## PRP Records

### Probable Primes Top 10000

#### (295792 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 ? 7001 2^349607-20109 105243 Enzo Doria 06/2013 7002 (85*10^105242+473)/9 105243 Robert Price 01/2020 7003 2^349594-19085 105239 Enzo Doria 05/2013 7004 2^349530+1874479 105220 Enzo Doria 06/2016 7005 (3^220528+8)/8081 105215 Lelio R Paula 12/2013 7006 (106*10^105199+17)/3 105201 Robert Price 04/2021 7007 (2^349452+3570)/2 105196 Stefano Morozzi 09/2020 7008 3^220464-112852 105189 Enzo Doria 07/2014 7009 2^349419-17349 105186 Enzo Doria 05/2013 7010 2^349400-2579 105180 Yves Minet 07/2014 7011 8*5^150471+3 105176 Lelio R Paula 11/2014 7012 (2^349359+2298)/2 105168 Stefano Morozzi 02/2021 7013 655^37342+37342^655 105165 Norbert Schneider 08/2018 7014 13^94403+94 105160 Lelio R Paula 12/2016 7015 2^349301-112309 105151 Enzo Doria 06/2014 7016 30291^2960+2960^30291 105149 Hans Havermann 09/2020 7017 27350^6981+6981^27350 105132 Hans Havermann 09/2020 7019 9*2^349220+5 105127 Lelio R Paula 09/2014 7018 (2^349225+3122)/2 105127 Stefano Morozzi 09/2020 7020 7*3^220317+8 105119 Lelio R Paula 09/2014 7021 7^124386+88 105119 Lelio R Paula 11/2016 7022 (2^349197+570)/2 105119 Stefano Morozzi 09/2020 7023 2^349171-19657 105111 Enzo Doria 06/2013 7024 (2^349115+590)/2 105094 Stefano Morozzi 09/2020 7025 (2^(6*58185+1)-5)/3 105093 Kevin Acres 11/2013 7026 (2^349111-5)/3 105093 Lelio R Paula 12/2013 7027 675^37142+37142^675 105087 Norbert Schneider 08/2018 7028 2^348981-2797573 105054 Enzo Doria 04/2016 7029 (445^39667+1)/446 105050 Jinyuan Wang 05/2024 7030 2^348869-6555 105021 Lelio R Paula 01/2017 7031 10^105003-17319 105003 Alfred Reich 08/2024 7032 5^150217+78 104998 Lelio R Paula 11/2016 7033 (88*10^104989-1)/3 104991 Robert Price 04/2020 7034 (28*10^104972+149)/3 104973 Robert Price 12/2019 7035 24927^16262+16262^24927 104972 Hans Havermann 10/2020 7036 2^348703-113005 104971 Enzo Doria 06/2014 7037 (191*10^104956-17)/3 104958 Robert Price 11/2021 7038 2^348612-809 104943 Yves Minet 05/2013 7039 (73*10^104942-1)/9 104943 Robert Price 01/2015 7040 2^348583-350407 104934 Enzo Doria 06/2015 7041 2^348531-949 104919 Yves Minet 05/2012 7042 20^80636-59 104910 Lelio R Paula 12/2016 7043 8*10^104893-13 104894 Robert Price 08/2019 7045 2^348437+35 104890 Lelio R Paula 09/2011 7044 25208^14487+14487^25208 104890 Hans Havermann 09/2020 7046 2^348348+135 104864 Lelio R Paula 09/2011 7047 (29*10^104858+349)/9 104859 Robert Price 06/2021 7048 6*10^104852-31 104853 Robert Price 07/2020 7050 (2^348284+9)/25 104843 Lelio R Paula 12/2013 7049 75^55914-74 104843 Norbert Schneider 01/2015 7051 2^348268+255255 104840 Lelio R Paula 01/2017 7052 35540^891+891^35540 104839 Hans Havermann 09/2020 7053 5^149985-52 104836 Lelio R Paula 11/2016 7054 2^348224-20249 104826 Enzo Doria 06/2013 7055 (2^348217+2522)/2 104824 Stefano Morozzi 09/2020 7056 2^348212-20105 104823 Enzo Doria 06/2013 7057 24647^17898+17898^24647 104819 Hans Havermann 10/2020 7058 20^80562+19 104814 Lelio R Paula 12/2016 7059 2*10^104811-87 104812 Robert Price 04/2018 7060 2^348149-20053 104804 Enzo Doria 06/2013 7061 2^348095-171 104788 Lelio R Paula 09/2011 7062 25383^13412+13412^25383 104769 Hans Havermann 09/2020 7063 2^348003-20377 104760 Enzo Doria 06/2013 7064 2^347994-741 104757 Lelio R Paula 12/2016 7065 (2^347993+2234)/2 104757 Stefano Morozzi 01/2021 7066 (2^347990+790)/2 104756 Stefano Morozzi 09/2020 7067 25137^14702+14702^25137 104756 Hans Havermann 09/2020 7068 (13*2^347972-1)/282309 104746 Lelio R Paula 03/2014 7069 12883^25484-25484^12883 104740 Norbert Schneider 08/2022 7070 2^347910-109937 104732 Enzo Doria 04/2014 7071 (88*10^104709-637)/9 104710 Robert Price 11/2020 7072 (13*10^104702+71)/3 104703 Robert Price 06/2021 7073 5^149794+28 104702 Lelio R Paula 11/2016 7074 105^51800-2 104698 Lelio R Paula 10/2017 7075 (16^86939+3^86939)/19 104684 Robert Price 06/2013 7076 (15^89009-1)/14 104682 Paul Bourdelais 03/2010 7077 2^347731-18609 104678 Enzo Doria 05/2013 7078 4*6^134519+7 104677 Lelio R Paula 11/2014 7079 (34*10^104672-259)/9 104673 Robert Price 12/2021 7080 25321^13588+13588^25321 104656 Hans Havermann 09/2020 7081 2^347625+5367 104646 Riley Fisher 04/2023 7082 2^347612-18545 104642 Enzo Doria 05/2013 7085 6^134465+95 104635 Lelio R Paula 11/2016 7084 (2^347588+3718)/2 104635 Stefano Morozzi 09/2020 7083 (166*10^104633-7)/3 104635 Robert Price 11/2020 7086 V(750972)/15019441 104621 Serge Batalov 07/2024 7087 2^347517-17301 104614 Enzo Doria 05/2013 7088 (2^347493+3186)/2 104606 Stefano Morozzi 09/2020 7089 (2^347490+2574)/2 104605 Stefano Morozzi 09/2020 7090 3^219222-310 104596 Lelio R Paula 11/2016 7091 25993^10554+10554^25993 104581 Hans Havermann 09/2020 7092 (15*2^347399-1)/13 104578 Lelio R Paula 03/2014 7093 2^347372-17853 104570 Enzo Doria 05/2013 7094 2^347314+99 104552 Lelio R Paula 09/2011 7095 2^347300-22233 104548 Enzo Doria 06/2013 7096 2^347287-19845 104544 Enzo Doria 06/2013 7097 2^347258-231191 104536 Harrison Mesh 06/2022 7098 (31*2^347254-1)/891 104533 Lelio R Paula 03/2014 7099 5*F(250091)*(F(250091)-1)+1 104532 Serge Batalov 04/2015 7100 7*2^347239-3 104531 Lelio R Paula 09/2014 7101 (3^219098-8)/514147439969 104525 Lelio R Paula 12/2013 7102 5*3^219047+8 104513 Lelio R Paula 09/2014 7103 2^347148-109073 104502 Enzo Doria 04/2014 7104 2^347129-20145 104497 Enzo Doria 06/2013 7105 4*10^104461-57 104462 Robert Price 10/2018 7106 (7*10^(2*52227+1)+9*10^52227-7)/9 104455 Robert Price 10/2023 7107 (2^346989+590)/2 104454 Stefano Morozzi 09/2020 7108 2^346923-19585 104435 Enzo Doria 05/2013 7109 (11*2^346864-1)/175 104416 Lelio R Paula 03/2014 7110 2^346854+346854^2+1 104414 Robert Price 06/2014 7111 2^346834+11715 104408 Lelio R Paula 04/2015 7112 24276^19961+19961^24276 104392 Hans Havermann 09/2020 7113 79^55009+78 104387 Norbert Schneider 02/2015 7114 3^218744+58 104368 Lelio R Paula 11/2016 7115 9*10^104361+89 104362 Robert Price 11/2019 7116 25048^14665+14665^25048 104358 Hans Havermann 09/2020 7117 2^346649+65 104352 Lelio R Paula 09/2011 7118 (19*33^68718-600883)/32 104350 Eric Chen 05/2023 7119 2^346638-17265 104349 Enzo Doria 05/2013 7120 (2^346606+2082)/2 104339 Stefano Morozzi 09/2020 7121 (2^346607+2070)/2 104339 Stefano Morozzi 09/2020 7122 (2^346582+3202)/2 104332 Stefano Morozzi 09/2020 7123 26092^9967+9967^26092 104331 Hans Havermann 09/2020 7124 5*10^104326+77 104327 Robert Price 12/2018 7125 (2^346564+2026)/2 104326 Stefano Morozzi 09/2020 7126 (8925^26569-1)/(8925^163-1) 104320 Ryan Propper 11/2023 7129 2^346527-111817 104316 Enzo Doria 05/2014 7128 6^134055+101 104316 Lelio R Paula 11/2016 7127 fibonacci(499147)-4 104316 Jon Grantham 08/2023 7130 92105!4+8 104312 Robert Price 09/2019 7131 (7^123407-5^123407)/2 104291 Jon Grantham 08/2023 7132 6^134013+163 104283 Lelio R Paula 11/2016 7133 10^(2*52140+1)-10^52140-1 104281 Robert Price 07/2023 7134 (22*10^104272-61)/3 104273 Robert Price 03/2022 7135 (2^346318+862)/2 104252 Stefano Morozzi 02/2021 7137 18^83049-89 104250 Lelio R Paula 01/2017 7136 (2^346311+606)/2 104250 Stefano Morozzi 09/2020 7138 (166*10^104230+11)/3 104232 Robert Price 03/2021 7139 2^346213+484049 104221 Enzo Doria 04/2017 7140 18^83021-91 104214 Lelio R Paula 01/2017 7141 10^104212+128779 104213 Patrick De Geest 05/2016 7142 10^104212+237447 104213 Patrick De Geest 05/2016 7143 10^104212+242139 104213 Patrick De Geest 05/2016 7144 10^104212+269199 104213 Patrick De Geest 05/2016 7145 24254^19803+19803^24254 104213 Hans Havermann 09/2020 7146 (10^104212-71)/1 104212 Serge Batalov 12/2014 7147 23678^23821-23821^23678 104202 Norbert Schneider 01/2020 7148 (13*31^69863+12407)/30 104191 Eric Chen 04/2024 7149 2^346078+7695 104180 Lelio R Paula 12/2016 7150 2^346055-19537 104173 Enzo Doria 05/2013 7151 (3*2^346057+1)/77 104173 Lelio R Paula 12/2013 7152 2^346037-20125 104168 Enzo Doria 06/2013 7153 (34*10^104168-7)/9/13/551179 104162 Makoto Morimoto 05/2016 7154 6^133854-17993 104159 Enzo Doria 03/2013 7155 2^345990+1874239 104154 Enzo Doria 06/2016 7156 2^345988-20373 104153 Enzo Doria 06/2013 7157 (2^345965+2214)/2 104146 Stefano Morozzi 09/2020 7158 (26*10^104132-503)/9 104133 Robert Price 07/2018 7159 3*5^148968+8 104125 Lelio R Paula 11/2014 7160 (7*10^104113+53)/3 104114 Robert Price 05/2018 7161 p(21253)#/2+8 104113 Robert Price 01/2017 7162 33582^1259+1259^33582 104106 Hans Havermann 09/2020 7163 32958^1441+1441^32958 104104 Hans Havermann 09/2020 7164 29127^3748+3748^29127 104095 Hans Havermann 09/2020 7165 322^41507+41507^322 104094 Norbert Schneider 12/2014 7166 6^133768-17423 104092 Enzo Doria 03/2013 7167 2^345786-19557 104092 Enzo Doria 05/2013 7169 171^46606-2 104072 Lelio R Paula 10/2017 7168 (29*10^104071+91)/3 104072 Robert Price 04/2020 7170 norm(Mod(x,x^3-x-1)^852167-1) 104070 Paul Vanderveen 09/2022 7171 2^345704-149 104068 Lelio R Paula 09/2011 7172 25821^10712+10712^25821 104056 Hans Havermann 09/2020 7173 (2^345662+2038)/2 104055 Stefano Morozzi 09/2020 7174 6^133704-17273 104042 Enzo Doria 02/2013 7175 (3*2^345590-1)/23 104033 Lelio R Paula 03/2014 7176 (19*2^345590+1)/33859 104030 Lelio R Paula 12/2013 7177 2^345547+11 104021 Lelio R Paula 09/2011 7178 (19*10^104014-49)/3 104015 Robert Price 05/2019 7179 (2^345519+1794)/2 104012 Stefano Morozzi 01/2021 7180 2^345504+723 104008 Lelio R Paula 09/2011 7181 2^345498-20037 104006 Enzo Doria 06/2013 7183 18^82854-37 104005 Lelio R Paula 01/2017 7182 (2^345497+2070)/2 104005 Stefano Morozzi 09/2020 7184 2^345486-109065 104002 Enzo Doria 04/2014 7185 2^345487-1851507 104002 Enzo Doria 08/2015 7186 2^345476+777 103999 Lelio R Paula 09/2011 7187 (2^345477+1554)/2 103999 Stefano Morozzi 09/2020 7188 4*10^103981-83 103982 Robert Price 10/2018 7189 (2^345327+3206)/2 103954 Stefano Morozzi 09/2020 7190 (5*2^345321-1)/3 103953 Lelio R Paula 03/2014 7191 (2^345267-9)/539049127 103927 Lelio R Paula 12/2013 7192 (19*10^103907+77)/3 103908 Robert Price 05/2019 7193 (78557*2^345163+1)/78589 103905 Lelio R Paula 07/2014 7194 2^345106-112181 103888 Enzo Doria 06/2014 7195 (2^345105+1326)/2 103887 Stefano Morozzi 02/2021 7196 2^345079+99 103880 Lelio R Paula 09/2011 7197 (2^345034+1198)/2 103866 Stefano Morozzi 09/2020 7198 11^99736-1500 103865 Enzo Doria 12/2012 7199 (569^37699-1)/568 103863 Serge Batalov 06/2022 7200 (2^345010+2082)/2 103859 Stefano Morozzi 09/2020 7201 23263^23784-23784^23263 103857 Norbert Schneider 01/2020 7202 3*10^103844+31 103845 Robert Price 06/2021 7203 444*33^68368+19 103821 Eric Chen 05/2023 7204 23927^21814+21814^23927 103813 Hans Havermann 09/2020 7205 2^344842-20157 103808 Enzo Doria 06/2013 7206 (47*2^344822+1)/1071 103801 Lelio R Paula 05/2015 7207 2^344802-20765 103796 Enzo Doria 06/2013 7208 2^344794-3821 103794 Yves Minet 05/2011 7209 2^344782-109103 103790 Enzo Doria 04/2014 7210 3^217521-112292 103784 Enzo Doria 06/2014 7211 2^344759-3505 103783 Lelio R Paula 11/2016 7212 2^344735-147 103776 Lelio R Paula 09/2011 7213 L(496533)-p(496533) 103770 Robert Price 02/2018 7214 2*10^103749-69 103750 Robert Price 03/2018 7215 (55459*2^344617+1)/3 103745 Lelio R Paula 07/2014 7216 2^344607-108891 103738 Enzo Doria 03/2014 7218 (2^344608+3798)/2 103738 Stefano Morozzi 02/2021 7217 (1097^34123-1)/1096 103738 Serge Batalov 06/2022 7219 2^344560+22411 103723 Enzo Doria 09/2023 7220 (148*10^103718-1)/3 103720 Robert Price 03/2020 7221 2^344541-19561 103718 Enzo Doria 05/2013 7222 (1017*2^344529-1)/569 103714 Lelio R Paula 05/2015 7223 (8896^26263-1)/8895 103714 Serge Batalov 06/2022 7224 (2^344503+1758)/2 103706 Stefano Morozzi 09/2020 7225 (4*10^103703-1)/3 103704 Serge Batalov 08/2009 7226 2^344444-455 103688 Yves Minet 03/2012 7227 (4*10^103678-43)/3 103679 Robert Price 01/2022 7228 (13*53^238539*617^9)/10^307661 103673 Hans Havermann 06/2017 7229 (2^344367+2738)/2 103665 Stefano Morozzi 01/2021 7231 2^344317-109933 103650 Enzo Doria 04/2014 7230 26055^9508+9508^26055 103650 Hans Havermann 09/2020 7232 2^344309-1852033 103648 Enzo Doria 08/2015 7233 25729^10672+10672^25729 103643 Hans Havermann 09/2020 7234 (2^344289+1166)/2 103642 Stefano Morozzi 09/2020 7235 3*10^103637+61 103638 Robert Price 09/2020 7236 (2^344246+1614)/2 103629 Stefano Morozzi 09/2020 7237 2^344213-21253 103619 Enzo Doria 06/2013 7238 2^344196-465 103614 Lelio R Paula 11/2016 7239 2^344187-20001 103611 Enzo Doria 06/2013 7240 (117191#+(355573#)/(117191#))/(200233679) 103602 Makoto Morimoto 10/2017 7241 (237^43627-1)/236 103601 Serge Batalov 06/2022 7242 20^79621-19^79621 103590 Jean-Louis Charton 03/2011 7243 Phi(155391,10)/1243129 103586 Maksym Voznyy 09/2015 7244 (9^108553-2^108553)/7 103586 Jon Grantham 07/2023 7245 2^344085-20365 103580 Enzo Doria 06/2013 7246 5^148169+54 103566 Lelio R Paula 11/2016 7247 2^344017-108795 103560 Enzo Doria 03/2014 7248 (2^343974+2670)/2 103547 Stefano Morozzi 09/2020 7249 2^343971-5077 103546 Lelio R Paula 09/2011 7250 (7*10^103531+71)/3 103532 Robert Price 05/2018

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 16 2024 09:03 (Time in France)

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