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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
6001 | 5^112070-54 | 78334 | Lelio R Paula | 02/2015 |
6002 | (10^(2*39165+1)+54*10^39165-1)/9 | 78331 | Robert Price | 04/2017 |
6003 | 2^260182-113453 | 78323 | Enzo Doria | 07/2014 |
6004 | f(16405) | 78319 | Robert Price | 09/2017 |
6005 | (78557*2^260084+1)/519 | 78296 | Lelio R Paula | 06/2014 |
6006 | 10^78288+9^(78288+1) | 78289 | Robert Price | 08/2016 |
6007 | 10^78288+39109 | 78289 | Patrick De Geest | 12/2016 |
6008 | 10^78288-216299 | 78288 | Patrick De Geest | 12/2016 |
6009 | 5^111997+36 | 78283 | Lelio R Paula | 02/2015 |
6010 | (21^59183+1)/22 | 78252 | Paul Bourdelais | 03/2010 |
6011 | (88*10^78242-7)/9 | 78243 | Robert Price | 11/2014 |
6012 | 2*6^100547+7 | 78242 | Lelio R Paula | 10/2014 |
6013 | 2^259860-111089 | 78226 | Enzo Doria | 05/2014 |
6014 | 37^49875-2 | 78215 | Lelio R Paula | 09/2013 |
6015 | (13*10^78213+401)/9 | 78214 | Robert Price | 10/2017 |
6016 | 7*5^111893-4 | 78211 | Lelio R Paula | 10/2014 |
6017 | (11*2^259809-1)/1437 | 78209 | Lelio R Paula | 02/2014 |
6018 | 7^92511-6 | 78181 | Theodore Burton | 11/2005 |
6019 | (3^163859-4)/253 | 78179 | Lelio R Paula | 10/2012 |
6020 | (27*2^259666-1)/625691 | 78163 | Lelio R Paula | 02/2014 |
6021 | 3*10^78146+17 | 78147 | Robert Price | 03/2017 |
6022 | (576^28307+1)/577 | 78137 | Richard Fischer | 01/2018 |
6023 | 2^259503+74333 | 78119 | Enzo Doria | 04/2016 |
6024 | (31*2^259504-1)/13365 | 78116 | Lelio R Paula | 02/2014 |
6026 | (58547^16384+1)/2 | 78111 | Lelio R Paula | 11/2011 |
6025 | 6^100379+13 | 78111 | Lelio R Paula | 03/2015 |
6027 | 2^259469-109909 | 78108 | Enzo Doria | 04/2014 |
6028 | 15^66413-26 | 78108 | Lelio R Paula | 02/2015 |
6029 | 7^92410-9266 | 78096 | Mike Oakes | 02/2010 |
6030 | 2^259398+75799 | 78087 | Enzo Doria | 04/2016 |
6031 | 2^259394+1876189 | 78086 | Enzo Doria | 07/2016 |
6032 | PIPrime(78073) | 78073 | Eric W. Weisstein | 07/2006 |
6033 | 5*2^259344-7 | 78072 | Lelio R Paula | 06/2014 |
6034 | 14^68097-87 | 78048 | Lelio R Paula | 02/2015 |
6035 | 2^259233-475573 | 78037 | Paul Bourdelais | 03/2013 |
6036 | 181^34554-2 | 78012 | Lelio R Paula | 10/2017 |
6037 | 3^163500-28 | 78010 | Robert Price | 12/2013 |
6038 | (65*10^77992+691)/9 | 77993 | Robert Price | 08/2016 |
6039 | 2^259013-112591 | 77971 | Enzo Doria | 06/2014 |
6040 | 7*10^77969-11 | 77970 | Robert Price | 10/2017 |
6041 | 6^100193-100193^6 | 77966 | Norbert Schneider | 04/2017 |
6042 | 2^258863-110235 | 77926 | Enzo Doria | 05/2014 |
6043 | 2^258852+1605 | 77923 | Lelio R Paula | 06/2013 |
6044 | (11*10^77909+49)/3 | 77910 | Robert Price | 05/2016 |
6045 | 2*7^92187-9 | 77908 | Lelio R Paula | 10/2014 |
6046 | 2^258763-110155 | 77896 | Enzo Doria | 04/2014 |
6047 | 2^258694-110387 | 77875 | Enzo Doria | 05/2014 |
6048 | 11^74773-94 | 77869 | Lelio R Paula | 02/2015 |
6049 | 6^100067+125 | 77868 | Lelio R Paula | 03/2015 |
6050 | 15^66205+8 | 77864 | Lelio R Paula | 07/2014 |
6051 | 5^111373-18136 | 77847 | Enzo Doria | 05/2014 |
6052 | 2^258524-109877 | 77824 | Enzo Doria | 04/2014 |
6053 | 6^100002-16643 | 77817 | Enzo Doria | 02/2013 |
6054 | (13*10^77811+347)/9 | 77812 | Robert Price | 10/2017 |
6055 | 65^42916+28 | 77803 | Lelio R Paula | 01/2016 |
6056 | (89*10^77781-17)/9 | 77782 | Robert Price | 11/2015 |
6057 | 2^258382-110405 | 77781 | Enzo Doria | 05/2014 |
6058 | 5^111278-14996 | 77780 | Enzo Doria | 02/2013 |
6059 | 14^67862+61 | 77779 | Lelio R Paula | 02/2015 |
6060 | 10^77777+48483 | 77778 | Patrick De Geest | 11/2010 |
6061 | 10^77777-183243 | 77777 | Patrick De Geest | 11/2010 |
6062 | (27*2^258352+1)/43 | 77772 | Lelio R Paula | 08/2012 |
6063 | 337^30756-10002 | 77740 | Enzo Doria | 07/2012 |
6064 | 10^77726+99 | 77727 | Robert Price | 03/2011 |
6065 | 10^77726-85947 | 77726 | Patrick De Geest | 06/2013 |
6066 | 89^39870-2 | 77723 | Lelio R Paula | 08/2013 |
6067 | 7^91966-32 | 77721 | Lelio R Paula | 02/2015 |
6068 | 35^50327+2 | 77709 | Lelio R Paula | 05/2013 |
6069 | 24^56298+23 | 77704 | Norbert Schneider | 12/2016 |
6070 | (2^258105+78557)/19 | 77697 | Lelio R Paula | 10/2012 |
6071 | 2^258079+179 | 77690 | Lelio R Paula | 03/2012 |
6072 | 2^258062-113111 | 77685 | Enzo Doria | 07/2014 |
6073 | 80^40807-79 | 77660 | Norbert Schneider | 03/2015 |
6074 | (10^77637+359)/9 | 77637 | Serge Batalov | 12/2014 |
6075 | 2^257862-165 | 77625 | Lelio R Paula | 03/2012 |
6076 | (25*2^257853+1)/3 | 77623 | Lelio R Paula | 07/2012 |
6077 | (2^257869+1)/(3*18645362967379) | 77613 | Henri Lifchitz | 04/2005 |
6078 | 6^99728+71 | 77604 | Lelio R Paula | 01/2015 |
6079 | 2^257778-112767 | 77599 | Enzo Doria | 06/2014 |
6080 | (31*2^257771+1)/537 | 77596 | Lelio R Paula | 07/2012 |
6081 | 2^257729-73 | 77585 | Lelio R Paula | 03/2012 |
6082 | 2^257689-63 | 77573 | Lelio R Paula | 03/2012 |
6083 | (47*10^77572+493)/9 | 77573 | Robert Price | 11/2017 |
6084 | (78557*2^257665+1)/6108725 | 77564 | Lelio R Paula | 06/2014 |
6085 | (3^162563+8)/2885 | 77559 | Lelio R Paula | 10/2012 |
6086 | 2^257636-110235 | 77557 | Enzo Doria | 05/2014 |
6087 | (23*10^77556+97)/3 | 77557 | Robert Price | 02/2017 |
6088 | 2^257621-110071 | 77552 | Enzo Doria | 04/2014 |
6089 | 2^257567-64875 | 77536 | Lelio R Paula | 06/2013 |
6090 | 2*7^91674+9 | 77474 | Lelio R Paula | 10/2014 |
6091 | (17*10^77427-47)/3 | 77428 | Robert Price | 05/2017 |
6092 | 10^77418+841683 | 77419 | Patrick De Geest | 06/2013 |
6093 | 10^77418-33 | 77418 | Robert Price | 05/2011 |
6094 | 19^60539-36 | 77415 | Lelio R Paula | 03/2015 |
6095 | 37401!!-1024 | 77397 | Robert Price | 11/2015 |
6096 | 11^74313-18750 | 77390 | Enzo Doria | 12/2012 |
6098 | 2^257044-112883 | 77378 | Enzo Doria | 06/2014 |
6097 | 8*10^77377+51 | 77378 | Robert Price | 05/2017 |
6099 | 2*7^91553+9 | 77372 | Lelio R Paula | 10/2014 |
6100 | 713^27118+27118^713 | 77371 | Norbert Schneider | 12/2016 |
6101 | 2^256920-111155 | 77341 | Enzo Doria | 05/2014 |
6102 | 2^256896-6555 | 77334 | Lelio R Paula | 06/2013 |
6103 | (52*10^77322-7)/9 | 77323 | Robert Price | 12/2014 |
6104 | 2^256849-112939 | 77320 | Enzo Doria | 06/2014 |
6105 | (4*10^77309-31)/9 | 77309 | Erik Branger | 05/2011 |
6106 | (3^161988+7)/41864 | 77284 | Lelio R Paula | 10/2012 |
6107 | (14^67421-1)/13 | 77272 | Paul Bourdelais | 09/2008 |
6108 | 5*3^161923-4 | 77258 | Lelio R Paula | 06/2014 |
6109 | 2^256552-1499 | 77230 | Yves Minet | 05/2013 |
6110 | 2^256460-112757 | 77203 | Enzo Doria | 06/2014 |
6111 | 2^256398+23299 | 77184 | Yves Minet | 02/2011 |
6112 | 2^256391-1155*256391 | 77182 | Henri Lifchitz | 03/2005 |
6113 | (2^256391-9)/56593 | 77177 | Lelio R Paula | 10/2012 |
6114 | (2^256308+9)/10585 | 77153 | Lelio R Paula | 10/2012 |
6115 | 21^58348-2 | 77149 | Lelio R Paula | 08/2013 |
6116 | (17*2^256291-1)/4785 | 77149 | Lelio R Paula | 02/2014 |
6117 | (5*2^256274-1)/2141 | 77144 | Lelio R Paula | 02/2014 |
6118 | 19^60321+82 | 77136 | Lelio R Paula | 03/2015 |
6119 | 5*2^256233-3 | 77135 | Lelio R Paula | 06/2014 |
6120 | 3*2^256149+7 | 77110 | Lelio R Paula | 06/2014 |
6121 | 3^161594-106 | 77100 | Lelio R Paula | 02/2015 |
6122 | 2^256114-185 | 77098 | Lelio R Paula | 03/2012 |
6123 | 8^85349-85349^8 | 77078 | Norbert Schneider | 05/2017 |
6124 | 2^256043-2786377 | 77077 | Enzo Doria | 03/2016 |
6125 | 2^255973+1869947 | 77056 | Enzo Doria | 05/2016 |
6126 | 12^71393-43 | 77046 | Lelio R Paula | 02/2015 |
6127 | 15^65490+44 | 77023 | Lelio R Paula | 02/2015 |
6128 | (3^161411-7)/940 | 77010 | Lelio R Paula | 10/2012 |
6130 | lucasU(1107,1,25297)-lucasU(1107,1,25296) | 77005 | Mike Oakes | 05/2009 |
6129 | (570^27943-1)/569 | 77005 | Serge Batalov | 12/2016 |
6131 | 2^255750-75 | 76989 | Lelio R Paula | 03/2012 |
6132 | 3*6^98926-5 | 76980 | Lelio R Paula | 10/2014 |
6133 | 18^61320-1433 | 76974 | Enzo Doria | 03/2013 |
6134 | 6^98916-17093 | 76972 | Enzo Doria | 02/2013 |
6135 | 2^255659-110131 | 76962 | Enzo Doria | 04/2014 |
6136 | 12^71303+91 | 76949 | Lelio R Paula | 02/2015 |
6137 | 18^61298+59 | 76946 | Lelio R Paula | 02/2015 |
6138 | (223^32768+1)/131074 | 76945 | Lelio R Paula | 02/2009 |
6139 | (2^255613-5)/281517 | 76942 | Lelio R Paula | 10/2012 |
6140 | 18^61290-11 | 76936 | Lelio R Paula | 02/2015 |
6142 | 63^42752-2 | 76926 | Lelio R Paula | 08/2013 |
6141 | (11*2^255545-1)/117 | 76926 | Lelio R Paula | 02/2014 |
6143 | 2^255517+56387 | 76919 | Yves Minet | 02/2011 |
6144 | 2^255499-112567 | 76913 | Enzo Doria | 06/2014 |
6145 | 2^255492+345 | 76911 | Lelio R Paula | 06/2013 |
6146 | 10^76875+217591 | 76876 | Patrick De Geest | 05/2013 |
6148 | 10^76875-53 | 76875 | Robert Price | 05/2011 |
6147 | 11^73819-5880 | 76875 | Enzo Doria | 01/2013 |
6149 | 2^255313+18915 | 76857 | Lelio R Paula | 06/2013 |
6150 | (2^255320-1017)/1446667 | 76853 | Lelio R Paula | 10/2012 |
6151 | 2^255296+5775 | 76852 | Lelio R Paula | 06/2013 |
6152 | 14^67052-29 | 76851 | Lelio R Paula | 02/2015 |
6153 | (8*10^76840+43)/3 | 76841 | Robert Price | 10/2017 |
6154 | (7*10^76818-313)/9 | 76818 | Robert Price | 11/2016 |
6155 | 10^76801+69 | 76802 | Robert Price | 03/2011 |
6156 | 10^76801-80943 | 76801 | Patrick De Geest | 06/2013 |
6157 | 2^255105+57 | 76795 | Lelio R Paula | 03/2012 |
6158 | (lucasV(1,2,510187)+2)/(3*5*11) | 76789 | Mike Oakes | 04/2017 |
6159 | (2^255097-7)/20020055 | 76785 | Lelio R Paula | 10/2012 |
6160 | 2^255055+1869353 | 76780 | Enzo Doria | 05/2016 |
6161 | 17^62396-90 | 76776 | Lelio R Paula | 03/2015 |
6162 | 7^90833-60 | 76763 | Lelio R Paula | 02/2015 |
6163 | 13^68901-56 | 76752 | Lelio R Paula | 03/2015 |
6164 | 2^254961+1869917 | 76751 | Enzo Doria | 05/2016 |
6165 | 9*5^109791-8 | 76742 | Lelio R Paula | 10/2014 |
6166 | 82^40089+40089^82 | 76723 | Serge Batalov | 02/2012 |
6167 | 2^254861-2790013 | 76721 | Enzo Doria | 03/2016 |
6168 | 10^76705+13 | 76706 | Robert Price | 01/2011 |
6169 | 10^76705-94077 | 76705 | Patrick De Geest | 06/2013 |
6170 | (5*2^254785-1)/999 | 76696 | Lelio R Paula | 02/2014 |
6171 | 2^254758-110405 | 76690 | Enzo Doria | 05/2014 |
6172 | 2^254716-3779 | 76678 | Yves Minet | 04/2017 |
6173 | 2^254708-110507 | 76675 | Enzo Doria | 05/2014 |
6174 | (47*10^76672+133)/9 | 76673 | Robert Price | 04/2017 |
6175 | 2^254670-112901 | 76664 | Enzo Doria | 06/2014 |
6176 | (3^160665+7)/981350 | 76651 | Lelio R Paula | 10/2012 |
6177 | 2^254598-113183 | 76642 | Enzo Doria | 07/2014 |
6178 | 19^59932+22 | 76639 | Lelio R Paula | 01/2015 |
6179 | 2^254569-112213 | 76633 | Enzo Doria | 06/2014 |
6180 | 2*5^109626+9 | 76626 | Lelio R Paula | 10/2014 |
6181 | 2^254521+1872527 | 76619 | Enzo Doria | 05/2016 |
6182 | (76*10^76615+167)/9 | 76616 | Robert Price | 08/2016 |
6183 | 25^54799-24^54799 | 76606 | Robert Price | 07/2012 |
6184 | (24737*2^254464+1)/9 | 76605 | Lelio R Paula | 06/2014 |
6185 | 12^70961-85 | 76580 | Lelio R Paula | 02/2015 |
6186 | 7^90590-38 | 76558 | Lelio R Paula | 02/2015 |
6187 | 2^254304+5227 | 76554 | Lelio R Paula | 06/2013 |
6188 | (76*10^76547-211)/9 | 76548 | Robert Price | 10/2017 |
6189 | 18^60979-5363 | 76546 | Enzo Doria | 03/2013 |
6190 | (21181*2^254264+1)/55314379 | 76538 | Lelio R Paula | 06/2014 |
6192 | (34*10^76547-7)/9/61/94529/214807 | 76536 | Makoto Morimoto | 05/2016 |
6191 | (7*10^76536-313)/9 | 76536 | Robert Price | 11/2016 |
6194 | 2^254239-27 | 76534 | Lelio R Paula | 03/2012 |
6193 | 2^254238-1841 | 76534 | Yves Minet | 03/2013 |
6195 | (10^76537-1)/9/66127969 | 76529 | Jens K. Andersen | 04/2009 |
6196 | 2^254189-112225 | 76519 | Enzo Doria | 06/2014 |
6197 | 18^60938-1397 | 76494 | Enzo Doria | 03/2013 |
6198 | 2^254075-2788417 | 76485 | Enzo Doria | 03/2016 |
6199 | 7*10^76483-23 | 76484 | Robert Price | 04/2016 |
6200 | 2^254042-112913 | 76475 | Enzo Doria | 06/2014 |
6201 | 14^66723-37 | 76474 | Lelio R Paula | 02/2015 |
6202 | 2^254037-110305 | 76473 | Enzo Doria | 05/2014 |
6203 | 2^253931-111109 | 76441 | Enzo Doria | 05/2014 |
6204 | 2^253926-1167 | 76440 | Lelio R Paula | 05/2013 |
6205 | (49*10^76438-13)/9 | 76439 | Robert Price | 07/2015 |
6206 | (21*2^253845-1)/143 | 76415 | Lelio R Paula | 02/2014 |
6207 | 10^76374+31 | 76375 | Robert Price | 03/2011 |
6208 | 10^76374-222159 | 76374 | Patrick De Geest | 05/2013 |
6209 | 2^253561-110533 | 76330 | Enzo Doria | 05/2014 |
6210 | gcd(V(917285),5*F(183457)*(F(183457)+1)+1) | 76321 | Serge Batalov | 04/2015 |
6211 | 9*5^109182+2 | 76316 | Lelio R Paula | 10/2014 |
6212 | 11^73279-3690 | 76313 | Enzo Doria | 12/2012 |
6213 | (598*10^76309-31)/9 | 76311 | Robert Price | 02/2017 |
6214 | 11^73274-24000 | 76308 | Enzo Doria | 12/2012 |
6215 | 7^90291-6 | 76305 | Theodore Burton | 11/2005 |
6216 | (21181*2^253432+1)/21437 | 76291 | Lelio R Paula | 06/2014 |
6217 | 6^98025+145 | 76279 | Lelio R Paula | 01/2015 |
6218 | 2^253355+1155 | 76268 | Lelio R Paula | 05/2013 |
6219 | (73*10^76262+413)/9 | 76263 | Robert Price | 10/2017 |
6220 | 2^253292-71219 | 76249 | Enzo Doria | 04/2016 |
6221 | 7^90221-36 | 76246 | Lelio R Paula | 02/2015 |
6222 | 18^60727-3473 | 76229 | Enzo Doria | 03/2013 |
6223 | (78557*2^253184+1)/3 | 76221 | Lelio R Paula | 06/2014 |
6224 | (8*10^76220-83)/3 | 76221 | Robert Price | 10/2017 |
6225 | (44791^20480+1)/(44791^4096+1) | 76206 | Serge Batalov | 01/2017 |
6226 | 11^73163-2010 | 76192 | Enzo Doria | 12/2012 |
6227 | 2^253060+54615 | 76179 | Lelio R Paula | 05/2013 |
6228 | 2^253029+1869761 | 76170 | Enzo Doria | 05/2016 |
6229 | 2^252955-111007 | 76148 | Enzo Doria | 05/2014 |
6230 | 2*5^108931+7 | 76140 | Lelio R Paula | 10/2014 |
6231 | (86*10^76128+121)/9 | 76129 | Robert Price | 03/2017 |
6232 | 22154*29^52050+9 | 76123 | Curtis Bright | 05/2015 |
6233 | 3^159530-112358 | 76116 | Enzo Doria | 06/2014 |
6234 | 11^73089-48 | 76115 | Lelio R Paula | 02/2015 |
6235 | 86^39337-85 | 76098 | Norbert Schneider | 10/2015 |
6236 | (3^159505-7)/313297316 | 76095 | Lelio R Paula | 06/2012 |
6237 | 6^97783+77 | 76090 | Lelio R Paula | 01/2015 |
6238 | 2^252712-105 | 76074 | Lelio R Paula | 03/2012 |
6239 | (10^76069-19)/9 | 76069 | Robert Price | 10/2017 |
6241 | 131^35927+2 | 76068 | Lelio R Paula | 05/2013 |
6240 | (41*10^76067+373)/9 | 76068 | Robert Price | 04/2017 |
6242 | 2^252683-139 | 76066 | Lelio R Paula | 03/2012 |
6243 | 137^35597-136 | 76061 | Norbert Schneider | 05/2015 |
6244 | 3^159413+106 | 76060 | Lelio R Paula | 01/2015 |
6245 | 9^79677+3*8^79677-2*4^79677-3*2^79677 | 76032 | Mike Oakes | 12/2010 |
6246 | (2^252557-9)/71 | 76026 | Lelio R Paula | 07/2012 |
6247 | (85*10^76021-103)/9 | 76022 | Robert Price | 10/2017 |
6248 | 11^72989+80 | 76011 | Lelio R Paula | 02/2015 |
6249 | 99877!6-36 | 75996 | Robert Price | 11/2018 |
6250 | 2^252449-459523 | 75995 | Enzo Doria | 05/2015 |