PRP Records

Probable Primes Top 10000

(271019 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 ?
8751(22*10^74874-31)/974875Robert Price04/2015
875211^71892-7680000074868Enzo Doria01/2013
87539*5^107107-474866Lelio R Paula10/2014
87542^248678-71011174860Paul Bourdelais03/2013
8755(14*10^74858+211)/974859Robert Price11/2017
875613^67194+1274851Lelio R Paula01/2015
8757(7*2^248634+1)/7174846Lelio R Paula08/2012
875811^71867-309074842Enzo Doria12/2012
875968057!4-1674841Robert Price11/2019
87602^248609+26214574839Lelio R Paula05/2013
87613^156852+5074838Lelio R Paula01/2015
876218^59607-1174824Lelio R Paula01/2015
87632^248556-11050774823Enzo Doria05/2014
87647^88531-3674818Lelio R Paula01/2015
8765p(15738)#/2+102474814Robert Price07/2017
8766(2^248505+422)/274808Stefano Morozzi01/2020
8767(2^248507+1938)/274808Stefano Morozzi01/2020
876821137^3454+3454^2113774790Hans Havermann11/2019
87694*3^156740-574785Lelio R Paula05/2014
877017918^14907+14907^1791874779Hans Havermann12/2019
8771(32*10^74773-41)/974774Robert Price05/2015
8772(29*2^248384-1)/1374772Lelio R Paula01/2014
877319401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
87742^248357-1279741374763Enzo Doria03/2016
877542^46057+4174762Lelio R Paula07/2012
8776(2^248339+1686)/274758Stefano Morozzi01/2020
877711^71784-300074756Enzo Doria12/2012
877819^58458+1874754Lelio R Paula01/2015
877912^69265-3574750Lelio R Paula02/2015
8780(2^248291+830)/274743Stefano Morozzi01/2020
878211^71771-4800074742Enzo Doria12/2012
8781(7*10^74741+197)/374742Robert Price07/2017
8783(2^248282-5)/5012974736Lelio R Paula06/2012
87842^248252-11010574732Enzo Doria04/2014
8785(7*10^74729+71)/374730Robert Price03/2016
87863^156614-5074724Lelio R Paula01/2015
8787(7*2^248213+1)/13574719Lelio R Paula07/2012
8788(2^248193+870)/274714Stefano Morozzi01/2020
8789(2^248167+1178)/274706Stefano Morozzi01/2020
8790(2^248173+78557)/76774705Lelio R Paula07/2012
8791(2^248145+3866)/274699Stefano Morozzi01/2020
8792125^35622+12474697Norbert Schneider02/2015
8793(2^248114+994)/274690Stefano Morozzi01/2020
8794(19*2^248099-1)/2974686Lelio R Paula01/2014
879520780^3927+3927^2078074685Hans Havermann12/2019
8796(86*10^74676-41)/974677Robert Price11/2015
8797(2^248065+3650)/274675Stefano Morozzi01/2020
8798(p(15711)#-4)/274672Robert Price09/2017
879910^74670+3174671Robert Price01/2011
880010^74670-12246374670Patrick De Geest05/2013
88012^248036-6974667Lelio R Paula03/2012
880211^71698-600074666Enzo Doria12/2012
8803(2^248032+406)/274665Stefano Morozzi01/2020
880458*(10^(3*24887)-1)/111-174661Robert Price10/2014
880514^65139-4574658Lelio R Paula01/2015
880617967^14288+14288^1796774653Hans Havermann11/2019
88076^95921-13374642Lelio R Paula01/2015
880811^71675+7874642Lelio R Paula02/2015
880917875^14986+14986^1787574641Hans Havermann12/2019
8810(2^247931+1458)/274635Stefano Morozzi01/2020
881118^59449-9174625Lelio R Paula01/2015
8812(12696^18181-1)/1269574605Serge Batalov08/2020
88136^95864-1604374597Enzo Doria02/2013
88145*7^88261+674590Lelio R Paula10/2014
88159*5^106710+474589Lelio R Paula10/2014
8816(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
881721157^3352+3352^2115774585Hans Havermann12/2019
8818(265*10^74579+17)/374581Robert Price05/2016
881917798^15489+15489^1779874575Hans Havermann11/2019
8820(2^247759-1017)/331831171774574Lelio R Paula07/2012
88215^106682-2474568Lelio R Paula08/2014
8822(2^247686+1450)/274561Stefano Morozzi01/2020
8823474^27863+27863^47474556Norbert Schneider01/2017
8824(14*10^74540+79)/374541Robert Price11/2017
8825(2^247582+1630)/274530Stefano Morozzi01/2020
8826(35365^16384+1)/274524Lelio R Paula11/2011
8827(1705^23059-1)/170474518Serge Batalov08/2020
88283^156161+266074508Lelio R Paula01/2015
88302^247474-5869574498Lelio R Paula05/2013
8829(2^247476+886)/274498Stefano Morozzi01/2020
883111^71519-9074480Enzo Doria07/2012
8832(19*2^247419-1)/2320298374475Lelio R Paula01/2014
8834(2^247394-7)/374473Lelio R Paula06/2012
883318^59328+1774473Lelio R Paula01/2015
88352^247379-18174469Lelio R Paula03/2012
8836(15*2^247370-1)/47974465Lelio R Paula01/2014
883718860^8877+8877^1886074465Hans Havermann12/2019
883817355^17564-17564^1735574462Norbert Schneider11/2019
88392^247344+204774458Lelio R Paula05/2013
88402^247311-101774449Lelio R Paula05/2013
8841(2^247288+1938)/274441Stefano Morozzi01/2020
88422^247280+774439Lelio R Paula03/2012
8843(68*10^74434+13)/974435Ray Chandler11/2010
88443^156004-6274433Lelio R Paula01/2015
884521865^2536+2536^2186574432Hans Havermann11/2019
8846(2^247223+1050)/274422Stefano Morozzi01/2020
884736095!2-6474416Robert Price06/2015
884867699!4+1674409Robert Price09/2019
88492^247165-374405M. Frind & P. Underwood07/2002
88502^247150+3276974400Lelio R Paula05/2013
8851(2^247130+3858)/274394Stefano Morozzi01/2020
8852(2^247055+2426)/274371Stefano Morozzi01/2020
885312^68911+7374368Lelio R Paula01/2015
88542^246999+7490374355Enzo Doria04/2016
88552^246989-11064374352Enzo Doria05/2014
885610^74350+27943974351Patrick De Geest07/2017
8859(10^74350+11)/374350Robert Price11/2014
885710^74350-40000000174350Robert Price07/2017
885810^74350-71624174350Patrick De Geest07/2017
886067647!4-51274346Robert Price11/2019
886110^74335+1365974336Patrick De Geest05/2013
886210^74335-5374335Robert Price05/2011
886323360^1521+1521^2336074335Hans Havermann11/2019
8864(2^246914+3418)/274329Stefano Morozzi01/2020
88652^246906-121574327Lelio R Paula05/2013
8866(2^246879+1494)/274318Stefano Morozzi01/2020
88672^246848+11174309Lelio R Paula03/2012
8868(2^246842+2490)/274307Stefano Morozzi01/2020
88706^95490-1844374306Enzo Doria03/2013
8869(2^246840+2902)/274306Stefano Morozzi01/2020
887118^59188-236974298Enzo Doria03/2013
8872(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
88732^246744+4075574278Lelio R Paula05/2013
8874(29*10^74276+91)/374277Robert Price03/2016
887517222^17533-17533^1722274272Norbert Schneider11/2019
8876(2^246720+3606)/274270Stefano Morozzi01/2020
88776^95441+16374268Lelio R Paula01/2015
8878(14235^17881-1)/1423474263Serge Batalov08/2020
8879V(390863)74258Serge Batalov03/2015
888010^74254+9174255Robert Price03/2011
8882(19*10^74253-1)/974254Ray Chandler02/2012
888110^74254-13056974254Patrick De Geest05/2013
8883771^25718+25718^77174250Norbert Schneider10/2016
88842^246618+42774240Henri Lifchitz02/2005
888588*10^74234+374236Robert Price11/2016
88868*10^74234-4974235Robert Price04/2016
8887(19648^17291-1)/1964774232Serge Batalov08/2020
88882^246578+1228574228Lelio R Paula05/2013
8889(3^155569-5)/274225Lelio R Paula06/2012
889013^66628+4674220Lelio R Paula01/2015
8891(2^246534+3034)/274214Stefano Morozzi01/2020
8892(2^246486+798)/274200Stefano Morozzi01/2020
88932^246476-1729574197Lelio R Paula05/2013
8894(2^246465+446)/274194Stefano Morozzi01/2020
8895(61*10^74189-1)/374191Robert Price11/2017
8896(15185*2^246432-1)/1374187Lelio R Paula04/2015
88975*2^246413-374179Lelio R Paula05/2014
88982^246386-2863574170Lelio R Paula05/2013
8899(2^246371+3050)/274165Stefano Morozzi01/2020
89002^246334-11124574154Enzo Doria05/2014
89013*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
890215^63045+8274147Lelio R Paula01/2015
890319255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
8904(199^32251-1)/19874139Serge Batalov08/2020
8905(2^246277+2114)/274137Stefano Morozzi01/2020
89062^246268-11050774135Enzo Doria05/2014
89073^155328+266074111Lelio R Paula01/2015
89092^246148-278624974098Enzo Doria03/2016
890819740^5671+5671^1974074098Hans Havermann01/2020
8910(2^246135+3386)/274094Stefano Morozzi01/2020
8911(16*10^74092-19)/374093Robert Price03/2016
89122^246115-11076774088Enzo Doria05/2014
89137^87666-6874087Lelio R Paula08/2014
8914(2^246091+1938)/274081Stefano Morozzi01/2020
891610^74079+114514191974080Marisa Kirisame03/2015
891510^74079+621974080Patrick De Geest03/2016
891710^74079-28270774079Patrick De Geest03/2016
8918129^35098+274078Lelio R Paula05/2013
891922193^2176+2176^2219374073Hans Havermann12/2019
892017703^15278+15278^1770374071Hans Havermann12/2019
89212^246025-11212374061Enzo Doria06/2014
8922(67*10^74045+17)/374047Robert Price02/2017
8923(2^245944+2202)/274037Stefano Morozzi01/2020
8924(2^245885+1446)/274019Stefano Morozzi01/2020
8925(13769^17881-1)/1376874004Serge Batalov08/2020
89262^245823+6683174001Marek Hubal02/2017
89275^105869+4274000Lelio R Paula08/2014
8928(21*2^245806+1)/63455573991Lelio R Paula08/2012
8929(22699*2^245762+1)/11973985Lelio R Paula06/2014
8930(3^155048-7)/26273975Lelio R Paula06/2012
89319998*2^245696+373966Donovan Johnson10/2004
893213^66400-8073966Lelio R Paula01/2015
8934(2^245704+9)/2573963Lelio R Paula07/2012
893511^71023-717073963Enzo Doria01/2013
89333*10^73962+1373963Robert Price08/2017
8936(31*2^245660-1)/11419573948Lelio R Paula01/2014
89372^245629-279781373942Eric Chen03/2016
89382^245557-15373921Lelio R Paula03/2012
8939(77*10^73917-59)/973918Robert Price11/2017
894015010^17699+17699^1501073918Norbert Schneider11/2019
8941(12975^17971-1)/1297473913Serge Batalov08/2020
89422^245525+186988173911Enzo Doria06/2016
89432^245522+15973910Lelio R Paula03/2012
8944(2^245507+1986)/273905Stefano Morozzi01/2020
8945(13*10^73891-43)/373892Robert Price08/2017
894619^57783-5673891Lelio R Paula01/2015
89477*10^73888+7973889Robert Price02/2017
8948(2^245449+942)/273888Stefano Morozzi01/2020
89496^94948+17428173884Mike Oakes02/2011
8950(2^245431+3630)/273882Stefano Morozzi01/2020
895111^70939-486073876Enzo Doria01/2013
895218637^9196+9196^1863773870Hans Havermann01/2020
89532^245372+5461573865Lelio R Paula05/2013
89542^245362-14373862Lelio R Paula03/2012
89557^87396+6^(87396-1)73859Robert Price03/2016
8956(22*10^73853-37)/373854Robert Price05/2017
89575^105646-1424673844Enzo Doria02/2013
89592^245290-4173840Lelio R Paula03/2012
89582^245290-9439573840Lelio R Paula05/2013
896015770^17589+17589^1577073836Norbert Schneider10/2019
896112352^18043+18043^1235273828Norbert Schneider11/2019
8962(2^245240+3598)/273825Stefano Morozzi01/2020
8963(2^245242+498)/273825Stefano Morozzi01/2020
89648*5^105600-773813Lelio R Paula10/2014
89657*5^105573-473794Lelio R Paula10/2014
8966(2^245112+1122)/273786Stefano Morozzi01/2020
896720151^4570+4570^2015173751Hans Havermann12/2019
8968(2^244968+1318)/273743Stefano Morozzi01/2020
896918^58742-480573738Enzo Doria03/2013
8970(7*10^73729+23)/373730Robert Price06/2020
897113^66179+6673720Lelio R Paula01/2015
8972(2^244881+942)/273717Stefano Morozzi01/2020
8973(2^244883+1946)/273717Stefano Morozzi01/2020
8974(82*10^73714-1)/973715Robert Price12/2014
8975(2^244862+3682)/273711Stefano Morozzi01/2020
8976(29*2^244856-1)/18612173706Lelio R Paula01/2014
8977(13*2^244840-1)/279973702Lelio R Paula01/2014
8978(13*10^73701+17)/373702Robert Price06/2015
89796*10^73686-2973687Robert Price08/2020
8980(2^244787-1017)/2841173684Lelio R Paula07/2012
898121213^2974+2974^2121373680Hans Havermann01/2020
8982(3^154421-4)/2373677Lelio R Paula06/2012
898314596^17691+17691^1459673670Norbert Schneider11/2019
89848*7^87170+573669Lelio R Paula10/2014
8985(29*10^73659-113)/373660Robert Price11/2017
8986Phi(40100,-40100)73651Henri Lifchitz06/2013
8987(3883^20521-1)/388273650Serge Batalov08/2020
8988(4*10^73647-19)/373648Robert Price06/2017
89892^244618-229773638Yves Minet10/2009
89903*5^105344+873633Lelio R Paula10/2014
8991(2^244588+2562)/273629Stefano Morozzi01/2020
89925^105334-1409673626Enzo Doria02/2013
8993(2^244562+1534)/273621Stefano Morozzi01/2020
8994(2^244584-7)/1323707424303373614Lelio R Paula07/2012
89952^244465-11018573592Enzo Doria05/2014
8996(2^244465+2934)/273591Stefano Morozzi01/2020
89972^244443+4075573585Lelio R Paula05/2013
899823155^1506+1506^2315573583Hans Havermann12/2019
899910^73579+98765432173580Robert Price12/2019
900010^73579+12417373580Patrick De Geest02/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

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