PRP Records

Probable Primes Top 10000

(212140 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 ?
4501(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4502(3^183915+5)/12887748Lelio R Paula01/2013
450319^68619+2487747Lelio R Paula12/2015
45052^291480+118587745Lelio R Paula10/2013
45042^291482+186736987745Enzo Doria03/2016
45062^291467-93787741Yves Minet05/2013
4507(25*10^87726+161)/387727Robert Price01/2017
450811^84239-285087726Enzo Doria12/2012
450910^87720+21554187721Patrick De Geest01/2011
451010^87720-387720Markus Tervooren07/2010
4511(5*10^87712-473)/987712Robert Price12/2017
4512(2^291357+5)/684787704Lelio R Paula01/2013
451493^44541-287679Lelio R Paula09/2013
45132^291261-10956187679Enzo Doria04/2014
4515(4*10^87669+149)/987669Robert Price03/2017
45162^291217+425787666Lelio R Paula10/2013
45172*12^81214-5^8121487645Mike Oakes12/2010
4518(5*10^87622-473)/987622Robert Price12/2017
451912^81188+8587617Lelio R Paula11/2015
4520(21*2^290980-1)/587595Lelio R Paula02/2014
45212^290958+12787588Lelio R Paula09/2012
45222^290923-6787577Lelio R Paula09/2012
45233*10^87573-9787574Robert Price08/2017
4524(13*10^87565+11)/387566Robert Price05/2015
4525(2^290857-7)/5587555Lelio R Paula01/2013
45262^290802+8287587541Lelio R Paula10/2013
4527(509203*2^290792-1)/756098787536Lelio R Paula04/2015
45283^183441+23687524Lelio R Paula12/2015
45292^290618-3387485Lelio R Paula09/2012
4530(184*10^87473-1)/387475Robert Price02/2017
45312^290534-11515187460Enzo Doria06/2015
45322^290512-10975787453Enzo Doria04/2014
4533(32*10^87448-41)/987449Robert Price05/2015
4534(2^290491+9)/317987444Lelio R Paula01/2013
4535(25*2^290489-1)/5180987443Lelio R Paula02/2014
45362^290426+8287587427Lelio R Paula11/2013
45373*2^290415-787425Lelio R Paula08/2014
453810^87408+5787409Robert Price03/2011
45392^290366+7477987409Enzo Doria04/2016
454010^87408-12356987408Patrick De Geest07/2013
45412^290265+5890587379Lelio R Paula10/2013
45427^103391+1687376Lelio R Paula10/2015
4543(115*10^87368-7)/987370Robert Price11/2017
4544(92^44491-1)/9187369Paul Bourdelais08/2017
45458*7^103379+387367Lelio R Paula10/2014
4546(2^290226+7)/7187365Lelio R Paula01/2013
454713^78407-3087341Lelio R Paula11/2015
45484*10^87337-9987338Robert Price12/2016
45497*10^87319+3987320Robert Price07/2016
45503*5^124921+287317Lelio R Paula10/2014
45513^182984+8887306Lelio R Paula12/2015
45524*10^87287-9987288Robert Price12/2016
455311^83813-186087283Enzo Doria12/2012
4554734^30453+30453^73487270Norbert Schneider04/2017
455512^80855+2987258Lelio R Paula11/2015
45563*6^112119-587247Lelio R Paula10/2014
455712^80806+7987205Lelio R Paula11/2015
455891382^9+9^9138287201Andrey Kulsha11/2004
4559(21181*2^289657+1)/8187198Lelio R Paula06/2014
45606^112054-4787195Lelio R Paula12/2015
4561(55459*2^289632+1)/5587191Lelio R Paula06/2014
456215^74131-6887185Lelio R Paula11/2015
45632^289583-74187174Lelio R Paula10/2013
45647^103146+1287169Lelio R Paula10/2015
45655*2^289556-387166Lelio R Paula08/2014
45662^289543-11273587162Enzo Doria06/2014
45678*3^182655-787150Lelio R Paula08/2014
45682*10^87144+8187145Robert Price01/2017
45697^103106+2*3^10310687135Mike Oakes08/2010
45708*3^182614+787130Lelio R Paula08/2014
4571(2^289368-509203)/987108Lelio R Paula01/2013
45723^182566+1487107Robert Price09/2013
4573(3^182385-5)/287020Lelio R Paula01/2013
457411^83534-886992Lelio R Paula11/2015
45754^144479-1426786986Mike Oakes03/2011
4576(145*10^86982-1)/986984Serge Batalov12/2014
4577(151*10^86963-1)/386965Robert Price04/2017
457815^73940-5886961Lelio R Paula11/2015
45792^288761-11314386926Enzo Doria07/2014
45802^288747+308386922Yves Minet03/2011
458130^58842+2986917Norbert Schneider03/2017
4582(10^86906-13)/386906Robert Price02/2017
45832^288692-11002786905Enzo Doria04/2014
4584(2^288682+7)/25989544986894Lelio R Paula01/2013
4585(2^288636+47)/129386885Lelio R Paula01/2013
45863^182089-3486879Robert Price11/2013
45872^288543-10980186861Enzo Doria04/2014
458860^48847-5986858Norbert Schneider10/2014
45892^288470-6487586839Lelio R Paula10/2013
459010^86816+3299786817Patrick De Geest07/2013
459110^86816-9986816Robert Price05/2011
4592(89*10^86802-539)/986803Robert Price11/2017
459341487!2+25686786Robert Price01/2015
4594(5*2^288301-1)/99986785Lelio R Paula02/2014
45952^288243+7604386770Enzo Doria04/2016
4596(29*2^288232+1)/1586767Lelio R Paula01/2013
45979*6^111495+586761Lelio R Paula10/2014
4598(5*2^288202+1)/8186757Lelio R Paula01/2013
45999*7^102654-286754Lelio R Paula10/2014
46002^288122-11284186734Enzo Doria06/2014
46015^124062-6886716Lelio R Paula10/2015
4602(2^288007-3)/12586697Lelio R Paula01/2013
4603379*10^86691+986694Arkadiusz Wesolowski10/2011
46047^102555+4886670Lelio R Paula10/2015
460577779!4+286660Robert Price08/2017
46062^287809-11135586640Enzo Doria05/2014
4607(47*2^287795+1)/786636Lelio R Paula04/2015
46089*7^102504+886627Lelio R Paula10/2014
46093^181551+3286622Robert Price11/2013
46102^287735-52134786617Paul Bourdelais05/2013
4611(1017*2^287600-1)/9186578Lelio R Paula04/2015
46122^287540-11296786559Enzo Doria06/2014
46133^181407+2086554Robert Price10/2013
4614(13*10^86546+83)/386547Robert Price09/2016
46153^181378-2^(181378-1)86540Robert Price01/2016
461683^45080-286513Lelio R Paula08/2013
4617(78557*2^287351+1)/61186504Lelio R Paula06/2014
461825*29^59147+2093686498Curtis Bright05/2015
46192^287298+187135986486Enzo Doria05/2016
46203*10^86478+8986479Robert Price03/2017
46212^287272-7904986478Paul Bourdelais02/2012
4622906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4623811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4624779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4625768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4626700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4627652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4628377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4629255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4630187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4631(10^86453-1)/986453Lew Baxter10/2000
463287^44563-86^4456386431Robert Price05/2015
46336^111057+6186420Lelio R Paula12/2015
46342^287057-10990986413Enzo Doria04/2014
46355^123608+2286399Lelio R Paula10/2015
4636(31*10^86364-121)/986365Robert Price06/2016
46372^286859+7166386354Enzo Doria04/2016
46382^286740+2983586318Lelio R Paula10/2013
46392*10^86310+9^8631086311Mike Oakes05/2011
464011^82878-186086309Enzo Doria12/2012
46412^286547+1609586260Lelio R Paula10/2013
4642(58*10^86242+329)/986243Robert Price11/2017
46432^286455-11042786232Enzo Doria05/2014
4644(37*10^86230+53)/986231Robert Price05/2015
46458*3^180700+586217Lelio R Paula08/2014
46463^180697-4086215Lelio R Paula12/2015
4647(13*2^286318-1)/1325786188Lelio R Paula02/2014
46482^286165+7786145Lelio R Paula08/2012
46499*2^286140+786138Lelio R Paula08/2014
4650(29*2^286108-1)/200236786123Lelio R Paula02/2014
465110^86110+16111386111Patrick De Geest07/2013
465210^86110-6986110Robert Price05/2011
46532^286036-86968810586106Lelio R Paula07/2016
4654(77*10^86072+31)/986073Robert Price10/2015
46552^285923+34586072Lelio R Paula09/2013
465613^77266-9086070Lelio R Paula11/2015
46572^285910-45890386068Enzo Doria04/2015
46582^285904-12586066Lelio R Paula08/2012
46592^285836+6583586046Lelio R Paula09/2013
4660(2^285766+78557)/386024Lelio R Paula01/2013
4661(5*10^86011-107)/386012Robert Price01/2017
46626^110522+16386003Lelio R Paula12/2015
466341^53323-40^5332385999Robert Price07/2012
46642^285678-10961785998Enzo Doria04/2014
46656^110506-1667385991Enzo Doria02/2013
46672^285569-74185965Lelio R Paula09/2013
4666(32*10^85964+31)/985965Robert Price05/2015
46686*10^85910-785911Dmitry Domanov11/2010
4669(412*10^85897-7)/985899Robert Price10/2017
46704*10^85881+6385882Robert Price06/2016
4671(10^85864+53)/985864Robert Price01/2015
46722^285230+34585863Lelio R Paula09/2013
4673(5*10^85855-473)/985855Robert Price12/2017
46742^285199+7568385854Enzo Doria04/2016
4675(76*10^85847-211)/985848Robert Price10/2017
4676p(17832)#/2+51285845Robert Price05/2017
4677(16*10^85839+167)/385840Robert Price10/2017
467811^82426-123085838Enzo Doria11/2012
46792^285113-10988185828Enzo Doria04/2014
46805^122746-9285796Lelio R Paula10/2015
46812^285001-11346185794Enzo Doria08/2014
4682(11*10^85782-131)/385783Robert Price02/2017
46832^284913-11049185768Enzo Doria05/2014
46846^110220+4785768Lelio R Paula12/2015
46853*6^110202-585755Lelio R Paula10/2014
4686(157^39047-1)/15685742Alexander Zhirkov06/2016
4687(3^179705+7)/25085739Lelio R Paula12/2012
46882^284734-655585714Lelio R Paula09/2013
4689(10^85712+53)/985712Robert Price01/2015
46903*10^85703+1185704Robert Price11/2017
4691(6883*2^284668-1)/385697Lelio R Paula04/2015
469220^65855+8385680Lelio R Paula01/2016
46936^110105+5385679Lelio R Paula12/2015
4694(10^85666-97)/385666Robert Kinser10/2017
46952^284567-760585664Lelio R Paula09/2013
46969*5^122555-285664Lelio R Paula10/2014
46975^122554-1485662Lelio R Paula10/2015
46989*5^122543+485655Lelio R Paula10/2014
46993^179489-2^(179489-1)85639Robert Price01/2016
47002^284429+17785622Lelio R Paula08/2012
47012*3^179452+585621Lelio R Paula07/2014
4702(19^66919+3^66919)/2285572Robert Price07/2013
470366^47023-6585561Norbert Schneider11/2014
47046^109943+1385553Lelio R Paula12/2015
4705(2^284167-509203)/3456477585536Lelio R Paula01/2013
47062^284133-385533M. Frind & P. Underwood07/2002
47072^284113+31585527Lelio R Paula09/2013
4708(28*10^85500+149)/385501Robert Price10/2017
4709(16*10^85495-19)/385496Robert Price03/2016
47102^284004+17785494Lelio R Paula08/2012
4711(16*10^85473-91)/385474Robert Price06/2016
47123^179120+2285462Robert Price12/2013
47132^283872-279224985454Enzo Doria03/2016
4714(29*10^85438+259)/985439Robert Price04/2017
47152^283817+8287585438Lelio R Paula09/2013
4716(2^283815-5)/20185435Lelio R Paula01/2013
47172^283796-12585432Lelio R Paula08/2012
4718(29*2^283784-1)/1385428Lelio R Paula02/2014
471915^72592-2885375Lelio R Paula11/2015
47202^283604-5869585374Lelio R Paula09/2013
4721(44*10^85370-503)/985371Robert Price10/2017
4722496^31671+31671^49685369Norbert Schneider07/2017
4723(15*2^283583-1)/10305185364Lelio R Paula02/2014
472415^72572+9285352Lelio R Paula11/2015
47252^283473-161585334Lelio R Paula09/2013
47262^283466-1585332Lelio R Paula08/2012
472711^81916-702085307Enzo Doria02/2013
47286^109626-785306Lelio R Paula11/2014
47292^283374-11032785305Enzo Doria05/2014
473033*10^85297+785299Robert Price07/2016
473118^67933+4185275Lelio R Paula11/2015
47322^283271-10934185274Enzo Doria04/2014
4733(25*10^85249-73)/385250Robert Price09/2016
47342*5^121959+385246Lelio R Paula10/2014
473519834^19834+894785235Henri Lifchitz11/2004
47362^283140+191585234Lelio R Paula09/2013
47373*10^85227-9785228Robert Price08/2017
4738(16*10^85221-31)/385222Robert Price03/2016
47392^283083+186938385217Enzo Doria05/2016
4740(24737*2^283051+1)/1785211Lelio R Paula06/2014
4741(2^283032+78557)/385201Lelio R Paula01/2013
47422^283026-10989385200Enzo Doria04/2014
4743(2^283012+78557)/12985193Lelio R Paula01/2013
4744(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
47452^282860-10972785150Enzo Doria04/2014
47462^282819+186941385138Enzo Doria05/2016
47473^178428+285132Ray Chandler07/2011
4748(22699*2^282742+1)/7385117Lelio R Paula06/2014
4749(16^70687+5^70687)/2185115Robert Price07/2013
4750(3^178352-2)/785095Lelio R Paula12/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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