## PRP Records

### Probable Primes Top 10000

#### (295765 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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See the Latest PRPs
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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 ? 6751 (66^58741+1)/67 106881 Paul Bourdelais 08/2017 6752 2^355001+335931 106866 Enzo Doria 08/2024 6753 2^354946-3 106850 M. Frind & P. Underwood 08/2002 6754 (2^354945+3134)/2 106849 Stefano Morozzi 09/2020 6755 (46^64384+1)/(46^128+1) 106843 Martin Hopf 12/2023 6756 2^354873-18693 106828 Enzo Doria 05/2013 6757 (2^354831+3186)/2 106815 Stefano Morozzi 09/2020 6759 2^354828+4257 106814 Lelio R Paula 01/2017 6758 25216^17217+17217^25216 106814 Hans Havermann 10/2020 6760 (2^354799+1218)/2 106805 Stefano Morozzi 09/2020 6761 436^40459+40459^436 106791 Norbert Schneider 03/2019 6762 (21^80761+1)/22 106783 Paul Bourdelais 03/2010 6763 (115*10^106772-7)/9 106774 Robert Price 02/2020 6764 2^354640-354640+1 106758 Robert Price 10/2014 6765 (2^354603+2606)/2 106746 Stefano Morozzi 09/2020 6766 2^354585+95 106741 Lelio R Paula 10/2011 6767 (206*10^106737+1)/9 106739 Robert Price 04/2022 6768 2^354553+189 106732 Lelio R Paula 10/2011 6770 (2^354546+1338)/2 106729 Stefano Morozzi 02/2021 6769 (8*10^106729-71)/9 106729 Serge Batalov 11/2022 6771 2^354514-109031 106720 Enzo Doria 04/2014 6772 2^354509-109465 106718 Enzo Doria 04/2014 6773 fibonacci(510628)+2 106715 Jon Grantham 08/2023 6774 (15*2^354478-1)/26983 106706 Lelio R Paula 03/2014 6775 Phi(217618,10)/899798636917 106693 Makoto Kamada 06/2019 6776 15^90710+28 106684 Lelio R Paula 04/2017 6777 7^126237+34 106683 Lelio R Paula 03/2017 6778 2^354385-115315 106681 Enzo Doria 06/2015 6779 2^354327-19305 106664 Enzo Doria 06/2013 6780 (35*10^106649+1)/9 106650 Serge Batalov 11/2010 6781 10^106636+97 106637 Lelio R Paula 02/2017 6782 10^106636-22923 106636 Patrick De Geest 03/2017 6783 2^354220-57 106631 Lelio R Paula 10/2011 6784 (68*10^106628-329)/9 106629 Robert Price 03/2021 6785 (29*10^106620-77)/3 106621 Robert Price 02/2020 6786 (746*10^106618+1)/9 106620 Robert Price 03/2020 6787 2*10^106613+29 106614 Robert Price 02/2021 6788 2^354157-17041 106612 Enzo Doria 05/2013 6789 12^98778+73 106600 Lelio R Paula 02/2017 6790 33333^1576+1576^33333 106585 Hans Havermann 11/2020 6791 2^354064+1870651 106584 Enzo Doria 05/2016 6792 24568^21779+21779^24568 106577 Hans Havermann 11/2020 6793 2^353992-57 106563 Lelio R Paula 10/2011 6794 9*10^106559+59 106560 Robert Price 01/2020 6795 7*10^106553+27 106554 Robert Price 11/2020 6796 28847^4938+4938^28847 106548 Hans Havermann 10/2020 6797 NSW(139160) 106535 Robert Price 12/2018 6798 f(278321) 106535 Robert Price 07/2023 6799 (7*10^106516+113)/3 106517 Robert Price 02/2018 6800 2^353832-1853849 106515 Enzo Doria 09/2015 6801 (7^126037-1)/6 106513 Paul Bourdelais 09/2008 6802 2^353794-18453 106503 Enzo Doria 05/2013 6803 (2^353761+2094)/2 106493 Stefano Morozzi 09/2020 6804 2^353728+7695 106483 Lelio R Paula 01/2017 6805 26476^10509+10509^26476 106475 Hans Havermann 10/2020 6806 2^353672-303 106466 Yves Minet 02/2012 6807 6^136811+101 106460 Lelio R Paula 02/2017 6808 2^353641+1871981 106457 Enzo Doria 05/2016 6809 (8*10^106454-29)/3 106455 Robert Price 07/2018 6810 27845^6654+6654^27845 106454 Hans Havermann 11/2020 6811 10^106449-700001 106449 Robert Price 08/2021 6812 25316^16017+16017^25316 106444 Hans Havermann 11/2020 6813 2^353553+54615 106431 Lelio R Paula 01/2017 6814 2^353544-18897 106428 Enzo Doria 05/2013 6815 28894^4823+4823^28894 106426 Hans Havermann 11/2020 6816 (19*10^106422+29)/3 106423 Robert Price 12/2021 6817 (694*10^106418+53)/9 106420 Robert Price 02/2022 6818 6*10^106412-13 106413 Robert Price 07/2022 6819 25696^13829+13829^25696 106402 Hans Havermann 11/2020 6820 6^136729-133 106396 Lelio R Paula 02/2017 6821 2^353418+1605 106390 Lelio R Paula 01/2017 6822 2^353387+65 106381 Lelio R Paula 10/2011 6823 2^353372+74311 106376 Enzo Doria 04/2016 6824 2^353344-3693 106368 Yves Minet 03/2017 6825 (772*10^106365-7)/9 106367 Robert Price 06/2022 6826 (56*10^106351+619)/9 106352 Robert Price 05/2021 6827 2^353277-20089 106347 Enzo Doria 06/2013 6828 2^353275+72173 106347 Enzo Doria 04/2016 6829 2^353268-17705 106345 Enzo Doria 05/2013 6830 2^353267-19857 106344 Enzo Doria 06/2013 6831 (46*10^106343+143)/9 106344 Robert Price 01/2019 6833 (2^353189+3054)/2 106321 Stefano Morozzi 09/2020 6832 35087^1072+1072^35087 106321 Hans Havermann 10/2020 6834 (2^353184+1290)/2 106319 Stefano Morozzi 01/2021 6835 F(508799)/24738824977/1990778864897 106310 Serge Batalov 07/2024 6836 26985^8684+8684^26985 106287 Hans Havermann 10/2020 6837 (2^353051+606)/2 106279 Stefano Morozzi 09/2020 6839 222748^3+3^222748 106278 Anatoly F. Selevich 12/2010 6838 (46*10^106277+107)/9 106278 Robert Price 06/2022 6840 (9179*2^353019-1)/9 106273 Lelio R Paula 05/2015 6841 2^353025+72257 106272 Enzo Doria 04/2016 6844 2^352932-20345 106244 Enzo Doria 06/2013 6842 (2^353011-3)/745325861246794515484535 106244 Lelio R Paula 12/2013 6843 25628^13983+13983^25628 106244 Hans Havermann 10/2020 6845 2^352883-187 106229 Lelio R Paula 10/2011 6846 20^81649-19^81649 106228 Jean-Louis Charton 03/2011 6847 (55*10^106222+377)/9 106223 Robert Price 02/2019 6848 2^352814-131 106208 Lelio R Paula 10/2011 6849 2^352752+73951 106189 Enzo Doria 04/2016 6850 11876*25^75945+357 106171 Eric Chen 10/2023 6851 6^136434+5 106167 Lelio R Paula 11/2014 6852 25296^15737+15737^25296 106166 Hans Havermann 09/2020 6853 8*10^106157-13 106158 Robert Price 08/2019 6854 2^352641+225677 106156 Enzo Doria 08/2024 6855 7*5^151872-8 106155 Lelio R Paula 11/2014 6856 105^52520-2 106153 Lelio R Paula 10/2017 6857 (23*10^106152-29)/3 106153 Robert Price 03/2022 6858 2^352601-1604809 106144 Enzo Doria 05/2015 6859 12^98353-43 106141 Lelio R Paula 02/2017 6860 2^352585-18901 106139 Enzo Doria 05/2013 6861 26363^10614+10614^26363 106135 Hans Havermann 09/2020 6862 (2^352554-3)/193 106128 Lelio R Paula 12/2013 6863 2^352540+15015 106126 Lelio R Paula 01/2017 6864 25068^17119+17119^25068 106125 Hans Havermann 09/2020 6865 2^352524-3149 106121 Yves Minet 10/2014 6866 (7*10^106119-67)/3 106120 Robert Price 10/2021 6867 2^352486-1858781 106109 Enzo Doria 04/2016 6868 2^352444+12705 106097 Lelio R Paula 01/2017 6869 28561^5182+5182^28561 106090 Hans Havermann 10/2020 6870 (182*10^106083+43)/9 106085 Robert Price 02/2020 6871 (266*10^106066+1)/3 106068 Robert Price 04/2020 6872 (7*10^106066-187)/9 106066 Tyler Busby 01/2023 6873 2^352228-18953 106032 Enzo Doria 05/2013 6874 (2^352223+1118)/2 106030 Stefano Morozzi 09/2020 6875 (2^352212+2250)/2 106027 Stefano Morozzi 01/2021 6876 (2^352136+2638)/2 106004 Stefano Morozzi 09/2020 6877 2^352107+1872533 105995 Enzo Doria 05/2016 6878 (2^352096+2086)/2 105992 Stefano Morozzi 09/2020 6879 2^352066-2591 105983 Yves Minet 07/2014 6880 2^352030+715 105972 Lelio R Paula 10/2011 6881 9*6^136176-5 105967 Lelio R Paula 11/2014 6882 17099*2^351991+58329 105965 Paul Vanderveen 12/2017 6883 122^50789-50789^122 105965 Norman Luhn 09/2024 6884 28582^5097+5097^28582 105963 Hans Havermann 09/2020 6885 155^48377+2 105962 Lelio R Paula 08/2013 6886 (23*10^105944-119)/3 105945 Robert Price 07/2021 6887 2^351865+1869707 105922 Enzo Doria 05/2016 6888 24974^17427+17427^24974 105921 Hans Havermann 09/2020 6889 25163^16194+16194^25163 105920 Hans Havermann 09/2020 6890 2^351831+23 105912 Lelio R Paula 10/2011 6891 (2^351818+3798)/2 105908 Stefano Morozzi 02/2021 6892 9*2^351784-5 105899 Lelio R Paula 09/2014 6893 (2^351776+2766)/2 105895 Stefano Morozzi 01/2021 6894 (85*10^105881+203)/9 105882 Robert Price 09/2020 6895 2^351671-112387 105864 Enzo Doria 06/2014 6896 2^351669-109501 105863 Enzo Doria 04/2014 6897 2^351644+74731 105856 Enzo Doria 04/2016 6898 13^95025-42 105853 Lelio R Paula 12/2016 6899 2^351599+15015 105842 Lelio R Paula 01/2017 6900 19^82763+90 105834 Lelio R Paula 01/2017 6901 (205*10^105831-1)/3 105833 Robert Price 11/2021 6902 26050^11551+11551^26050 105832 Hans Havermann 09/2020 6903 (9179*2^351540-1)/221 105826 Lelio R Paula 05/2015 6904 20^81329-51 105812 Lelio R Paula 01/2017 6905 (5*10^105811+211)/9 105811 Robert Price 02/2018 6906 2^351483+28425 105807 Lelio R Paula 01/2017 6907 25231^15610+15610^25231 105804 Hans Havermann 09/2020 6908 15^89960+86 105802 Lelio R Paula 02/2017 6909 2^351460-17289 105801 Enzo Doria 05/2013 6910 19^82735+22 105798 Lelio R Paula 01/2017 6911 2^351435-109077 105793 Enzo Doria 04/2014 6912 2^351393+1089 105780 Lelio R Paula 01/2017 6913 2^351364+72631 105772 Enzo Doria 04/2016 6914 (2^351333+3626)/2 105762 Stefano Morozzi 09/2020 6915 26818^8783+8783^26818 105761 Hans Havermann 09/2020 6918 2^351305+1872467 105754 Enzo Doria 05/2016 6917 3^221649+16 105754 Lelio R Paula 11/2016 6916 32511^1790+1790^32511 105754 Hans Havermann 09/2020 6919 8*3^221637-5 105749 Lelio R Paula 09/2014 6920 2^351279-2780449 105746 Enzo Doria 03/2016 6921 (2^351263+3198)/2 105741 Stefano Morozzi 09/2020 6922 15^89903-26 105735 Lelio R Paula 02/2017 6924 2^351213-73 105726 Lelio R Paula 10/2011 6923 (2^351214+1210)/2 105726 Stefano Morozzi 09/2020 6925 2^351192-4589 105720 Yves Minet 07/2011 6926 20^81250-33 105709 Lelio R Paula 12/2016 6927 (2^351133+3530)/2 105702 Stefano Morozzi 09/2020 6928 (2^351103+534)/2 105693 Stefano Morozzi 09/2020 6929 2^351076-113159 105685 Enzo Doria 07/2014 6930 93^53688-2 105684 Lelio R Paula 09/2013 6931 2^351060-4559 105680 Yves Minet 07/2011 6932 ((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9 105676 Hans Havermann 08/2019 6933 11^101473-750 105674 Enzo Doria 11/2012 6934 3*5^151181-8 105672 Lelio R Paula 11/2014 6935 15^89831-34 105650 Lelio R Paula 02/2017 6937 11^101448-360 105648 Enzo Doria 08/2012 6936 3*7^125011+4 105648 Lelio R Paula 11/2014 6938 2^350943-113269 105645 Enzo Doria 07/2014 6939 2*10^105636-91 105637 Robert Price 04/2020 6940 24231^22880+22880^24231 105634 Hans Havermann 09/2020 6941 35296^983+983^35296 105626 Hans Havermann 09/2020 6942 2^350868-19725 105622 Enzo Doria 06/2013 6943 2^350858-59291 105619 Enzo Doria 10/2015 6944 V(758484)/1516967/19720583 105618 Serge Batalov 07/2024 6945 2^350851+135 105617 Lelio R Paula 10/2011 6946 2^350841-741 105614 Lelio R Paula 01/2017 6947 3*10^105582+77 105583 Robert Price 09/2018 6948 24915^17284+17284^24915 105581 Hans Havermann 09/2020 6949 (5*10^105576-53)/3 105577 Robert Price 09/2020 6950 8*10^105571+3 105572 Robert Price 08/2015 6951 2^350674-78557 105564 Jorge Menendez 03/2018 6952 2*5^151026-3 105563 Lelio R Paula 11/2014 6953 (2^350702+5)/34264674063 105562 Lelio R Paula 12/2013 6954 6^135647-5^135647 105554 Jean-Louis Charton 02/2009 6955 3^221211+236 105545 Lelio R Paula 11/2016 6956 (32*10^105530-77)/9 105531 Robert Price 06/2018 6957 10^105515+33 105516 Lelio R Paula 11/2016 6958 24644^19125+19125^24644 105516 Hans Havermann 10/2020 6959 10^105515-41033 105515 Patrick De Geest 12/2016 6960 (29*2^350473-1)/267927 105499 Lelio R Paula 03/2014 6961 2^350455-430567 105498 Harrison Mesh 06/2022 6962 17^85732-72 105489 Lelio R Paula 01/2017 6963 (2^350399+3618)/2 105481 Stefano Morozzi 09/2020 6964 (2^350379+1010)/2 105475 Stefano Morozzi 09/2020 6965 2^350356+24241 105468 Enzo Doria 10/2023 6966 25233^15118+15118^25233 105462 Hans Havermann 09/2020 6967 26261^10366+10366^26261 105454 Hans Havermann 09/2020 6968 2^350307-110329 105453 Enzo Doria 05/2014 6969 2^350253-20365 105437 Enzo Doria 06/2013 6970 (3*29^72089-1075)/4 105423 Curtis Bright 05/2015 6971 (2^350187+2658)/2 105417 Stefano Morozzi 09/2020 6972 4*10^105415-69 105416 Robert Price 01/2022 6973 (22*10^105407+179)/3 105408 Robert Price 02/2022 6974 2^350139-109009 105403 Enzo Doria 04/2014 6975 (2^350129+3026)/2 105400 Stefano Morozzi 09/2020 6976 (2^350097+2070)/2 105390 Stefano Morozzi 09/2020 6977 3*5^150763+4 105380 Lelio R Paula 11/2014 6978 12^97643+91 105375 Lelio R Paula 02/2017 6979 6*5^150744-7 105367 Lelio R Paula 11/2014 6980 (2^350018+2074)/2 105366 Stefano Morozzi 09/2020 6981 4*10^105364-39 105365 Robert Price 09/2020 6983 2^349996-112169 105360 Enzo Doria 06/2014 6982 (2^349997+3702)/2 105360 Stefano Morozzi 09/2020 6984 (418*10^105343+23)/9 105345 Robert Price 02/2020 6985 25490^13563+13563^25490 105334 Hans Havermann 10/2020 6986 11^101142-1080 105329 Enzo Doria 12/2012 6987 (68*10^105320-41)/9 105321 Robert Price 10/2013 6988 24800^17649+17649^24800 105319 Hans Havermann 09/2020 6989 3^220712-9934 105307 Enzo Doria 05/2014 6990 7*10^105296+9 105297 Robert Price 09/2015 6991 89*10^105284-7 105286 Robert Price 04/2020 6992 2^349739+1873373 105282 Enzo Doria 06/2016 6993 7^124574+24 105278 Lelio R Paula 11/2016 6994 2^349708-20957 105273 Enzo Doria 06/2013 6995 34115^1218+1218^34115 105267 Hans Havermann 09/2020 6996 24029^24029-24020^24020 105265 Henri Lifchitz 09/2024 6997 2^349649-20469 105255 Enzo Doria 06/2013 6998 2^349607-20109 105243 Enzo Doria 06/2013 6999 (85*10^105242+473)/9 105243 Robert Price 01/2020 7000 2^349594-19085 105239 Enzo Doria 05/2013

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2024 17:43 (Time in France)

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