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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 751 | 2^1455129+218027 | 438038 | Enzo Doria | 01/2024 |
| 752 | 2^1454061+216977 | 437716 | Enzo Doria | 01/2024 |
| 753 | 2^1453419+26783 | 437523 | Enzo Doria | 01/2024 |
| 754 | (67^239053+1)/68 | 436527 | Paul Bourdelais | 09/2021 |
| 755 | 2^1448714+231559 | 436107 | Enzo Doria | 02/2025 |
| 756 | 2^1448122+74209 | 435929 | Enzo Doria | 08/2023 |
| 757 | 2^1448111+49853 | 435925 | Enzo Doria | 09/2025 |
| 758 | 2^1446449+221087 | 435425 | Enzo Doria | 05/2024 |
| 759 | 2^1446263+74333 | 435369 | Enzo Doria | 08/2023 |
| 760 | 2^1445551+47333 | 435155 | Enzo Doria | 08/2025 |
| 761 | 2^1444386+221029 | 434804 | Enzo Doria | 03/2024 |
| 762 | (80^228419+1)/81 | 434701 | Paul Bourdelais | 02/2021 |
| 763 | 2^1443374+244609 | 434499 | Enzo Doria | 02/2026 |
| 764 | 2^1443089+60227 | 434414 | Enzo Doria | 10/2017 |
| 765 | 2^1441410+54589 | 433908 | Enzo Doria | 02/2026 |
| 766 | (21^328129-1)/20 | 433858 | Paul Bourdelais | 06/2014 |
| 767 | (35^280979+1)/36 | 433850 | Paul Bourdelais | 09/2021 |
| 768 | 2^1439822+51799 | 433430 | Enzo Doria | 11/2025 |
| 769 | 2^1438663+214175 | 433081 | Enzo Doria | 11/2023 |
| 770 | 2^1436073+241547 | 432302 | Enzo Doria | 10/2025 |
| 771 | 2^1434519+215813 | 431834 | Enzo Doria | 01/2024 |
| 772 | 2^1434400+3 | 431798 | Paul Bourdelais | 06/2019 |
| 773 | 2^1434298+31669 | 431767 | Enzo Doria | 08/2024 |
| 774 | 2^1434097+215207 | 431707 | Enzo Doria | 11/2023 |
| 775 | 2^1433033+212987 | 431386 | Enzo Doria | 10/2023 |
| 776 | 2^1432308+1888801 | 431168 | Enzo Doria | 10/2017 |
| 777 | (2^1430131+1)/(3*356468732537*36519993971459) | 430487 | Gord Palameta | 12/2018 |
| 778 | 2^1429978+233839 | 430467 | Enzo Doria | 04/2025 |
| 779 | (7^508867-2^508867)/5 | 430042 | Jon Grantham | 08/2023 |
| 780 | 2^1428489+25097 | 430019 | Enzo Doria | 11/2023 |
| 781 | 2^1425595+237413 | 429147 | Enzo Doria | 07/2025 |
| 782 | 2^1425483+1886813 | 429114 | Enzo Doria | 04/2017 |
| 783 | (63^238481+1)/64 | 429107 | Paul Bourdelais | 12/2020 |
| 784 | (((91969+1)/2)^91969+((91969-1)/2)^91969)/(91969^2) | 428807 | Henri Lifchitz | 11/2025 |
| 785 | (17^348259+1)/18 | 428514 | Paul Bourdelais | 05/2014 |
| 786 | 2^1422688+24391 | 428272 | Enzo Doria | 12/2023 |
| 787 | 2^1422654+226249 | 428262 | Enzo Doria | 09/2024 |
| 788 | 2^1421514+2351163 | 427919 | Enzo Doria | 05/2025 |
| 789 | (10^427912+89)/9 | 427912 | Serge Batalov | 12/2014 |
| 790 | 2^1421311+40613 | 427858 | Enzo Doria | 01/2025 |
| 791 | 2^1421089+1890167 | 427791 | Enzo Doria | 09/2017 |
| 792 | 2^1420902+221149 | 427735 | Enzo Doria | 05/2024 |
| 793 | 2^1418388+25771 | 426978 | Enzo Doria | 12/2023 |
| 794 | 2^1416724+214981 | 426477 | Enzo Doria | 11/2023 |
| 795 | (96228^85849-1)/(96228^293-1) | 426352 | Ryan Propper | 11/2023 |
| 796 | 2^1414012+36991 | 425661 | Enzo Doria | 09/2024 |
| 797 | 2^1413774+49789 | 425589 | Enzo Doria | 10/2025 |
| 798 | 2^1413721+225269 | 425573 | Enzo Doria | 10/2024 |
| 799 | 2^1412006+233899 | 425057 | Enzo Doria | 04/2025 |
| 800 | 20^326600+3 | 424917 | Paul Bourdelais | 01/2021 |
| 801 | 2^1411443+228023 | 424887 | Enzo Doria | 11/2024 |
| 802 | (10^424861-7)/3 | 424861 | Leonid Durman | 01/2012 |
| 803 | 10^424821-11 | 424821 | Mischa Rodermond | 04/2023 |
| 804 | (2^1411200+13)/7 | 424813 | Stefano Morozzi | 09/2022 |
| 805 | 2^1411117+35927 | 424789 | Enzo Doria | 09/2024 |
| 806 | 2^1410894+219859 | 424722 | Enzo Doria | 03/2024 |
| 807 | 2^1410310+30409 | 424546 | Enzo Doria | 05/2024 |
| 808 | 2^1410233+218447 | 424523 | Enzo Doria | 03/2024 |
| 809 | 2^1408670+238579 | 424052 | Enzo Doria | 09/2025 |
| 810 | 2^1408457+232007 | 423988 | Enzo Doria | 02/2025 |
| 811 | 2^1407515+241883 | 423705 | Enzo Doria | 11/2025 |
| 812 | 2^1407208+45751 | 423612 | Enzo Doria | 06/2025 |
| 813 | 2^1406408+50371 | 423371 | Enzo Doria | 09/2025 |
| 814 | 2^1405715-1405715^2 | 423163 | Henri Lifchitz | 03/2025 |
| 815 | 1+3^605376+5^605376 | 423140 | Jon Grantham | 08/2023 |
| 816 | 2^1405367+213413 | 423058 | Enzo Doria | 10/2023 |
| 817 | 2^1404213+184217 | 422711 | Enzo Doria | 09/2017 |
| 818 | 2^1403156+40921 | 422393 | Enzo Doria | 02/2025 |
| 819 | 2^1402886+50629 | 422311 | Enzo Doria | 12/2025 |
| 820 | 2^1401872+1884385 | 422006 | Enzo Doria | 04/2017 |
| 821 | 2^1401257+6077 | 421821 | Enzo Doria | 09/2017 |
| 822 | 2^1400648+44881 | 421638 | Enzo Doria | 05/2025 |
| 823 | 138^196873-137^196873 | 421285 | Jean-Louis Charton | 12/2009 |
| 824 | 2^1398726+7 | 421059 | Stefano Morozzi | 10/2022 |
| 825 | 2^1398269+131595 | 420921 | Makoto Morimoto | 10/2013 |
| 826 | 2^1398238+227119 | 420912 | Enzo Doria | 10/2024 |
| 827 | 2^1398062+40639 | 420859 | Enzo Doria | 01/2025 |
| 828 | 2^1398016+229357 | 420845 | Enzo Doria | 02/2025 |
| 829 | 2^1397089-1397089 | 420566 | Henri Lifchitz | 10/2024 |
| 830 | 2^1397071+684443 | 420561 | Enzo Doria | 07/2017 |
| 831 | 953^141023-952^141023 | 420121 | Jean-Louis Charton | 10/2016 |
| 832 | 2^1393449+45197 | 419470 | Enzo Doria | 05/2025 |
| 833 | 2^1393409+52037 | 419458 | Enzo Doria | 11/2025 |
| 834 | 2^1393111+1867211 | 419369 | Enzo Doria | 09/2023 |
| 835 | 2^1392384+44371 | 419150 | Enzo Doria | 03/2025 |
| 836 | 2^1391771+36623 | 418965 | Enzo Doria | 09/2024 |
| 837 | (3^877843-1)/2 | 418838 | Paul Bourdelais | 07/2010 |
| 838 | 2^1389843+53273 | 418385 | Enzo Doria | 01/2026 |
| 839 | 2^1389628+28651 | 418320 | Enzo Doria | 03/2024 |
| 840 | 2^1389064+45751 | 418150 | Enzo Doria | 06/2025 |
| 841 | 2^1388780+50311 | 418065 | Enzo Doria | 09/2025 |
| 842 | 2^1386321+60299 | 417325 | Enzo Doria | 02/2018 |
| 843 | 2^1386320+184531 | 417324 | Enzo Doria | 09/2017 |
| 844 | 2^1382806+109 | 416267 | Enzo Doria | 03/2026 |
| 845 | 2^1382074+1883587 | 416046 | Enzo Doria | 01/2017 |
| 846 | 2^1380651+215843 | 415618 | Enzo Doria | 12/2023 |
| 847 | 2^1380634+40639 | 415613 | Enzo Doria | 01/2025 |
| 848 | 2^1379907+1885223 | 415394 | Enzo Doria | 03/2017 |
| 849 | 2^1379815+47333 | 415366 | Enzo Doria | 07/2025 |
| 850 | 2^1379792+45421 | 415359 | Enzo Doria | 06/2025 |
| 851 | 2^1379111+29693 | 415154 | Enzo Doria | 05/2024 |
| 852 | 2^1377927+45083 | 414798 | Enzo Doria | 06/2025 |
| 853 | 2^1377501+46427 | 414670 | Enzo Doria | 07/2025 |
| 854 | 2^1376707+25763 | 414431 | Enzo Doria | 12/2023 |
| 855 | 2^1376534+54913 | 414379 | Enzo Doria | 01/2026 |
| 856 | 2^1375751+24443 | 414143 | Enzo Doria | 12/2023 |
| 857 | 2^1375574+1886719 | 414090 | Enzo Doria | 04/2017 |
| 858 | 2^1373958+42649 | 413603 | Enzo Doria | 02/2025 |
| 859 | 2^1373551+49343 | 413481 | Enzo Doria | 08/2025 |
| 860 | 2^1373111+1884833 | 413348 | Enzo Doria | 02/2017 |
| 861 | 2^1372996+15 | 413313 | Stefano Morozzi | 10/2022 |
| 862 | 2^1372515+32393 | 413169 | Enzo Doria | 05/2024 |
| 863 | 2^1372092+228751 | 413041 | Enzo Doria | 11/2024 |
| 864 | 2^1372033+238427 | 413024 | Enzo Doria | 07/2025 |
| 865 | 2^1370877+38747 | 412676 | Enzo Doria | 11/2024 |
| 866 | 2^1369291+40943 | 412198 | Enzo Doria | 02/2025 |
| 867 | 2^1369207+36833 | 412173 | Enzo Doria | 10/2024 |
| 868 | 2^1369171+216593 | 412162 | Enzo Doria | 01/2024 |
| 869 | 2^1368632+1889731 | 412000 | Enzo Doria | 10/2017 |
| 870 | (65245^85849-1)/(65245^293-1) | 411914 | Ryan Propper | 11/2023 |
| 871 | (89*10^411590+1)/9 | 411591 | Serge Batalov | 09/2014 |
| 872 | F(1968721) | 411439 | Henri Lifchitz | 11/2009 |
| 873 | 2^1366066+683749 | 411227 | Enzo Doria | 02/2017 |
| 874 | 2^1365324+233341 | 411004 | Enzo Doria | 03/2025 |
| 875 | 2^1365077+228257 | 410930 | Enzo Doria | 11/2024 |
| 876 | 2^1364401+217727 | 410726 | Enzo Doria | 02/2024 |
| 877 | 2^1364303+219533 | 410697 | Enzo Doria | 03/2024 |
| 878 | 2^1363802+51169 | 410546 | Enzo Doria | 10/2025 |
| 879 | 2^1363434+27589 | 410435 | Enzo Doria | 02/2024 |
| 880 | 2^1363068+222631 | 410325 | Enzo Doria | 06/2024 |
| 881 | 2^1360101+51287 | 409432 | Enzo Doria | 10/2025 |
| 882 | 2^1359599+245243 | 409281 | Enzo Doria | 02/2026 |
| 883 | 2^1359550+25819 | 409266 | Enzo Doria | 12/2023 |
| 884 | 2^1359515+236423 | 409255 | Enzo Doria | 05/2025 |
| 885 | 2^1357392+224401 | 408616 | Enzo Doria | 06/2024 |
| 886 | 2^1355826+15 | 408145 | Stefano Morozzi | 10/2022 |
| 887 | 2^1355790+1888939 | 408134 | Enzo Doria | 07/2017 |
| 888 | 2^1355635+1884203 | 408087 | Enzo Doria | 01/2017 |
| 889 | (22071^94249-1)/(22071^307-1) | 408068 | Ryan Propper | 11/2023 |
| 890 | 2^1355083+221603 | 407921 | Enzo Doria | 05/2024 |
| 891 | 2^1355041+239777 | 407908 | Enzo Doria | 08/2025 |
| 892 | 2^1351989+36587 | 406990 | Enzo Doria | 09/2024 |
| 893 | 2^1351675+231083 | 406895 | Enzo Doria | 02/2025 |
| 894 | 2^1349535+218783 | 406251 | Enzo Doria | 03/2024 |
| 895 | (55766^85849-1)/(55766^293-1) | 406081 | Ryan Propper | 11/2023 |
| 896 | 2^1348956+24241 | 406077 | Enzo Doria | 11/2023 |
| 897 | (88^208739+1)/89 | 405888 | Paul Bourdelais | 12/2020 |
| 898 | (2^1347781-2^673891+1)/5 | 405722 | Borys Jaworski | 10/2008 |
| 899 | 2^1347744-3 | 405712 | Paul Bourdelais | 07/2019 |
| 900 | 2^1347546+39133 | 405652 | Enzo Doria | 12/2024 |
| 901 | 2^1346431+691203 | 405317 | Boyan Hu | 09/2024 |
| 902 | 82358^82358+2025^2025 | 404848 | Henri Lifchitz | 01/2025 |
| 903 | 9*10^404644-11 | 404645 | Mischa Rodermond | 04/2023 |
| 904 | 2^1343509+237947 | 404437 | Enzo Doria | 07/2025 |
| 905 | 1215^131072+242^131072 | 404302 | Kellen Shenton | 08/2022 |
| 906 | 2^1341908+212911 | 403955 | Enzo Doria | 09/2023 |
| 907 | 2^1341625+226187 | 403870 | Enzo Doria | 09/2024 |
| 908 | 2^1340881+53255 | 403646 | Enzo Doria | 01/2026 |
| 909 | 2^1340284+43801 | 403466 | Enzo Doria | 04/2025 |
| 910 | 2^1340172+240991 | 403432 | Enzo Doria | 10/2025 |
| 911 | 1196^131072+595^131072 | 403405 | Kellen Shenton | 08/2022 |
| 912 | 2^1339302+29389 | 403171 | Enzo Doria | 04/2024 |
| 913 | 2^1335130+31669 | 401915 | Enzo Doria | 07/2024 |
| 914 | 2^1333062+236449 | 401292 | Enzo Doria | 07/2025 |
| 915 | 2^1330791+46763 | 400609 | Enzo Doria | 06/2025 |
| 916 | 2^1330712+45631 | 400585 | Enzo Doria | 05/2025 |
| 917 | 2^1330388+38527 | 400487 | Enzo Doria | 11/2024 |
| 918 | 2^1330371+28313 | 400482 | Enzo Doria | 03/2024 |
| 919 | 10^400310+9 | 400311 | Boyan Hu | 06/2025 |
| 920 | 10^400000+1415223 | 400001 | Patrick De Geest | 10/2020 |
| 921 | 10^400000-339233 | 400000 | Patrick De Geest | 10/2020 |
| 922 | 2^1327766+48019 | 399698 | Enzo Doria | 06/2025 |
| 923 | 2^1323373+27317 | 398375 | Enzo Doria | 01/2024 |
| 924 | Tau(863^24630) | 397727 | Nik Lygeros / Olivier Rozier | 01/2016 |
| 925 | 2^1320423+24293 | 397487 | Enzo Doria | 11/2023 |
| 926 | 2^1320057+211517 | 397377 | Enzo Doria | 08/2023 |
| 927 | 2^1319770+1884949 | 397291 | Enzo Doria | 06/2017 |
| 928 | 2^1319616+30091 | 397244 | Enzo Doria | 04/2024 |
| 929 | 2^1317657+31367 | 396655 | Enzo Doria | 04/2024 |
| 930 | 2^1316848+43021 | 396411 | Enzo Doria | 02/2025 |
| 931 | 2^1316687+45983 | 396363 | Enzo Doria | 05/2025 |
| 932 | 2^1315753+226187 | 396082 | Enzo Doria | 09/2024 |
| 933 | 2^1314741+219257 | 395777 | Enzo Doria | 03/2024 |
| 934 | 2^1313062+1888849 | 395272 | Enzo Doria | 08/2017 |
| 935 | (1073516^81920+1)/(1073516^16384+1) | 395236 | Serge Batalov | 01/2017 |
| 936 | 2^1312349+221177 | 395057 | Enzo Doria | 04/2024 |
| 937 | (1059995^81920+1)/(1059995^16384+1) | 394875 | Serge Batalov | 01/2017 |
| 938 | 2^1311618+783529 | 394837 | Enzo Doria | 01/2017 |
| 939 | 2^1310192+232531 | 394408 | Enzo Doria | 03/2025 |
| 940 | 2^1308992+28111 | 394046 | Enzo Doria | 02/2024 |
| 941 | 2^1308000+1883521 | 393748 | Enzo Doria | 02/2017 |
| 942 | 2^1307563+232133 | 393616 | Enzo Doria | 03/2025 |
| 943 | 2^1307324+224611 | 393544 | Enzo Doria | 07/2024 |
| 944 | 2^1307262+28759 | 393526 | Enzo Doria | 02/2024 |
| 945 | (1009565^81920+1)/(1009565^16384+1) | 393487 | Serge Batalov | 01/2017 |
| 946 | 2^1306643+47333 | 393339 | Enzo Doria | 07/2025 |
| 947 | 2^1305860+35461 | 393104 | Enzo Doria | 08/2024 |
| 948 | (995042^81920+1)/(995042^16384+1) | 393075 | Serge Batalov | 01/2017 |
| 949 | 2^1305333+47717 | 392945 | Enzo Doria | 06/2025 |
| 950 | 2^1305200+54571 | 392905 | Enzo Doria | 01/2026 |
| 951 | (988945^81920+1)/(988945^16384+1) | 392900 | Serge Batalov | 01/2017 |
| 952 | (988823^81920+1)/(988823^16384+1) | 392897 | Serge Batalov | 01/2017 |
| 953 | (2^1304983-1)/52199321 | 392832 | Tony Prest / Never Odd Or Even | 03/2014 |
| 954 | 2^1304675+243713 | 392747 | Enzo Doria | 01/2026 |
| 955 | (978970^81920+1)/(978970^16384+1) | 392612 | Serge Batalov | 01/2017 |
| 956 | 2^1303816+38251 | 392488 | Enzo Doria | 11/2024 |
| 957 | 2^1303257+48527 | 392320 | Enzo Doria | 07/2025 |
| 958 | 2^1303102+1866409 | 392273 | Enzo Doria | 09/2017 |
| 959 | 2^1302818+283429 | 392188 | Enzo Doria | 01/2017 |
| 960 | 2^1301430+22669 | 391770 | Enzo Doria | 10/2023 |
| 961 | 2^1301229+222467 | 391709 | Enzo Doria | 04/2024 |
| 962 | 2^1300835+232523 | 391591 | Enzo Doria | 03/2025 |
| 963 | (934422^81920+1)/(934422^16384+1) | 391286 | Serge Batalov | 01/2017 |
| 964 | 2^1299181+1886867 | 391093 | Enzo Doria | 04/2017 |
| 965 | (37^249341-1)/36 | 391016 | Paul Bourdelais | 08/2020 |
| 966 | 2^1298304+1882891 | 390829 | Enzo Doria | 01/2017 |
| 967 | 2^1297732+228721 | 390657 | Enzo Doria | 11/2024 |
| 968 | Phi(87181,13#) | 390354 | Henri Lifchitz | 02/2026 |
| 969 | 2^1295728+240751 | 390053 | Enzo Doria | 09/2025 |
| 970 | 95196^12497+12497^95196 | 390000 | Hans Havermann | 12/2021 |
| 971 | 2^1295539+35633 | 389997 | Enzo Doria | 08/2024 |
| 972 | 86206^33381+33381^86206 | 389953 | Hans Havermann | 05/2023 |
| 973 | 2^1294976+236731 | 389827 | Enzo Doria | 06/2025 |
| 974 | 2^1294324+25171 | 389631 | Enzo Doria | 12/2023 |
| 975 | 2^1294298+243649 | 389623 | Enzo Doria | 01/2026 |
| 976 | (874207^81920+1)/(874207^16384+1) | 389390 | Serge Batalov | 01/2017 |
| 977 | 2^1292338+229249 | 389033 | Enzo Doria | 11/2024 |
| 978 | 2^1289624+32551 | 388216 | Enzo Doria | 05/2024 |
| 979 | 2^1286857+37967 | 387383 | Enzo Doria | 10/2024 |
| 980 | 2^1285458+46159 | 386962 | Enzo Doria | 06/2025 |
| 981 | 2^1285456+230611 | 386961 | Enzo Doria | 01/2025 |
| 982 | (7^457871-5^457871)/2 | 386946 | Jon Grantham | 08/2023 |
| 983 | 79455^73828+73828^79455 | 386805 | Hans Havermann | 03/2023 |
| 984 | 81650^54369+54369^81650 | 386642 | Yusuf AttarBashi | 06/2021 |
| 985 | 80565^62824+62824^80565 | 386561 | Hans Havermann | 08/2021 |
| 986 | 83747^41272+41272^83747 | 386548 | Hans Havermann | 08/2021 |
| 987 | 15^328574+328574^15 | 386434 | Serge Batalov | 05/2014 |
| 988 | 2^1283304+53551 | 386313 | Enzo Doria | 01/2026 |
| 989 | 2^1283147+54833 | 386266 | Enzo Doria | 02/2026 |
| 990 | 2^1282676+30493 | 386124 | Enzo Doria | 12/2024 |
| 991 | 2^1280078+1885099 | 385342 | Enzo Doria | 08/2017 |
| 992 | 2^1279921+17 | 385295 | Stefano Morozzi | 10/2022 |
| 993 | 2^1279245+224087 | 385092 | Enzo Doria | 07/2024 |
| 994 | 2^1278091+47963 | 384744 | Enzo Doria | 07/2025 |
| 995 | 2^1277980+231391 | 384711 | Enzo Doria | 01/2025 |
| 996 | 2^1277688+231241 | 384623 | Enzo Doria | 01/2025 |
| 997 | 2^1277142+234979 | 384459 | Enzo Doria | 04/2025 |
| 998 | 2^1276977+71657 | 384409 | Enzo Doria | 08/2023 |
| 999 | (76803^78961-1)/(76803^281-1) | 384382 | Ryan Propper | 11/2023 |
| 1000 | 2^1276571+26213 | 384287 | Enzo Doria | 12/2023 |
