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 ? |
8001 | 2^338414+26083 | 101873 | Stefano Morozzi | 12/2021 |
8002 | 2^338412-152379 | 101873 | Stefano Morozzi | 12/2021 |
8003 | 2^338413+54797 | 101873 | Stefano Morozzi | 01/2022 |
8004 | 2^338412+157951 | 101873 | Stefano Morozzi | 02/2022 |
8005 | 2^338414+81627 | 101873 | Stefano Morozzi | 02/2022 |
8006 | 2^338413+133679 | 101873 | Stefano Morozzi | 03/2022 |
8007 | 2^338413+197735 | 101873 | Stefano Morozzi | 11/2022 |
8008 | 2^338413-114301 | 101873 | Stefano Morozzi | 01/2023 |
8009 | 11*32^67682+395 | 101873 | Eric Chen | 04/2023 |
8010 | 2^338409-52183 | 101872 | Stefano Morozzi | 12/2021 |
8011 | 2^338411-3789 | 101872 | Stefano Morozzi | 01/2022 |
8012 | 2^338409+173237 | 101872 | Stefano Morozzi | 11/2022 |
8013 | 2^338406-184175 | 101871 | Stefano Morozzi | 04/2022 |
8014 | 2^338405+94451 | 101871 | Stefano Morozzi | 09/2022 |
8015 | 2^338406-161217 | 101871 | Stefano Morozzi | 12/2022 |
8016 | 2^338406+199929 | 101871 | Stefano Morozzi | 02/2023 |
8017 | 2^338404+55717 | 101870 | Stefano Morozzi | 01/2022 |
8018 | 2^338403+36261 | 101870 | Stefano Morozzi | 04/2022 |
8019 | 2^338402-34431 | 101870 | Stefano Morozzi | 04/2022 |
8020 | 2^338404-159215 | 101870 | Stefano Morozzi | 04/2022 |
8021 | 2^338403+18363 | 101870 | Stefano Morozzi | 09/2022 |
8022 | 2^338403+170235 | 101870 | Stefano Morozzi | 11/2022 |
8023 | 2^338399+23045 | 101869 | Stefano Morozzi | 11/2022 |
8024 | 2^338399-65535 | 101869 | Stefano Morozzi | 01/2023 |
8025 | 2^338395-127449 | 101868 | Stefano Morozzi | 12/2021 |
8026 | 2^338398-127637 | 101868 | Stefano Morozzi | 01/2022 |
8027 | 2^338398-166533 | 101868 | Stefano Morozzi | 01/2023 |
8028 | 2^338394+100317 | 101867 | Stefano Morozzi | 11/2021 |
8029 | 2^338393-152749 | 101867 | Stefano Morozzi | 01/2022 |
8030 | 2^338393+163025 | 101867 | Stefano Morozzi | 04/2022 |
8031 | 2^338393+89229 | 101867 | Stefano Morozzi | 05/2022 |
8032 | 2^338393+99647 | 101867 | Stefano Morozzi | 02/2023 |
8033 | 2^338394-192471 | 101867 | Stefano Morozzi | 02/2023 |
8034 | 2^338390+76627 | 101866 | Stefano Morozzi | 12/2021 |
8035 | 2^338389-85081 | 101866 | Stefano Morozzi | 06/2022 |
8036 | 2^338390+148113 | 101866 | Stefano Morozzi | 11/2022 |
8037 | 2^338389-14253 | 101866 | Stefano Morozzi | 01/2023 |
8038 | 2^338390-114297 | 101866 | Stefano Morozzi | 01/2023 |
8039 | 2^338391-64225 | 101866 | Stefano Morozzi | 01/2023 |
8040 | 2^338389-16971 | 101866 | Stefano Morozzi | 02/2023 |
8041 | 2^338387-75685 | 101865 | Stefano Morozzi | 12/2021 |
8042 | 2^338388-53459 | 101865 | Stefano Morozzi | 01/2022 |
8043 | 2^338388-36575 | 101865 | Stefano Morozzi | 12/2022 |
8044 | 2^338385-190311 | 101865 | Stefano Morozzi | 01/2023 |
8045 | 2^338384+131563 | 101864 | Stefano Morozzi | 01/2022 |
8046 | 2^338382+109069 | 101864 | Stefano Morozzi | 03/2022 |
8047 | 2^338384+168987 | 101864 | Stefano Morozzi | 09/2022 |
8048 | 2^338383-42367 | 101864 | Stefano Morozzi | 02/2023 |
8049 | 2^338380+77125 | 101863 | Stefano Morozzi | 12/2021 |
8050 | 2^338381-35539 | 101863 | Stefano Morozzi | 06/2022 |
8051 | 2^338378-125841 | 101862 | Stefano Morozzi | 12/2021 |
8052 | 2^338375+27815 | 101862 | Stefano Morozzi | 01/2022 |
8053 | 2^338375-28509 | 101862 | Stefano Morozzi | 01/2022 |
8054 | 2^338375+29985 | 101862 | Stefano Morozzi | 01/2022 |
8055 | 2^338377+157881 | 101862 | Stefano Morozzi | 02/2022 |
8056 | 2^338375+59589 | 101862 | Stefano Morozzi | 03/2022 |
8057 | 2^338378+36399 | 101862 | Stefano Morozzi | 04/2022 |
8058 | 2^338378-159773 | 101862 | Stefano Morozzi | 04/2022 |
8059 | 2^338378+14883 | 101862 | Stefano Morozzi | 05/2022 |
8060 | 2^338376+140173 | 101862 | Stefano Morozzi | 06/2022 |
8061 | 2^338375+18761 | 101862 | Stefano Morozzi | 09/2022 |
8062 | 2^338373-75103 | 101861 | Stefano Morozzi | 12/2021 |
8063 | 2^338372+128877 | 101861 | Stefano Morozzi | 01/2022 |
8064 | 2^338374-28731 | 101861 | Stefano Morozzi | 01/2022 |
8065 | 2^338374-128427 | 101861 | Stefano Morozzi | 01/2022 |
8066 | 2^338372+37875 | 101861 | Stefano Morozzi | 04/2022 |
8067 | 2^338373+161541 | 101861 | Stefano Morozzi | 04/2022 |
8068 | 2^338374+37759 | 101861 | Stefano Morozzi | 04/2022 |
8069 | 2^338372+93235 | 101861 | Stefano Morozzi | 09/2022 |
8070 | 2^338373-63273 | 101861 | Stefano Morozzi | 12/2022 |
8071 | 2^338369+29427 | 101860 | Stefano Morozzi | 01/2022 |
8072 | 2^338370+179133 | 101860 | Stefano Morozzi | 01/2022 |
8073 | 2^338369+131501 | 101860 | Stefano Morozzi | 01/2022 |
8074 | 2^338369+181649 | 101860 | Stefano Morozzi | 02/2022 |
8075 | 2^338370-4787 | 101860 | Stefano Morozzi | 02/2022 |
8076 | 2^338371-133491 | 101860 | Stefano Morozzi | 04/2022 |
8077 | 2^338371+42023 | 101860 | Stefano Morozzi | 09/2022 |
8078 | 2^338371+145323 | 101860 | Stefano Morozzi | 11/2022 |
8079 | 2^338371-138145 | 101860 | Stefano Morozzi | 12/2022 |
8086 | 2^338368-20369 | 101859 | Enzo Doria | 06/2013 |
8087 | 2^338366+74179 | 101859 | Enzo Doria | 04/2016 |
8080 | 2^338366+53853 | 101859 | Stefano Morozzi | 01/2022 |
8081 | 2^338365-31665 | 101859 | Stefano Morozzi | 03/2022 |
8082 | 2^338368-156345 | 101859 | Stefano Morozzi | 03/2022 |
8083 | 2^338366-159867 | 101859 | Stefano Morozzi | 04/2022 |
8084 | 2^338368-63509 | 101859 | Stefano Morozzi | 12/2022 |
8085 | 2^338365-190975 | 101859 | Stefano Morozzi | 01/2023 |
8088 | 2^338362-180845 | 101858 | Stefano Morozzi | 02/2022 |
8089 | 2^338364-155769 | 101858 | Stefano Morozzi | 02/2022 |
8090 | 2^338362+142843 | 101858 | Stefano Morozzi | 09/2022 |
8091 | 2^338362+170019 | 101858 | Stefano Morozzi | 11/2022 |
8092 | 2^338361-100875 | 101857 | Stefano Morozzi | 12/2021 |
8093 | 2^338361+154169 | 101857 | Stefano Morozzi | 01/2022 |
8094 | 2^338359-189645 | 101857 | Stefano Morozzi | 01/2023 |
8095 | 2^338356+101271 | 101856 | Stefano Morozzi | 12/2021 |
8096 | 2^338356+53383 | 101856 | Stefano Morozzi | 01/2022 |
8097 | 2^338355+59393 | 101856 | Stefano Morozzi | 03/2022 |
8098 | 2^338356+60775 | 101856 | Stefano Morozzi | 03/2022 |
8099 | 2^338356-106257 | 101856 | Stefano Morozzi | 03/2022 |
8100 | 2^338357-58921 | 101856 | Stefano Morozzi | 04/2022 |
8101 | 2^338356+94605 | 101856 | Stefano Morozzi | 09/2022 |
8102 | 2^338356+117813 | 101856 | Stefano Morozzi | 09/2022 |
8103 | 2^338358-38475 | 101856 | Stefano Morozzi | 12/2022 |
8104 | 2^338353-190291 | 101855 | Stefano Morozzi | 01/2023 |
8105 | 2^338350-152933 | 101854 | Stefano Morozzi | 01/2022 |
8106 | 2^338350+6337 | 101854 | Stefano Morozzi | 01/2022 |
8107 | 2^338350+168759 | 101854 | Stefano Morozzi | 09/2022 |
8110 | 27088^5755+5755^27088 | 101853 | Hans Havermann | 01/2019 |
8108 | 2^338347+125901 | 101853 | Stefano Morozzi | 11/2021 |
8109 | 2^338346-10643 | 101853 | Stefano Morozzi | 06/2022 |
8111 | 2^338343+152271 | 101852 | Stefano Morozzi | 12/2021 |
8112 | 2^338345+154107 | 101852 | Stefano Morozzi | 01/2022 |
8113 | 2^338342+155397 | 101852 | Stefano Morozzi | 01/2022 |
8114 | 2^338342-130767 | 101852 | Stefano Morozzi | 02/2022 |
8115 | 2^338345-30123 | 101852 | Stefano Morozzi | 02/2022 |
8116 | 2^338345+35747 | 101852 | Stefano Morozzi | 03/2022 |
8117 | 2^338345-133131 | 101852 | Stefano Morozzi | 04/2022 |
8118 | 2^338345-134559 | 101852 | Stefano Morozzi | 04/2022 |
8119 | 2^338342+170073 | 101852 | Stefano Morozzi | 11/2022 |
8120 | 2^338344+46567 | 101852 | Stefano Morozzi | 11/2022 |
8121 | 2^338344+97141 | 101852 | Stefano Morozzi | 11/2022 |
8122 | 2^338342-162213 | 101852 | Stefano Morozzi | 12/2022 |
8123 | 2^338339+2753 | 101851 | Stefano Morozzi | 12/2021 |
8124 | 2^338341+128415 | 101851 | Stefano Morozzi | 01/2022 |
8125 | 2^338338+2677 | 101850 | Stefano Morozzi | 12/2021 |
8126 | 2^338336+54607 | 101850 | Stefano Morozzi | 01/2022 |
8127 | 2^338338+109999 | 101850 | Stefano Morozzi | 03/2022 |
8128 | 2^338336+161575 | 101850 | Stefano Morozzi | 04/2022 |
8129 | 2^338335+51975 | 101849 | Stefano Morozzi | 12/2021 |
8130 | 2^338335-152607 | 101849 | Stefano Morozzi | 01/2022 |
8131 | 2^338334+55273 | 101849 | Stefano Morozzi | 01/2022 |
8132 | 2^338332+34315 | 101849 | Stefano Morozzi | 03/2022 |
8133 | 2^338335+158759 | 101849 | Stefano Morozzi | 03/2022 |
8134 | 2^338332+67621 | 101849 | Stefano Morozzi | 09/2022 |
8135 | 2^338332-66099 | 101849 | Stefano Morozzi | 01/2023 |
8136 | 2^338334-191043 | 101849 | Stefano Morozzi | 01/2023 |
8137 | 2^338331+83403 | 101848 | Stefano Morozzi | 02/2022 |
8138 | 2^338330-110865 | 101848 | Stefano Morozzi | 06/2022 |
8139 | 2^338330+71047 | 101848 | Stefano Morozzi | 11/2022 |
8140 | 2^338328-5295 | 101847 | Stefano Morozzi | 02/2022 |
8141 | 2^338327+143585 | 101847 | Stefano Morozzi | 09/2022 |
8142 | 2^338324-179667 | 101846 | Stefano Morozzi | 02/2022 |
8143 | 2^338322+21903 | 101846 | Stefano Morozzi | 11/2022 |
8144 | 2^338324+98047 | 101846 | Stefano Morozzi | 11/2022 |
8145 | 2^338323-87729 | 101846 | Stefano Morozzi | 12/2022 |
8146 | 2^338322-16667 | 101846 | Stefano Morozzi | 01/2023 |
8147 | 2^338325-142159 | 101846 | Stefano Morozzi | 02/2023 |
8148 | 2^338316-175857 | 101844 | Stefano Morozzi | 12/2021 |
8149 | 2^338318+54405 | 101844 | Stefano Morozzi | 01/2022 |
8150 | 2^338316+32961 | 101844 | Stefano Morozzi | 02/2022 |
8151 | 2^338317+68175 | 101844 | Stefano Morozzi | 09/2022 |
8152 | 2^338318-86171 | 101844 | Stefano Morozzi | 12/2022 |
8153 | 2^338315-178635 | 101843 | Stefano Morozzi | 01/2022 |
8154 | 2^338315+34899 | 101843 | Stefano Morozzi | 03/2022 |
8155 | 2^338314-106973 | 101843 | Stefano Morozzi | 03/2022 |
8156 | 2^338313+170411 | 101843 | Stefano Morozzi | 11/2022 |
8157 | 2^338315-88807 | 101843 | Stefano Morozzi | 12/2022 |
8158 | 2^338311-51799 | 101842 | Stefano Morozzi | 12/2021 |
8159 | 2^338309+157259 | 101842 | Stefano Morozzi | 02/2022 |
8160 | 2^338310+40903 | 101842 | Stefano Morozzi | 06/2022 |
8161 | 2^338309-168051 | 101842 | Stefano Morozzi | 02/2023 |
8162 | 2^338308-55853 | 101841 | Stefano Morozzi | 02/2022 |
8163 | 2^338307+134871 | 101841 | Stefano Morozzi | 03/2022 |
8164 | 2^338307+19689 | 101841 | Stefano Morozzi | 09/2022 |
8165 | 2^338308+66873 | 101841 | Stefano Morozzi | 09/2022 |
8166 | 2^338306+124399 | 101841 | Stefano Morozzi | 02/2023 |
8167 | 2^338306-91913 | 101841 | Stefano Morozzi | 02/2023 |
8168 | 2^338304+78757 | 101840 | Stefano Morozzi | 01/2022 |
8169 | 2^338304-5807 | 101840 | Stefano Morozzi | 02/2022 |
8170 | 2^338305+110879 | 101840 | Stefano Morozzi | 03/2022 |
8171 | 2^338304+91147 | 101840 | Stefano Morozzi | 06/2022 |
8172 | 2^338304-64475 | 101840 | Stefano Morozzi | 01/2023 |
8173 | 2^338299+85611 | 101839 | Stefano Morozzi | 03/2022 |
8174 | 2^338299-189985 | 101839 | Stefano Morozzi | 01/2023 |
8175 | 2^338298-25571 | 101838 | Stefano Morozzi | 12/2021 |
8176 | 2^338297+35547 | 101838 | Stefano Morozzi | 03/2022 |
8177 | 2^338298+111199 | 101838 | Stefano Morozzi | 03/2022 |
8178 | 2^338297+145455 | 101838 | Stefano Morozzi | 11/2022 |
8179 | 2^338297-166285 | 101838 | Stefano Morozzi | 01/2023 |
8180 | 2^338294-150711 | 101837 | Stefano Morozzi | 12/2021 |
8181 | 2^338294+177597 | 101837 | Stefano Morozzi | 12/2021 |
8182 | 2^338294-177807 | 101837 | Stefano Morozzi | 01/2022 |
8183 | 2^338295-52929 | 101837 | Stefano Morozzi | 01/2022 |
8184 | 2^338293+37407 | 101837 | Stefano Morozzi | 04/2022 |
8185 | 2^338292+40573 | 101837 | Stefano Morozzi | 06/2022 |
8186 | 2^338294+172425 | 101837 | Stefano Morozzi | 11/2022 |
8187 | 2^338293-191799 | 101837 | Stefano Morozzi | 02/2023 |
8188 | 2^338289+30957 | 101836 | Stefano Morozzi | 01/2022 |
8189 | 2^338291+131825 | 101836 | Stefano Morozzi | 02/2022 |
8190 | 2^338291+110111 | 101836 | Stefano Morozzi | 03/2022 |
8191 | 2^338290-156423 | 101836 | Stefano Morozzi | 03/2022 |
8192 | 2^338291-157845 | 101836 | Stefano Morozzi | 03/2022 |
8193 | 2^338290+69243 | 101836 | Stefano Morozzi | 09/2022 |
8194 | 2^338291-189327 | 101836 | Stefano Morozzi | 01/2023 |
8195 | 2^338291+74079 | 101836 | Stefano Morozzi | 02/2023 |
8196 | 2^338288+26623 | 101835 | Stefano Morozzi | 12/2021 |
8197 | 2^338286+33325 | 101835 | Stefano Morozzi | 02/2022 |
8198 | 2^338287+132633 | 101835 | Stefano Morozzi | 02/2022 |
8199 | 2^338287+157149 | 101835 | Stefano Morozzi | 02/2022 |
8200 | 2^338288-107193 | 101835 | Stefano Morozzi | 03/2022 |
8201 | 2^338286-83333 | 101835 | Stefano Morozzi | 04/2022 |
8202 | 2^338287+114425 | 101835 | Stefano Morozzi | 05/2022 |
8203 | 2^338288+194403 | 101835 | Stefano Morozzi | 09/2022 |
8204 | 2^338288-113177 | 101835 | Stefano Morozzi | 12/2022 |
8205 | 2^338288-65747 | 101835 | Stefano Morozzi | 01/2023 |
8206 | 2^338285+82131 | 101834 | Stefano Morozzi | 02/2022 |
8207 | 2^338284-104217 | 101834 | Stefano Morozzi | 02/2022 |
8208 | 2^338282-84533 | 101834 | Stefano Morozzi | 04/2022 |
8209 | 2^338283+67545 | 101834 | Stefano Morozzi | 09/2022 |
8210 | 2^338283-65439 | 101834 | Stefano Morozzi | 01/2023 |
8219 | 2^338280-19745 | 101833 | Enzo Doria | 06/2013 |
8211 | 2^338279-125947 | 101833 | Stefano Morozzi | 12/2021 |
8212 | 2^338280-50343 | 101833 | Stefano Morozzi | 12/2021 |
8213 | 2^338279+133331 | 101833 | Stefano Morozzi | 02/2022 |
8214 | 2^338281-54561 | 101833 | Stefano Morozzi | 02/2022 |
8215 | 2^338280+192063 | 101833 | Stefano Morozzi | 09/2022 |
8216 | 2^338281+18971 | 101833 | Stefano Morozzi | 09/2022 |
8217 | 2^338281-186711 | 101833 | Stefano Morozzi | 12/2022 |
8218 | 2^338281-91273 | 101833 | Stefano Morozzi | 01/2023 |
8220 | 2^338278+188215 | 101832 | Stefano Morozzi | 05/2022 |
8221 | 2^338273+181101 | 101831 | Stefano Morozzi | 01/2022 |
8222 | 2^338275+32909 | 101831 | Stefano Morozzi | 02/2022 |
8223 | 2^338272+166431 | 101831 | Stefano Morozzi | 06/2022 |
8224 | 2^338272+22011 | 101831 | Stefano Morozzi | 11/2022 |
8225 | 2^338275+148271 | 101831 | Stefano Morozzi | 11/2022 |
8226 | 2^338270-135725 | 101830 | Stefano Morozzi | 06/2022 |
8227 | 2^338269-136951 | 101830 | Stefano Morozzi | 12/2022 |
8228 | 2^338270-192701 | 101830 | Stefano Morozzi | 02/2023 |
8229 | 2^338271-42831 | 101830 | Stefano Morozzi | 02/2023 |
8230 | 2^338266+110665 | 101829 | Stefano Morozzi | 03/2022 |
8231 | 2^338267+110481 | 101829 | Stefano Morozzi | 03/2022 |
8232 | 2^338267-166035 | 101829 | Stefano Morozzi | 01/2023 |
8233 | 2^338265-154893 | 101828 | Stefano Morozzi | 02/2022 |
8234 | 2^338264+163611 | 101828 | Stefano Morozzi | 05/2022 |
8235 | 2^338263-62767 | 101828 | Stefano Morozzi | 12/2022 |
8236 | 2^338261-188119 | 101827 | Stefano Morozzi | 12/2022 |
8237 | 2^338259-40327 | 101827 | Stefano Morozzi | 01/2023 |
8238 | 2^338256+5223 | 101826 | Stefano Morozzi | 01/2022 |
8239 | 2^338257+178425 | 101826 | Stefano Morozzi | 01/2022 |
8240 | 2^338256-180569 | 101826 | Stefano Morozzi | 02/2022 |
8241 | 2^338257-5965 | 101826 | Stefano Morozzi | 02/2022 |
8242 | 2^338258-9225 | 101826 | Stefano Morozzi | 04/2022 |
8243 | 2^338255-127021 | 101825 | Stefano Morozzi | 12/2021 |
8244 | 2^338253+159005 | 101825 | Stefano Morozzi | 03/2022 |
8245 | 2^338253+64817 | 101825 | Stefano Morozzi | 05/2022 |
8246 | 2^338254-85403 | 101825 | Stefano Morozzi | 06/2022 |
8247 | 2^338254+142947 | 101825 | Stefano Morozzi | 09/2022 |
8248 | 2^338253+121095 | 101825 | Stefano Morozzi | 11/2022 |
8249 | 2^338254+196725 | 101825 | Stefano Morozzi | 11/2022 |
8250 | 2^338254-91007 | 101825 | Stefano Morozzi | 01/2023 |