PRP Records

Probable Primes Top 10000

(271023 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
825119376^10365+10365^1937677806Hans Havermann04/2020
825265^42916+2877803Lelio R Paula01/2016
8253(2^258405+3302)/277788Stefano Morozzi01/2020
8254(89*10^77781-17)/977782Robert Price11/2015
82552^258382-11040577781Enzo Doria05/2014
82575^111278-1499677780Enzo Doria02/2013
8256(2^258378+2314)/277780Stefano Morozzi01/2020
825814^67862+6177779Lelio R Paula02/2015
825910^77777+4848377778Patrick De Geest11/2010
826010^77777-18324377777Patrick De Geest11/2010
8261(27*2^258352+1)/4377772Lelio R Paula08/2012
8262(22329^17881-1)/2232877758Serge Batalov08/2020
8263(2^258294+2454)/277754Stefano Morozzi01/2020
8264337^30756-1000277740Enzo Doria07/2012
826510^77726+9977727Robert Price03/2011
826610^77726-8594777726Patrick De Geest06/2013
826789^39870-277723Lelio R Paula08/2013
82687^91966-3277721Lelio R Paula02/2015
826935^50327+277709Lelio R Paula05/2013
827024^56298+2377704Norbert Schneider12/2016
8271(2^258128+3502)/277704Stefano Morozzi01/2020
8273(2^258105+78557)/1977697Lelio R Paula10/2012
8272(2^258102+2842)/277697Stefano Morozzi01/2020
82742^258079+17977690Lelio R Paula03/2012
82762^258062-11311177685Enzo Doria07/2014
8275(21752^17911-1)/2175177685Serge Batalov08/2020
8277(2^258022+2422)/277673Stefano Morozzi01/2020
827810^77669+12345678977670Robert Price10/2019
827910^77669+5912777670Patrick De Geest12/2019
828010^77669-10910377669Patrick De Geest12/2019
8281(2^258002+3822)/277667Stefano Morozzi01/2020
828280^40807-7977660Norbert Schneider03/2015
828370385!4-477658Robert Price11/2019
8284(10^77637+359)/977637Serge Batalov12/2014
82852^257862-16577625Lelio R Paula03/2012
8286(25*2^257853+1)/377623Lelio R Paula07/2012
8287(2^257832+1362)/277615Stefano Morozzi01/2020
8288(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
82896^99728+7177604Lelio R Paula01/2015
82902^257778-11276777599Enzo Doria06/2014
8291(31*2^257771+1)/53777596Lelio R Paula07/2012
8292(2^257762+2214)/277594Stefano Morozzi01/2020
82932^257729-7377585Lelio R Paula03/2012
8294(2^257728+1890)/277584Stefano Morozzi01/2020
82962^257689-6377573Lelio R Paula03/2012
8295(47*10^77572+493)/977573Robert Price11/2017
8297(78557*2^257665+1)/610872577564Lelio R Paula06/2014
8298(5570^20707-1)/556977562Serge Batalov08/2020
8299(3^162563+8)/288577559Lelio R Paula10/2012
83012^257636-11023577557Enzo Doria05/2014
8302(23*10^77556+97)/377557Robert Price02/2017
8300(2^257639+2630)/277557Stefano Morozzi01/2020
8303(2^257625+3354)/277553Stefano Morozzi01/2020
83042^257621-11007177552Enzo Doria04/2014
830519580^9129+9129^1958077546Hans Havermann03/2020
83062^257567-6487577536Lelio R Paula06/2013
8307(18098^18211-1)/1809777532Serge Batalov08/2020
8308(2^257429+2394)/277494Stefano Morozzi01/2020
8309(2^257373+1206)/277477Stefano Morozzi01/2020
83102*7^91674+977474Lelio R Paula10/2014
8311(2^257248+2442)/277440Stefano Morozzi01/2020
8312(17*10^77427-47)/377428Robert Price05/2017
831310^77418+84168377419Patrick De Geest06/2013
831410^77418-3377418Robert Price05/2011
831519^60539-3677415Lelio R Paula03/2015
8316(9562^19447-1)/956177406Serge Batalov08/2020
831737401!!-102477397Robert Price11/2015
8318(2^257095+1410)/277394Stefano Morozzi01/2020
831911^74313-1875077390Enzo Doria12/2012
83202^257044-11288377378Enzo Doria06/2014
83218*10^77377+5177378Robert Price05/2017
8322Phi(258121,2)/71977375Jeppe Stig Nielsen09/2020
83232*7^91553+977372Lelio R Paula10/2014
8324713^27118+27118^71377371Norbert Schneider12/2016
8325(22711^17761-1)/2271077367Serge Batalov08/2020
832618652^14043+14043^1865277359Hans Havermann03/2020
8327(11391^19069-1)/1139077351Serge Batalov08/2020
83286*10^77346-2977347Robert Price08/2020
83292^256920-11115577341Enzo Doria05/2014
83302^256896-655577334Lelio R Paula06/2013
8331(52*10^77322-7)/977323Robert Price12/2014
83322^256849-11293977320Enzo Doria06/2014
833317275^18246+18246^1727577316Norbert Schneider01/2020
8334(4*10^77309-31)/977309Erik Branger05/2011
833520936^4923+4923^2093677301Hans Havermann04/2020
8336(25376^17551-1)/2537577298Serge Batalov08/2020
8337(3^161988+7)/4186477284Lelio R Paula10/2012
8338(14^67421-1)/1377272Paul Bourdelais09/2008
8339(2^256679+3554)/277268Stefano Morozzi01/2020
83415*3^161923-477258Lelio R Paula06/2014
834020465^5958+5958^2046577258Hans Havermann02/2020
8342(2^256591+954)/277242Stefano Morozzi01/2020
834324806^1299+1299^2480677237Hans Havermann05/2020
83442^256552-149977230Yves Minet05/2013
834518339^16258+16258^1833977227Hans Havermann04/2020
834621243^4316+4316^2124377221Hans Havermann04/2020
8347(2^256493+3126)/277212Stefano Morozzi01/2020
83482^256460-11275777203Enzo Doria06/2014
8349(2^256444+2578)/277198Stefano Morozzi01/2020
83502^256398+2329977184Yves Minet02/2011
83512^256391-1155*25639177182Henri Lifchitz03/2005
8352(2^256391-9)/5659377177Lelio R Paula10/2012
8353(7665^19867-1)/766477170Serge Batalov08/2020
8354(2^256338+3834)/277166Stefano Morozzi01/2020
8355(2^256339+546)/277166Stefano Morozzi01/2020
8356(2^256308+9)/1058577153Lelio R Paula10/2012
835721^58348-277149Lelio R Paula08/2013
8358(17*2^256291-1)/478577149Lelio R Paula02/2014
8359(5*2^256274-1)/214177144Lelio R Paula02/2014
8360(2^256244+2326)/277137Stefano Morozzi01/2020
836119^60321+8277136Lelio R Paula03/2015
83625*2^256233-377135Lelio R Paula06/2014
8363(2^256155+1566)/277111Stefano Morozzi01/2020
83643*2^256149+777110Lelio R Paula06/2014
8365(2^256128+1890)/277102Stefano Morozzi01/2020
83663^161594-10677100Lelio R Paula02/2015
83672^256114-18577098Lelio R Paula03/2012
83688^85349-85349^877078Norbert Schneider05/2017
83692^256043-278637777077Enzo Doria03/2016
83702^255973+186994777056Enzo Doria05/2016
837112^71393-4377046Lelio R Paula02/2015
8372(2^255882+3630)/277028Stefano Morozzi01/2020
837315^65490+4477023Lelio R Paula02/2015
8374(3^161411-7)/94077010Lelio R Paula10/2012
8375lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
8377(570^27943-1)/56977005Serge Batalov12/2016
8376(570^27943-1)/(570-1)77005Michael Stocker04/2020
83782^255750-7576989Lelio R Paula03/2012
83793*6^98926-576980Lelio R Paula10/2014
8380(2^255708+478)/276976Stefano Morozzi01/2020
838118^61320-143376974Enzo Doria03/2013
83826^98916-1709376972Enzo Doria02/2013
8383(2^255691+806)/276971Stefano Morozzi01/2020
83842^255659-11013176962Enzo Doria04/2014
838569805!4-12876956Robert Price11/2019
838612^71303+9176949Lelio R Paula02/2015
838718^61298+5976946Lelio R Paula02/2015
8388(223^32768+1)/13107476945Lelio R Paula02/2009
8389(2^255613-5)/28151776942Lelio R Paula10/2012
839018^61290-1176936Lelio R Paula02/2015
8391(2^255567+1286)/276934Stefano Morozzi01/2020
839363^42752-276926Lelio R Paula08/2013
8392(11*2^255545-1)/11776926Lelio R Paula02/2014
83942^255517+5638776919Yves Minet02/2011
8395(7*10^76916+89)/376917Robert Price08/2020
839618376^15329+15329^1837676914Hans Havermann03/2020
83972^255499-11256776913Enzo Doria06/2014
83982^255492+34576911Lelio R Paula06/2013
8399(2^255488+1678)/276910Stefano Morozzi01/2020
840010^76875+21759176876Patrick De Geest05/2013
840210^76875-5376875Robert Price05/2011
840111^73819-588076875Enzo Doria01/2013
84032^255313+1891576857Lelio R Paula06/2013
8404(2^255320-1017)/144666776853Lelio R Paula10/2012
84052^255296+577576852Lelio R Paula06/2013
840614^67052-2976851Lelio R Paula02/2015
8407(8*10^76840+43)/376841Robert Price10/2017
8408(2^255246+1642)/276837Stefano Morozzi01/2020
8409(2^255243+2250)/276836Stefano Morozzi01/2020
8410(2^255240+1218)/276835Stefano Morozzi01/2020
8411(7*10^76818-313)/976818Robert Price11/2016
841210^76801+6976802Robert Price03/2011
841310^76801-8094376801Patrick De Geest06/2013
84142^255105+5776795Lelio R Paula03/2012
8415(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
8416(2^255097-7)/2002005576785Lelio R Paula10/2012
8417(2^255063+3098)/276782Stefano Morozzi01/2020
84182^255055+186935376780Enzo Doria05/2016
841917^62396-9076776Lelio R Paula03/2015
842018797^12130+12130^1879776765Hans Havermann03/2020
84217^90833-6076763Lelio R Paula02/2015
842213^68901-5676752Lelio R Paula03/2015
84232^254961+186991776751Enzo Doria05/2016
8424(2^254950+594)/276748Stefano Morozzi01/2020
842520734^5027+5027^2073476743Hans Havermann03/2020
84269*5^109791-876742Lelio R Paula10/2014
8427(469^28729-1)/46876738Serge Batalov08/2020
8428(2^254908+982)/276735Stefano Morozzi01/2020
8429(2^254903+2766)/276734Stefano Morozzi01/2020
8430(4143^21211-1)/414276724Serge Batalov08/2020
843182^40089+40089^8276723Serge Batalov02/2012
84322^254861-279001376721Enzo Doria03/2016
8433(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
843410^76705+1376706Robert Price01/2011
843510^76705-9407776705Patrick De Geest06/2013
8436(13709^18541-1)/1370876701Serge Batalov08/2020
8437(5*2^254785-1)/99976696Lelio R Paula02/2014
84382^254758-11040576690Enzo Doria05/2014
8439(2^254721+470)/276679Stefano Morozzi01/2020
84402^254716-377976678Yves Minet04/2017
84412^254708-11050776675Enzo Doria05/2014
8442(47*10^76672+133)/976673Robert Price04/2017
84432^254670-11290176664Enzo Doria06/2014
8444(3^160665+7)/98135076651Lelio R Paula10/2012
84452^254598-11318376642Enzo Doria07/2014
844619^59932+2276639Lelio R Paula01/2015
844777*10^76635+376637Robert Price06/2020
84482^254569-11221376633Enzo Doria06/2014
84492*5^109626+976626Lelio R Paula10/2014
84502^254521+187252776619Enzo Doria05/2016
8451(2^254515+2570)/276617Stefano Morozzi01/2020
8452(76*10^76615+167)/976616Robert Price08/2016
8453(2^254495+918)/276611Stefano Morozzi01/2020
845425^54799-24^5479976606Robert Price07/2012
8455(24737*2^254464+1)/976605Lelio R Paula06/2014
845625863^916+916^2586376604Hans Havermann01/2020
8457(2^254458+2398)/276600Stefano Morozzi01/2020
8458(2^254434+1354)/276592Stefano Morozzi01/2020
8459(2^254410+2842)/276585Stefano Morozzi01/2020
846019878^7121+7121^1987876581Hans Havermann01/2020
846112^70961-8576580Lelio R Paula02/2015
846218867^11452+11452^1886776579Hans Havermann01/2020
8463(2^254333+1806)/276562Stefano Morozzi01/2020
84647^90590-3876558Lelio R Paula02/2015
84652^254304+522776554Lelio R Paula06/2013
8466(76*10^76547-211)/976548Robert Price10/2017
846818^60979-536376546Enzo Doria03/2013
8467(2^254278+3250)/276546Stefano Morozzi01/2020
8469(19098^17881-1)/1909776545Serge Batalov08/2020
8470(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
8471(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
8472(7*10^76536-313)/976536Robert Price11/2016
84742^254239-2776534Lelio R Paula03/2012
84732^254238-184176534Yves Minet03/2013
8475(2^254235+3978)/276533Stefano Morozzi01/2020
8477(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
8476(2^254223+3938)/276529Stefano Morozzi01/2020
84782^254189-11222576519Enzo Doria06/2014
847918^60938-139776494Enzo Doria03/2013
84812^254075-278841776485Enzo Doria03/2016
848018239^15612+15612^1823976485Hans Havermann01/2020
84827*10^76483-2376484Robert Price04/2016
848318471^13822+13822^1847176481Hans Havermann01/2020
848418850^11407+11407^1885076478Hans Havermann01/2020
84852^254042-11291376475Enzo Doria06/2014
848614^66723-3776474Lelio R Paula02/2015
8487(2^254040+2970)/276474Stefano Morozzi01/2020
84882^254037-11030576473Enzo Doria05/2014
8489(2^254008+2290)/276464Stefano Morozzi01/2020
849015927^18196+18196^1592776463Norbert Schneider12/2019
8491(2^253979+1110)/276455Stefano Morozzi01/2020
8492(1575^23911-1)/157476447Serge Batalov08/2020
84932^253931-11110976441Enzo Doria05/2014
84942^253926-116776440Lelio R Paula05/2013
8495(49*10^76438-13)/976439Robert Price07/2015
8496(2^253876+1302)/276424Stefano Morozzi01/2020
8497(21*2^253845-1)/14376415Lelio R Paula02/2014
849810^76374+3176375Robert Price03/2011
849910^76374-22215976374Patrick De Geest05/2013
8500(6300^20101-1)/629976367Serge Batalov08/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!