802^246025-11212374061Enzo Doria06/2014
9381(67*10^74045+17)/374047Robert Price02/2017
9382(2^245944+2202)/274037Stefano Morozzi01/2020
9383(2^245885+1446)/274019Stefano Morozzi01/2020
9384(13769^17881-1)/1376874004Serge Batalov08/2020
93852^245823+6683174001Marek Hubal02/2017
93865^105869+4274000Lelio R Paula08/2014
9387(21*2^245806+1)/63455573991Lelio R Paula08/2012
9388(22699*2^245762+1)/11973985Lelio R Paula06/2014
9389(3^155048-7)/26273975Lelio R Paula06/2012
93909998*2^245696+373966Donovan Johnson10/2004
939113^66400-8073966Lelio R Paula01/2015
9393(2^245704+9)/2573963Lelio R Paula07/2012
939411^71023-717073963Enzo Doria01/2013
93923*10^73962+1373963Robert Price08/2017
9395(64758^15373-1)/6475773960Anonymous11/2020
9396(31*2^245660-1)/11419573948Lelio R Paula01/2014
93972^245629-279781373942Eric Chen03/2016
93982^245557-15373921Lelio R Paula03/2012
9399(77*10^73917-59)/973918Robert Price11/2017
940015010^17699+17699^1501073918Norbert Schneider11/2019
9401(12975^17971-1)/1297473913Serge Batalov08/2020
94022^245525+186988173911Enzo Doria06/2016
94032^245522+15973910Lelio R Paula03/2012
9404(2^245507+1986)/273905Stefano Morozzi01/2020
9405(13*10^73891-43)/373892Robert Price08/2017
940619^57783-5673891Lelio R Paula01/2015
94077*10^73888+7973889Robert Price02/2017
9408(2^245449+942)/273888Stefano Morozzi01/2020
94096^94948+17428173884Mike Oakes02/2011
9410(2^245431+3630)/273882Stefano Morozzi01/2020
941111^70939-486073876Enzo Doria01/2013
941218637^9196+9196^1863773870Hans Havermann01/2020
94132^245372+5461573865Lelio R Paula05/2013
94142^245362-14373862Lelio R Paula03/2012
94157^87396+6^(87396-1)73859Robert Price03/2016
9416(22*10^73853-37)/373854Robert Price05/2017
94175^105646-1424673844Enzo Doria02/2013
94192^245290-4173840Lelio R Paula03/2012
94182^245290-9439573840Lelio R Paula05/2013
942015770^17589+17589^1577073836Norbert Schneider10/2019
942112352^18043+18043^1235273828Norbert Schneider11/2019
9422(2^245240+3598)/273825Stefano Morozzi01/2020
9423(2^245242+498)/273825Stefano Morozzi01/2020
94248*5^105600-773813Lelio R Paula10/2014
94257*5^105573-473794Lelio R Paula10/2014
9426(2^245112+1122)/273786Stefano Morozzi01/2020
942720151^4570+4570^2015173751Hans Havermann12/2019
9428(2^244968+1318)/273743Stefano Morozzi01/2020
942918^58742-480573738Enzo Doria03/2013
9430(7*10^73729+23)/373730Robert Price06/2020
943113^66179+6673720Lelio R Paula01/2015
9432(2^244881+942)/273717Stefano Morozzi01/2020
9433(2^244883+1946)/273717Stefano Morozzi01/2020
9434(82*10^73714-1)/973715Robert Price12/2014
9435(2^244862+3682)/273711Stefano Morozzi01/2020
9436(29*2^244856-1)/18612173706Lelio R Paula01/2014
9437(13*2^244840-1)/279973702Lelio R Paula01/2014
9438(13*10^73701+17)/373702Robert Price06/2015
94396*10^73686-2973687Robert Price08/2020
9440(2^244787-1017)/2841173684Lelio R Paula07/2012
944121213^2974+2974^2121373680Hans Havermann01/2020
9442(3^154421-4)/2373677Lelio R Paula06/2012
944314596^17691+17691^1459673670Norbert Schneider11/2019
94448*7^87170+573669Lelio R Paula10/2014
9445(29*10^73659-113)/373660Robert Price11/2017
9446Phi(40100,-40100)73651Henri Lifchitz06/2013
9447(3883^20521-1)/388273650Serge Batalov08/2020
9448(4*10^73647-19)/373648Robert Price06/2017
94492^244618-229773638Yves Minet10/2009
94503*5^105344+873633Lelio R Paula10/2014
9451(2^244588+2562)/273629Stefano Morozzi01/2020
94525^105334-1409673626Enzo Doria02/2013
9453(2^244562+1534)/273621Stefano Morozzi01/2020
9454(2^244584-7)/1323707424303373614Lelio R Paula07/2012
94552^244465-11018573592Enzo Doria05/2014
9456(2^244465+2934)/273591Stefano Morozzi01/2020
94572^244443+4075573585Lelio R Paula05/2013
945823155^1506+1506^2315573583Hans Havermann12/2019
945910^73579+98765432173580Robert Price12/2019
946010^73579+12417373580Patrick De Geest02/2020
946110^73579-17637973579Patrick De Geest02/2020
94622^244404+384173573Yves Minet03/2011
946319770^5263+5263^1977073569Hans Havermann12/2019
94649*10^73565-4173566Robert Price08/2020
94652^244372-11062773564Enzo Doria05/2014
946619778^5241+5241^1977873563Hans Havermann12/2019
9467(2^244349+2186)/273557Stefano Morozzi01/2020
9468(2^244309+3710)/273545Stefano Morozzi01/2020
946918428^9783+9783^1842873537Hans Havermann01/2020
9470(3*2^244255+1)/24573527Lelio R Paula08/2012
9471(11*2^244245+1)/2373525Lelio R Paula08/2012
947218140^11301+11301^1814073524Hans Havermann12/2019
9473(15185*2^244187-1)/611173509Lelio R Paula04/2015
9474(9699^18439-1)/969873508Serge Batalov08/2020
9475(2^244152+2058)/273497Stefano Morozzi01/2020
9476(2^244109+1422)/273484Stefano Morozzi01/2020
947717063^17362+17362^1706373477Norbert Schneider04/2019
9478(91^37507+1)/9273476Paul Bourdelais08/2017
947918^58521+6573460Lelio R Paula01/2015
948013^65940+3673454Lelio R Paula01/2015
948119065^7112+7112^1906573439Hans Havermann12/2019
9482(625^26267+1)/62673437Richard Fischer12/2017
9483(16612^17401-1)/1661173436Serge Batalov08/2020
9484(2^243935+530)/273432Stefano Morozzi01/2020
94855^105050-1473427Lelio R Paula08/2014
9486(2^243850+1474)/273406Stefano Morozzi01/2020
9487(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
948815^62410-4673400Lelio R Paula01/2015
9489(2^243806+2494)/273393Stefano Morozzi01/2020
9490(2^243790+2530)/273388Stefano Morozzi01/2020
9491(2^243766+2362)/273381Stefano Morozzi01/2020
94922^243733+186970773371Enzo Doria05/2016
949310^73365-50000000173365Robert Price12/2020
949411^70439-543073355Enzo Doria01/2013
94952^243676-8773354Lelio R Paula03/2012
9496(101*10^73346-17)/373348Robert Price08/2016
949721639^2452+2452^2163973346Hans Havermann12/2019
9498(2^243647+2438)/273345Stefano Morozzi01/2020
94992^243621-11318573338Enzo Doria07/2014
9500(5*2^243610-1)/166973332Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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