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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 8001 | 24644^19125+19125^24644 | 105516 | Hans Havermann | 10/2020 |
| 8002 | 10^105515-41033 | 105515 | Patrick De Geest | 12/2016 |
| 8003 | (29*2^350473-1)/267927 | 105499 | Lelio R Paula | 03/2014 |
| 8004 | 2^350455-430567 | 105498 | Harrison Mesh | 06/2022 |
| 8005 | 17^85732-72 | 105489 | Lelio R Paula | 01/2017 |
| 8006 | (2^350399+3618)/2 | 105481 | Stefano Morozzi | 09/2020 |
| 8007 | (2^350379+1010)/2 | 105475 | Stefano Morozzi | 09/2020 |
| 8008 | 2^350356+24241 | 105468 | Enzo Doria | 10/2023 |
| 8009 | 25233^15118+15118^25233 | 105462 | Hans Havermann | 09/2020 |
| 8010 | 26261^10366+10366^26261 | 105454 | Hans Havermann | 09/2020 |
| 8011 | 2^350307-110329 | 105453 | Enzo Doria | 05/2014 |
| 8012 | 2^350253-20365 | 105437 | Enzo Doria | 06/2013 |
| 8013 | (3*29^72089-1075)/4 | 105423 | Curtis Bright | 05/2015 |
| 8014 | (2^350187+2658)/2 | 105417 | Stefano Morozzi | 09/2020 |
| 8015 | 4*10^105415-69 | 105416 | Robert Price | 01/2022 |
| 8016 | 21^79725-22 | 105414 | Anonymous | 09/2024 |
| 8017 | (22*10^105407+179)/3 | 105408 | Robert Price | 02/2022 |
| 8018 | 2^350139-109009 | 105403 | Enzo Doria | 04/2014 |
| 8019 | (2^350129+3026)/2 | 105400 | Stefano Morozzi | 09/2020 |
| 8020 | (2^350097+2070)/2 | 105390 | Stefano Morozzi | 09/2020 |
| 8021 | 3*5^150763+4 | 105380 | Lelio R Paula | 11/2014 |
| 8022 | 12^97643+91 | 105375 | Lelio R Paula | 02/2017 |
| 8023 | 6*5^150744-7 | 105367 | Lelio R Paula | 11/2014 |
| 8024 | (2^350018+2074)/2 | 105366 | Stefano Morozzi | 09/2020 |
| 8025 | 4*10^105364-39 | 105365 | Robert Price | 09/2020 |
| 8026 | Phi(156135,-5#) | 105361 | Henri Lifchitz | 12/2025 |
| 8028 | 2^349996-112169 | 105360 | Enzo Doria | 06/2014 |
| 8027 | (2^349997+3702)/2 | 105360 | Stefano Morozzi | 09/2020 |
| 8029 | (418*10^105343+23)/9 | 105345 | Robert Price | 02/2020 |
| 8030 | 25490^13563+13563^25490 | 105334 | Hans Havermann | 10/2020 |
| 8031 | (5^504004)%F(504004) | 105330 | Henri Lifchitz | 06/2025 |
| 8032 | 11^101142-1080 | 105329 | Enzo Doria | 12/2012 |
| 8033 | (68*10^105320-41)/9 | 105321 | Robert Price | 10/2013 |
| 8034 | 24800^17649+17649^24800 | 105319 | Hans Havermann | 09/2020 |
| 8035 | 3^220712-9934 | 105307 | Enzo Doria | 05/2014 |
| 8036 | 7*10^105296+9 | 105297 | Robert Price | 09/2015 |
| 8037 | 89*10^105284-7 | 105286 | Robert Price | 04/2020 |
| 8038 | 2^349739+1873373 | 105282 | Enzo Doria | 06/2016 |
| 8039 | 7^124574+24 | 105278 | Lelio R Paula | 11/2016 |
| 8040 | 2^349708-20957 | 105273 | Enzo Doria | 06/2013 |
| 8041 | 34115^1218+1218^34115 | 105267 | Hans Havermann | 09/2020 |
| 8042 | 24029^24029-24020^24020 | 105265 | Henri Lifchitz | 09/2024 |
| 8043 | 2^349649-20469 | 105255 | Enzo Doria | 06/2013 |
| 8044 | 2^349607-20109 | 105243 | Enzo Doria | 06/2013 |
| 8045 | (85*10^105242+473)/9 | 105243 | Robert Price | 01/2020 |
| 8046 | 2^349594-19085 | 105239 | Enzo Doria | 05/2013 |
| 8047 | 2^349530+1874479 | 105220 | Enzo Doria | 06/2016 |
| 8048 | (3^220528+8)/8081 | 105215 | Lelio R Paula | 12/2013 |
| 8049 | (106*10^105199+17)/3 | 105201 | Robert Price | 04/2021 |
| 8050 | (2^349452+3570)/2 | 105196 | Stefano Morozzi | 09/2020 |
| 8051 | 3^220464-112852 | 105189 | Enzo Doria | 07/2014 |
| 8052 | 2^349419-17349 | 105186 | Enzo Doria | 05/2013 |
| 8053 | 2^349400-2579 | 105180 | Yves Minet | 07/2014 |
| 8054 | 8*5^150471+3 | 105176 | Lelio R Paula | 11/2014 |
| 8055 | (2^349359+2298)/2 | 105168 | Stefano Morozzi | 02/2021 |
| 8056 | 655^37342+37342^655 | 105165 | Norbert Schneider | 08/2018 |
| 8057 | 13^94403+94 | 105160 | Lelio R Paula | 12/2016 |
| 8058 | 349315*2^349315+3 | 105160 | Anonymous | 09/2025 |
| 8059 | 2^349301-112309 | 105151 | Enzo Doria | 06/2014 |
| 8060 | 30291^2960+2960^30291 | 105149 | Hans Havermann | 09/2020 |
| 8061 | 27350^6981+6981^27350 | 105132 | Hans Havermann | 09/2020 |
| 8063 | 9*2^349220+5 | 105127 | Lelio R Paula | 09/2014 |
| 8062 | (2^349225+3122)/2 | 105127 | Stefano Morozzi | 09/2020 |
| 8064 | 7*3^220317+8 | 105119 | Lelio R Paula | 09/2014 |
| 8065 | 7^124386+88 | 105119 | Lelio R Paula | 11/2016 |
| 8066 | (2^349197+570)/2 | 105119 | Stefano Morozzi | 09/2020 |
| 8067 | 2^349171-19657 | 105111 | Enzo Doria | 06/2013 |
| 8068 | (2^349115+590)/2 | 105094 | Stefano Morozzi | 09/2020 |
| 8069 | (2^(6*58185+1)-5)/3 | 105093 | Kevin Acres | 11/2013 |
| 8070 | (2^349111-5)/3 | 105093 | Lelio R Paula | 12/2013 |
| 8071 | 675^37142+37142^675 | 105087 | Norbert Schneider | 08/2018 |
| 8072 | 2^348981-2797573 | 105054 | Enzo Doria | 04/2016 |
| 8073 | (445^39667+1)/446 | 105050 | Jinyuan Wang | 05/2024 |
| 8074 | 2^348869-6555 | 105021 | Lelio R Paula | 01/2017 |
| 8075 | 10^105003-17319 | 105003 | Alfred Reich | 08/2024 |
| 8076 | 5^150217+78 | 104998 | Lelio R Paula | 11/2016 |
| 8077 | (88*10^104989-1)/3 | 104991 | Robert Price | 04/2020 |
| 8078 | (28*10^104972+149)/3 | 104973 | Robert Price | 12/2019 |
| 8079 | 24927^16262+16262^24927 | 104972 | Hans Havermann | 10/2020 |
| 8080 | 2^348703-113005 | 104971 | Enzo Doria | 06/2014 |
| 8081 | (191*10^104956-17)/3 | 104958 | Robert Price | 11/2021 |
| 8082 | 2^348612-809 | 104943 | Yves Minet | 05/2013 |
| 8083 | (73*10^104942-1)/9 | 104943 | Robert Price | 01/2015 |
| 8084 | 2^348583-350407 | 104934 | Enzo Doria | 06/2015 |
| 8085 | 2^348531-949 | 104919 | Yves Minet | 05/2012 |
| 8086 | 20^80636-59 | 104910 | Lelio R Paula | 12/2016 |
| 8087 | 8*10^104893-13 | 104894 | Robert Price | 08/2019 |
| 8089 | 2^348437+35 | 104890 | Lelio R Paula | 09/2011 |
| 8088 | 25208^14487+14487^25208 | 104890 | Hans Havermann | 09/2020 |
| 8090 | 2^348348+135 | 104864 | Lelio R Paula | 09/2011 |
| 8091 | (29*10^104858+349)/9 | 104859 | Robert Price | 06/2021 |
| 8092 | 6*10^104852-31 | 104853 | Robert Price | 07/2020 |
| 8094 | (2^348284+9)/25 | 104843 | Lelio R Paula | 12/2013 |
| 8093 | 75^55914-74 | 104843 | Norbert Schneider | 01/2015 |
| 8095 | 2^348268+255255 | 104840 | Lelio R Paula | 01/2017 |
| 8096 | 35540^891+891^35540 | 104839 | Hans Havermann | 09/2020 |
| 8097 | 5^149985-52 | 104836 | Lelio R Paula | 11/2016 |
| 8098 | 2^348224-20249 | 104826 | Enzo Doria | 06/2013 |
| 8099 | (2^348217+2522)/2 | 104824 | Stefano Morozzi | 09/2020 |
| 8100 | 2^348212-20105 | 104823 | Enzo Doria | 06/2013 |
| 8101 | 24647^17898+17898^24647 | 104819 | Hans Havermann | 10/2020 |
| 8102 | 20^80562+19 | 104814 | Lelio R Paula | 12/2016 |
| 8103 | 2*10^104811-87 | 104812 | Robert Price | 04/2018 |
| 8104 | 2^348149-20053 | 104804 | Enzo Doria | 06/2013 |
| 8105 | Phi(341301,3) | 104792 | Henri Lifchitz | 12/2025 |
| 8106 | 2^348095-171 | 104788 | Lelio R Paula | 09/2011 |
| 8107 | 25383^13412+13412^25383 | 104769 | Hans Havermann | 09/2020 |
| 8108 | 2^348003-20377 | 104760 | Enzo Doria | 06/2013 |
| 8109 | 26^74036-27 | 104759 | Anonymous | 09/2024 |
| 8111 | 2^347994-741 | 104757 | Lelio R Paula | 12/2016 |
| 8110 | (2^347993+2234)/2 | 104757 | Stefano Morozzi | 01/2021 |
| 8112 | (2^347990+790)/2 | 104756 | Stefano Morozzi | 09/2020 |
| 8113 | 25137^14702+14702^25137 | 104756 | Hans Havermann | 09/2020 |
| 8114 | (13*2^347972-1)/282309 | 104746 | Lelio R Paula | 03/2014 |
| 8115 | 12883^25484-25484^12883 | 104740 | Norbert Schneider | 08/2022 |
| 8116 | 2^347910-109937 | 104732 | Enzo Doria | 04/2014 |
| 8117 | (88*10^104709-637)/9 | 104710 | Robert Price | 11/2020 |
| 8118 | (13*10^104702+71)/3 | 104703 | Robert Price | 06/2021 |
| 8119 | 5^149794+28 | 104702 | Lelio R Paula | 11/2016 |
| 8120 | 105^51800-2 | 104698 | Lelio R Paula | 10/2017 |
| 8121 | (16^86939+3^86939)/19 | 104684 | Robert Price | 06/2013 |
| 8122 | (15^89009-1)/14 | 104682 | Paul Bourdelais | 03/2010 |
| 8123 | 2^347731-18609 | 104678 | Enzo Doria | 05/2013 |
| 8124 | 4*6^134519+7 | 104677 | Lelio R Paula | 11/2014 |
| 8125 | (34*10^104672-259)/9 | 104673 | Robert Price | 12/2021 |
| 8126 | 25321^13588+13588^25321 | 104656 | Hans Havermann | 09/2020 |
| 8127 | 2^347625+5367 | 104646 | Riley Fisher | 04/2023 |
| 8128 | 2^347612-18545 | 104642 | Enzo Doria | 05/2013 |
| 8129 | 6^134465+95 | 104635 | Lelio R Paula | 11/2016 |
| 8131 | (2^347588+3718)/2 | 104635 | Stefano Morozzi | 09/2020 |
| 8130 | (166*10^104633-7)/3 | 104635 | Robert Price | 11/2020 |
| 8132 | V(750972)/15019441 | 104621 | Serge Batalov | 07/2024 |
| 8133 | 2^347517-17301 | 104614 | Enzo Doria | 05/2013 |
| 8134 | (2^347493+3186)/2 | 104606 | Stefano Morozzi | 09/2020 |
| 8135 | (2^347490+2574)/2 | 104605 | Stefano Morozzi | 09/2020 |
| 8136 | 3^219222-310 | 104596 | Lelio R Paula | 11/2016 |
| 8137 | 25993^10554+10554^25993 | 104581 | Hans Havermann | 09/2020 |
| 8138 | (15*2^347399-1)/13 | 104578 | Lelio R Paula | 03/2014 |
| 8139 | 2^347372-17853 | 104570 | Enzo Doria | 05/2013 |
| 8140 | 2^347314+99 | 104552 | Lelio R Paula | 09/2011 |
| 8141 | 2^347300-22233 | 104548 | Enzo Doria | 06/2013 |
| 8142 | 2^347287-19845 | 104544 | Enzo Doria | 06/2013 |
| 8143 | 2^347258-231191 | 104536 | Harrison Mesh | 06/2022 |
| 8144 | (31*2^347254-1)/891 | 104533 | Lelio R Paula | 03/2014 |
| 8145 | 5*F(250091)*(F(250091)-1)+1 | 104532 | Serge Batalov | 04/2015 |
| 8146 | 7*2^347239-3 | 104531 | Lelio R Paula | 09/2014 |
| 8147 | (3^219098-8)/514147439969 | 104525 | Lelio R Paula | 12/2013 |
| 8148 | 5*3^219047+8 | 104513 | Lelio R Paula | 09/2014 |
| 8149 | 2^347148-109073 | 104502 | Enzo Doria | 04/2014 |
| 8150 | 2^347129-20145 | 104497 | Enzo Doria | 06/2013 |
| 8151 | 4*10^104461-57 | 104462 | Robert Price | 10/2018 |
| 8152 | 2^346999+198831 | 104458 | Stefano Morozzi | 11/2024 |
| 8153 | 2^346996+166273 | 104457 | Stefano Morozzi | 11/2024 |
| 8154 | 2^346997+105755 | 104457 | Stefano Morozzi | 11/2024 |
| 8155 | 2^346997+115259 | 104457 | Stefano Morozzi | 11/2024 |
| 8156 | 2^346992+97515 | 104456 | Stefano Morozzi | 11/2024 |
| 8157 | 2^346992+169593 | 104456 | Stefano Morozzi | 11/2024 |
| 8158 | 2^346994+182215 | 104456 | Stefano Morozzi | 11/2024 |
| 8159 | 2^346994+187933 | 104456 | Stefano Morozzi | 11/2024 |
| 8160 | (7*10^(2*52227+1)+9*10^52227-7)/9 | 104455 | Robert Price | 10/2023 |
| 8163 | (2^346989+590)/2 | 104454 | Stefano Morozzi | 09/2020 |
| 8161 | 2^346988+295 | 104454 | Stefano Morozzi | 11/2024 |
| 8162 | 2^346988+47241 | 104454 | Stefano Morozzi | 11/2024 |
| 8164 | 2^346983+4203 | 104453 | Stefano Morozzi | 11/2024 |
| 8165 | 2^346983+119259 | 104453 | Stefano Morozzi | 11/2024 |
| 8166 | 2^346983+47729 | 104453 | Stefano Morozzi | 11/2024 |
| 8167 | 2^346985+124437 | 104453 | Stefano Morozzi | 11/2024 |
| 8168 | 2^346979+72443 | 104452 | Stefano Morozzi | 11/2024 |
| 8169 | 2^346980+167731 | 104452 | Stefano Morozzi | 11/2024 |
| 8170 | 2^346978+64933 | 104451 | Stefano Morozzi | 11/2024 |
| 8171 | 2^346974+105865 | 104450 | Stefano Morozzi | 11/2024 |
| 8172 | 2^346972+95343 | 104449 | Stefano Morozzi | 11/2024 |
| 8173 | 2^346966+63519 | 104448 | Stefano Morozzi | 11/2024 |
| 8174 | 2^346963+42825 | 104447 | Stefano Morozzi | 11/2024 |
| 8175 | 2^346963+140153 | 104447 | Stefano Morozzi | 11/2024 |
| 8176 | 2^346965+144537 | 104447 | Stefano Morozzi | 11/2024 |
| 8177 | 2^346962+128917 | 104446 | Stefano Morozzi | 11/2024 |
| 8178 | 2^346956+110455 | 104445 | Stefano Morozzi | 11/2024 |
| 8179 | 2^346956+72711 | 104445 | Stefano Morozzi | 11/2024 |
| 8180 | 2^346954+178093 | 104444 | Stefano Morozzi | 11/2024 |
| 8181 | 2^346955+46205 | 104444 | Stefano Morozzi | 11/2024 |
| 8182 | 2^346954+186043 | 104444 | Stefano Morozzi | 11/2024 |
| 8183 | 2^346949+140865 | 104443 | Stefano Morozzi | 11/2024 |
| 8184 | 2^346950+79857 | 104443 | Stefano Morozzi | 11/2024 |
| 8185 | 2^346951+161939 | 104443 | Stefano Morozzi | 11/2024 |
| 8186 | 2^346950+143647 | 104443 | Stefano Morozzi | 11/2024 |
| 8187 | 2^346950+103369 | 104443 | Stefano Morozzi | 11/2024 |
| 8188 | 2^346952+128895 | 104443 | Stefano Morozzi | 11/2024 |
| 8189 | 2^346946+106593 | 104442 | Stefano Morozzi | 11/2024 |
| 8190 | 2^346947+63431 | 104442 | Stefano Morozzi | 11/2024 |
| 8191 | 2^346947+75735 | 104442 | Stefano Morozzi | 11/2024 |
| 8192 | 2^346948+135547 | 104442 | Stefano Morozzi | 11/2024 |
| 8193 | 2^346944+20295 | 104441 | Stefano Morozzi | 11/2024 |
| 8194 | 2^346944+93783 | 104441 | Stefano Morozzi | 11/2024 |
| 8195 | 2^346939+116879 | 104440 | Stefano Morozzi | 11/2024 |
| 8196 | 2^346939+138489 | 104440 | Stefano Morozzi | 11/2024 |
| 8197 | 2^346940+40675 | 104440 | Stefano Morozzi | 11/2024 |
| 8198 | 2^346942+108495 | 104440 | Stefano Morozzi | 11/2024 |
| 8199 | 2^346942+137535 | 104440 | Stefano Morozzi | 11/2024 |
| 8200 | 2^346936+78235 | 104439 | Stefano Morozzi | 11/2024 |
| 8201 | 2^346936+156271 | 104439 | Stefano Morozzi | 11/2024 |
| 8202 | 2^346937+180909 | 104439 | Stefano Morozzi | 11/2024 |
| 8203 | 2^346938+159885 | 104439 | Stefano Morozzi | 11/2024 |
| 8204 | 2^346933+7865 | 104438 | Stefano Morozzi | 11/2024 |
| 8205 | 2^346933+119759 | 104438 | Stefano Morozzi | 11/2024 |
| 8206 | 2^346934+187797 | 104438 | Stefano Morozzi | 11/2024 |
| 8207 | 2^346935+198629 | 104438 | Stefano Morozzi | 11/2024 |
| 8208 | 2^346929+85449 | 104437 | Stefano Morozzi | 11/2024 |
| 8209 | 2^346929+155487 | 104437 | Stefano Morozzi | 11/2024 |
| 8210 | 2^346931+60719 | 104437 | Stefano Morozzi | 11/2024 |
| 8211 | 2^346932+49215 | 104437 | Stefano Morozzi | 11/2024 |
| 8212 | 2^346927+65709 | 104436 | Stefano Morozzi | 11/2024 |
| 8213 | 2^346928+126963 | 104436 | Stefano Morozzi | 11/2024 |
| 8214 | 2^346928+143721 | 104436 | Stefano Morozzi | 11/2024 |
| 8219 | 2^346923-19585 | 104435 | Enzo Doria | 05/2013 |
| 8215 | 2^346923+73001 | 104435 | Stefano Morozzi | 11/2024 |
| 8216 | 2^346924+28671 | 104435 | Stefano Morozzi | 11/2024 |
| 8217 | 2^346924+58657 | 104435 | Stefano Morozzi | 11/2024 |
| 8218 | 2^346924+173475 | 104435 | Stefano Morozzi | 11/2024 |
| 8220 | 2^346921+59357 | 104434 | Stefano Morozzi | 11/2024 |
| 8221 | 2^346916+18183 | 104433 | Stefano Morozzi | 11/2024 |
| 8222 | 2^346914+44625 | 104432 | Stefano Morozzi | 11/2024 |
| 8223 | 2^346912+26343 | 104431 | Stefano Morozzi | 11/2024 |
| 8224 | 2^346912+42367 | 104431 | Stefano Morozzi | 11/2024 |
| 8225 | 2^346908+123705 | 104430 | Stefano Morozzi | 11/2024 |
| 8226 | 2^346899+194015 | 104428 | Stefano Morozzi | 11/2024 |
| 8227 | 2^346900+63393 | 104428 | Stefano Morozzi | 11/2024 |
| 8228 | 2^346901+106215 | 104428 | Stefano Morozzi | 11/2024 |
| 8229 | 2^346901+119309 | 104428 | Stefano Morozzi | 11/2024 |
| 8230 | 2^346902+62587 | 104428 | Stefano Morozzi | 11/2024 |
| 8231 | 2^346897+120207 | 104427 | Stefano Morozzi | 11/2024 |
| 8232 | 2^346897+121107 | 104427 | Stefano Morozzi | 11/2024 |
| 8233 | 2^346897+134289 | 104427 | Stefano Morozzi | 11/2024 |
| 8234 | 2^346898+57429 | 104427 | Stefano Morozzi | 11/2024 |
| 8235 | 2^346898+162267 | 104427 | Stefano Morozzi | 11/2024 |
| 8236 | 2^346890+148989 | 104425 | Stefano Morozzi | 11/2024 |
| 8237 | 2^346891+46313 | 104425 | Stefano Morozzi | 11/2024 |
| 8238 | 2^346892+121191 | 104425 | Stefano Morozzi | 11/2024 |
| 8239 | 2^346888+39211 | 104424 | Stefano Morozzi | 11/2024 |
| 8240 | 2^346883+100949 | 104423 | Stefano Morozzi | 11/2024 |
| 8241 | 2^346883+138341 | 104423 | Stefano Morozzi | 11/2024 |
| 8242 | 2^346885+78357 | 104423 | Stefano Morozzi | 11/2024 |
| 8243 | 2^346882+167169 | 104422 | Stefano Morozzi | 11/2024 |
| 8244 | 2^346877+43587 | 104421 | Stefano Morozzi | 11/2024 |
| 8245 | 2^346879+69983 | 104421 | Stefano Morozzi | 11/2024 |
| 8246 | 2^346875+24885 | 104420 | Stefano Morozzi | 11/2024 |
| 8247 | 2^346875+131835 | 104420 | Stefano Morozzi | 11/2024 |
| 8248 | 2^346875+161301 | 104420 | Stefano Morozzi | 11/2024 |
| 8249 | 2^346871+85491 | 104419 | Stefano Morozzi | 11/2024 |
| 8250 | 2^346866+135849 | 104418 | Stefano Morozzi | 11/2024 |
