PRP Records

Probable Primes Top 10000

(280928 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 ?
975111^71771-4800074742Enzo Doria12/2012
9752(2^248282-5)/5012974736Lelio R Paula06/2012
97532^248252-11010574732Enzo Doria04/2014
9754(7*10^74729+71)/374730Robert Price03/2016
97553^156614-5074724Lelio R Paula01/2015
9756(7*2^248213+1)/13574719Lelio R Paula07/2012
9757(2^248193+870)/274714Stefano Morozzi01/2020
9758(2^248167+1178)/274706Stefano Morozzi01/2020
9759(2^248173+78557)/76774705Lelio R Paula07/2012
9760(2^248145+3866)/274699Stefano Morozzi01/2020
9761125^35622+12474697Norbert Schneider02/2015
9762(2^248114+994)/274690Stefano Morozzi01/2020
9763(19*2^248099-1)/2974686Lelio R Paula01/2014
976420780^3927+3927^2078074685Hans Havermann12/2019
9765(86*10^74676-41)/974677Robert Price11/2015
9766(2^248065+3650)/274675Stefano Morozzi01/2020
9767(p(15711)#-4)/274672Robert Price09/2017
976810^74670+3174671Robert Price01/2011
976910^74670-12246374670Patrick De Geest05/2013
97702^248036-6974667Lelio R Paula03/2012
977111^71698-600074666Enzo Doria12/2012
9772(2^248032+406)/274665Stefano Morozzi01/2020
977358*(10^(3*24887)-1)/111-174661Robert Price10/2014
977414^65139-4574658Lelio R Paula01/2015
977517967^14288+14288^1796774653Hans Havermann11/2019
97766^95921-13374642Lelio R Paula01/2015
977711^71675+7874642Lelio R Paula02/2015
977817875^14986+14986^1787574641Hans Havermann12/2019
9779(2^247931+1458)/274635Stefano Morozzi01/2020
9780(166*10^74624-7)/374626Robert Price11/2020
978118^59449-9174625Lelio R Paula01/2015
9782(12696^18181-1)/1269574605Serge Batalov08/2020
97836^95864-1604374597Enzo Doria02/2013
97845*7^88261+674590Lelio R Paula10/2014
97859*5^106710+474589Lelio R Paula10/2014
9786(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
978721157^3352+3352^2115774585Hans Havermann12/2019
9788(265*10^74579+17)/374581Robert Price05/2016
978917798^15489+15489^1779874575Hans Havermann11/2019
9790(2^247759-1017)/331831171774574Lelio R Paula07/2012
97915^106682-2474568Lelio R Paula08/2014
9792(2^247686+1450)/274561Stefano Morozzi01/2020
9793474^27863+27863^47474556Norbert Schneider01/2017
9794(14*10^74540+79)/374541Robert Price11/2017
9795(2^247582+1630)/274530Stefano Morozzi01/2020
9796(35365^16384+1)/274524Lelio R Paula11/2011
9797(1705^23059-1)/170474518Serge Batalov08/2020
97983^156161+266074508Lelio R Paula01/2015
98002^247474-5869574498Lelio R Paula05/2013
9799(2^247476+886)/274498Stefano Morozzi01/2020
980111^71519-9074480Enzo Doria07/2012
9802(19*2^247419-1)/2320298374475Lelio R Paula01/2014
9804(2^247394-7)/374473Lelio R Paula06/2012
980318^59328+1774473Lelio R Paula01/2015
98052^247379-18174469Lelio R Paula03/2012
9806(15*2^247370-1)/47974465Lelio R Paula01/2014
980718860^8877+8877^1886074465Hans Havermann12/2019
980817355^17564-17564^1735574462Norbert Schneider11/2019
98092^247344+204774458Lelio R Paula05/2013
98102^247311-101774449Lelio R Paula05/2013
9811(2^247288+1938)/274441Stefano Morozzi01/2020
98122^247280+774439Lelio R Paula03/2012
9813(68*10^74434+13)/974435Ray Chandler11/2010
98143^156004-6274433Lelio R Paula01/2015
981521865^2536+2536^2186574432Hans Havermann11/2019
9816(2^247223+1050)/274422Stefano Morozzi01/2020
981736095!2-6474416Robert Price06/2015
981867699!4+1674409Robert Price09/2019
98192^247165-374405M. Frind & P. Underwood07/2002
98202^247150+3276974400Lelio R Paula05/2013
9821(2^247130+3858)/274394Stefano Morozzi01/2020
9822(2^247055+2426)/274371Stefano Morozzi01/2020
982312^68911+7374368Lelio R Paula01/2015
98242^246999+7490374355Enzo Doria04/2016
98252^246989-11064374352Enzo Doria05/2014
982610^74350+27943974351Patrick De Geest07/2017
9829(10^74350+11)/374350Robert Price11/2014
982710^74350-40000000174350Robert Price07/2017
982810^74350-71624174350Patrick De Geest07/2017
983067647!4-51274346Robert Price11/2019
983110^74335+1365974336Patrick De Geest05/2013
983210^74335-5374335Robert Price05/2011
983323360^1521+1521^2336074335Hans Havermann11/2019
9834(2^246914+3418)/274329Stefano Morozzi01/2020
98352^246906-121574327Lelio R Paula05/2013
9836(2^246879+1494)/274318Stefano Morozzi01/2020
98372^246848+11174309Lelio R Paula03/2012
9838(2^246842+2490)/274307Stefano Morozzi01/2020
98406^95490-1844374306Enzo Doria03/2013
9839(2^246840+2902)/274306Stefano Morozzi01/2020
984118^59188-236974298Enzo Doria03/2013
9842(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
98432^246744+4075574278Lelio R Paula05/2013
9844(29*10^74276+91)/374277Robert Price03/2016
984517222^17533-17533^1722274272Norbert Schneider11/2019
9846(2^246720+3606)/274270Stefano Morozzi01/2020
98476^95441+16374268Lelio R Paula01/2015
9848(40734^16111-1)/4073374267Anonymous11/2020
9849(14235^17881-1)/1423474263Serge Batalov08/2020
9850V(390863)74258Serge Batalov03/2015
985110^74254+9174255Robert Price03/2011
9853(19*10^74253-1)/974254Ray Chandler02/2012
985210^74254-13056974254Patrick De Geest05/2013
9854771^25718+25718^77174250Norbert Schneider10/2016
98552^246618+42774240Henri Lifchitz02/2005
985688*10^74234+374236Robert Price11/2016
98578*10^74234-4974235Robert Price04/2016
9858(19648^17291-1)/1964774232Serge Batalov08/2020
98592^246578+1228574228Lelio R Paula05/2013
9860(3^155569-5)/274225Lelio R Paula06/2012
986113^66628+4674220Lelio R Paula01/2015
9862(2^246534+3034)/274214Stefano Morozzi01/2020
9863(2^246486+798)/274200Stefano Morozzi01/2020
98642^246476-1729574197Lelio R Paula05/2013
9865(2^246465+446)/274194Stefano Morozzi01/2020
9866(61*10^74189-1)/374191Robert Price11/2017
9867(15185*2^246432-1)/1374187Lelio R Paula04/2015
98685*2^246413-374179Lelio R Paula05/2014
98692^246386-2863574170Lelio R Paula05/2013
9870(2^246371+3050)/274165Stefano Morozzi01/2020
98712^246334-11124574154Enzo Doria05/2014
98723*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
987315^63045+8274147Lelio R Paula01/2015
987419255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
9875(199^32251-1)/19874139Serge Batalov08/2020
9876(2^246277+2114)/274137Stefano Morozzi01/2020
98772^246268-11050774135Enzo Doria05/2014
98783^155328+266074111Lelio R Paula01/2015
98802^246148-278624974098Enzo Doria03/2016
987919740^5671+5671^1974074098Hans Havermann01/2020
9881(2^246135+3386)/274094Stefano Morozzi01/2020
9882(16*10^74092-19)/374093Robert Price03/2016
98832^246115-11076774088Enzo Doria05/2014
98847^87666-6874087Lelio R Paula08/2014
9885(2^246091+1938)/274081Stefano Morozzi01/2020
988610^74079+114514191974080Marisa Kirisame03/2015
988710^74079+621974080Patrick De Geest03/2016
988810^74079-28270774079Patrick De Geest03/2016
9889129^35098+274078Lelio R Paula05/2013
989022193^2176+2176^2219374073Hans Havermann12/2019
989117703^15278+15278^1770374071Hans Havermann12/2019
98922^246025-11212374061Enzo Doria06/2014
9893(67*10^74045+17)/374047Robert Price02/2017
9894(2^245944+2202)/274037Stefano Morozzi01/2020
9895(2^245885+1446)/274019Stefano Morozzi01/2020
9896(13769^17881-1)/1376874004Serge Batalov08/2020
98972^245823+6683174001Marek Hubal02/2017
98985^105869+4274000Lelio R Paula08/2014
9899(21*2^245806+1)/63455573991Lelio R Paula08/2012
9900(22699*2^245762+1)/11973985Lelio R Paula06/2014
9901(3^155048-7)/26273975Lelio R Paula06/2012
99029998*2^245696+373966Donovan Johnson10/2004
990313^66400-8073966Lelio R Paula01/2015
9905(2^245704+9)/2573963Lelio R Paula07/2012
990611^71023-717073963Enzo Doria01/2013
99043*10^73962+1373963Robert Price08/2017
9907(64758^15373-1)/6475773960Anonymous11/2020
9908(31*2^245660-1)/11419573948Lelio R Paula01/2014
99092^245629-279781373942Eric Chen03/2016
99102^245557-15373921Lelio R Paula03/2012
9911(77*10^73917-59)/973918Robert Price11/2017
991215010^17699+17699^1501073918Norbert Schneider11/2019
9913(12975^17971-1)/1297473913Serge Batalov08/2020
99142^245525+186988173911Enzo Doria06/2016
99152^245522+15973910Lelio R Paula03/2012
9916(2^245507+1986)/273905Stefano Morozzi01/2020
9917(13*10^73891-43)/373892Robert Price08/2017
991819^57783-5673891Lelio R Paula01/2015
99197*10^73888+7973889Robert Price02/2017
9920(2^245449+942)/273888Stefano Morozzi01/2020
99216^94948+17428173884Mike Oakes02/2011
9922(2^245431+3630)/273882Stefano Morozzi01/2020
992311^70939-486073876Enzo Doria01/2013
992418637^9196+9196^1863773870Hans Havermann01/2020
99252^245372+5461573865Lelio R Paula05/2013
99262^245362-14373862Lelio R Paula03/2012
99277^87396+6^(87396-1)73859Robert Price03/2016
9928(22*10^73853-37)/373854Robert Price05/2017
99295*10^73851-6973852Robert Price02/2021
99305^105646-1424673844Enzo Doria02/2013
99322^245290-4173840Lelio R Paula03/2012
99312^245290-9439573840Lelio R Paula05/2013
993315770^17589+17589^1577073836Norbert Schneider10/2019
993412352^18043+18043^1235273828Norbert Schneider11/2019
9935(2^245240+3598)/273825Stefano Morozzi01/2020
9936(2^245242+498)/273825Stefano Morozzi01/2020
99378*5^105600-773813Lelio R Paula10/2014
99387*5^105573-473794Lelio R Paula10/2014
9939(2^245112+1122)/273786Stefano Morozzi01/2020
994020151^4570+4570^2015173751Hans Havermann12/2019
9941(2^244968+1318)/273743Stefano Morozzi01/2020
994218^58742-480573738Enzo Doria03/2013
9943(7*10^73729+23)/373730Robert Price06/2020
994413^66179+6673720Lelio R Paula01/2015
9945(2^244881+942)/273717Stefano Morozzi01/2020
9946(2^244883+1946)/273717Stefano Morozzi01/2020
9947(82*10^73714-1)/973715Robert Price12/2014
9948(2^244862+3682)/273711Stefano Morozzi01/2020
9949(29*2^244856-1)/18612173706Lelio R Paula01/2014
9950(13*2^244840-1)/279973702Lelio R Paula01/2014
9951(13*10^73701+17)/373702Robert Price06/2015
99522339662057597*10^73677+973690Robert Price03/2021
99536*10^73686-2973687Robert Price08/2020
9954(2^244787-1017)/2841173684Lelio R Paula07/2012
995521213^2974+2974^2121373680Hans Havermann01/2020
9956(3^154421-4)/2373677Lelio R Paula06/2012
995714596^17691+17691^1459673670Norbert Schneider11/2019
99588*7^87170+573669Lelio R Paula10/2014
9959(29*10^73659-113)/373660Robert Price11/2017
9960Phi(40100,-40100)73651Henri Lifchitz06/2013
9961(3883^20521-1)/388273650Serge Batalov08/2020
9962(4*10^73647-19)/373648Robert Price06/2017
99632^244618-229773638Yves Minet10/2009
99643*5^105344+873633Lelio R Paula10/2014
9965(2^244588+2562)/273629Stefano Morozzi01/2020
99665^105334-1409673626Enzo Doria02/2013
9967(2^244562+1534)/273621Stefano Morozzi01/2020
9968(2^244584-7)/1323707424303373614Lelio R Paula07/2012
99692^244465-11018573592Enzo Doria05/2014
9970(2^244465+2934)/273591Stefano Morozzi01/2020
99712^244443+4075573585Lelio R Paula05/2013
997223155^1506+1506^2315573583Hans Havermann12/2019
997310^73579+98765432173580Robert Price12/2019
997410^73579+12417373580Patrick De Geest02/2020
997510^73579-17637973579Patrick De Geest02/2020
99762^244404+384173573Yves Minet03/2011
997719770^5263+5263^1977073569Hans Havermann12/2019
99789*10^73565-4173566Robert Price08/2020
99792^244372-11062773564Enzo Doria05/2014
998019778^5241+5241^1977873563Hans Havermann12/2019
9981(2^244349+2186)/273557Stefano Morozzi01/2020
9982(2^244309+3710)/273545Stefano Morozzi01/2020
998318428^9783+9783^1842873537Hans Havermann01/2020
9984(3*2^244255+1)/24573527Lelio R Paula08/2012
9985(11*2^244245+1)/2373525Lelio R Paula08/2012
998618140^11301+11301^1814073524Hans Havermann12/2019
9987(15185*2^244187-1)/611173509Lelio R Paula04/2015
9988(9699^18439-1)/969873508Serge Batalov08/2020
9989(2^244152+2058)/273497Stefano Morozzi01/2020
9990(2^244109+1422)/273484Stefano Morozzi01/2020
999117063^17362+17362^1706373477Norbert Schneider04/2019
9992(91^37507+1)/9273476Paul Bourdelais08/2017
999318^58521+6573460Lelio R Paula01/2015
999413^65940+3673454Lelio R Paula01/2015
999519065^7112+7112^1906573439Hans Havermann12/2019
9996(625^26267+1)/62673437Richard Fischer12/2017
9997(16612^17401-1)/1661173436Serge Batalov08/2020
9998(2^243935+530)/273432Stefano Morozzi01/2020
99995^105050-1473427Lelio R Paula08/2014
10000(2^243850+1474)/273406Stefano Morozzi01/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 12 2021 20:10 (Time in France)

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