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 ? |
9751 | 2^325087-109057 | 97861 | Enzo Doria | 04/2014 |
9752 | 2^325074+1870657 | 97858 | Enzo Doria | 05/2016 |
9754 | 2^325066-2111 | 97855 | Yves Minet | 08/2013 |
9753 | CopelandErdos(97855) | 97855 | Eric W. Weisstein | 10/2015 |
9755 | (8694^24841-1)/8693 | 97851 | Serge Batalov | 06/2022 |
9756 | (21159^22621-1)/21158 | 97843 | Serge Batalov | 06/2022 |
9757 | 26660^4677+4677^26660 | 97842 | Hans Havermann | 12/2019 |
9758 | 18^77944-89 | 97841 | Lelio R Paula | 07/2016 |
9759 | 119^47136+118 | 97833 | Norbert Schneider | 09/2018 |
9760 | 6^125720-17663 | 97830 | Enzo Doria | 02/2013 |
9761 | (73640^20101-1)/73639 | 97829 | Serge Batalov | 06/2022 |
9762 | 2^324972-2069 | 97827 | Yves Minet | 05/2013 |
9763 | 2^324958-4691 | 97823 | Yves Minet | 05/2019 |
9764 | (8087^25033-1)/8086 | 97820 | Serge Batalov | 06/2022 |
9765 | 2^324944-2788319 | 97818 | Enzo Doria | 03/2016 |
9767 | 22845^19112+19112^22845 | 97807 | Hans Havermann | 10/2019 |
9766 | (317^39107-1)/316 | 97807 | Anonymous | 04/2024 |
9768 | (2^324898+1270)/2 | 97804 | Stefano Morozzi | 09/2020 |
9770 | 4*10^97799-9 | 97800 | Erik Branger | 11/2013 |
9769 | 2^324882+577294575 | 97800 | Lelio R Paula | 09/2016 |
9771 | 2^324863-1867921 | 97794 | Enzo Doria | 04/2016 |
9772 | 6^125662-18473 | 97785 | Enzo Doria | 03/2013 |
9773 | 12^90604+11 | 97779 | Lelio R Paula | 07/2016 |
9774 | (29*10^97751+49)/3 | 97752 | Robert Price | 09/2021 |
9775 | (37108^21391-1)/37107 | 97741 | Serge Batalov | 06/2022 |
9776 | 5^139830+24 | 97737 | Lelio R Paula | 04/2016 |
9777 | (2^324672+1198)/2 | 97736 | Stefano Morozzi | 09/2020 |
9778 | (101*10^97724+7)/9 | 97726 | Robert Price | 02/2022 |
9779 | 2^324612+1155 | 97718 | Lelio R Paula | 07/2016 |
9780 | (2^324597+3542)/2 | 97714 | Stefano Morozzi | 09/2020 |
9781 | 19^76404-44 | 97702 | Lelio R Paula | 07/2016 |
9782 | (5939^25889-1)/5938 | 97694 | Serge Batalov | 06/2022 |
9784 | 2^324505-2983 | 97686 | Yves Minet | 04/2011 |
9783 | (7740^25121-1)/7739 | 97686 | Serge Batalov | 06/2022 |
9785 | (144^45259+1)/145 | 97684 | Paul Bourdelais | 08/2019 |
9786 | (31*2^324496-1)/45 | 97683 | Lelio R Paula | 02/2014 |
9787 | (11234^24109-1)/11233 | 97651 | Serge Batalov | 06/2022 |
9788 | 6^125488-17843 | 97649 | Enzo Doria | 02/2013 |
9789 | (2^324350+3198)/2 | 97639 | Stefano Morozzi | 09/2020 |
9790 | (75638^20011-1)/75637 | 97624 | Serge Batalov | 06/2022 |
9791 | 7^115515-2 | 97622 | Lelio R Paula | 09/2013 |
9792 | (15672^23269-1)/15671 | 97613 | Serge Batalov | 06/2022 |
9793 | (89^50069-1)/88 | 97603 | Paul Bourdelais | 08/2017 |
9794 | 6^125418-5 | 97595 | Lelio R Paula | 11/2014 |
9795 | (2^324193+3522)/2 | 97592 | Stefano Morozzi | 09/2020 |
9796 | (2422^28837-1)/2421 | 97587 | Serge Batalov | 06/2022 |
9797 | (2^324172+666)/2 | 97586 | Stefano Morozzi | 09/2020 |
9798 | 2^324091+111546435 | 97562 | Paul Bourdelais | 10/2021 |
9799 | 2^324076+1155 | 97557 | Lelio R Paula | 07/2016 |
9800 | (2^324074+9)/13 | 97555 | Lelio R Paula | 10/2013 |
9801 | (11*10^97539-71)/3 | 97540 | Robert Price | 04/2022 |
9802 | (55459*2^323993+1)/21 | 97536 | Lelio R Paula | 07/2014 |
9803 | 13^87557-12^87557 | 97534 | Jean-Louis Charton | 12/2008 |
9804 | 2^323946+73939 | 97518 | Enzo Doria | 04/2016 |
9805 | 2^323937+1866947 | 97515 | Enzo Doria | 03/2016 |
9806 | (98339^19531-1)/98338 | 97508 | Serge Batalov | 06/2022 |
9808 | 6^125290-18533 | 97495 | Enzo Doria | 03/2013 |
9807 | (2^323870+1650)/2 | 97495 | Stefano Morozzi | 09/2020 |
9809 | 2^323845+101 | 97488 | Lelio R Paula | 12/2012 |
9810 | 18^77662+65 | 97487 | Lelio R Paula | 07/2016 |
9811 | 22634^20265+20265^22634 | 97479 | Hans Havermann | 04/2020 |
9812 | (5533^26041-1)/5532 | 97467 | Serge Batalov | 06/2022 |
9813 | 2^323772+76771 | 97466 | Enzo Doria | 05/2016 |
9814 | 2^323765-112213 | 97463 | Enzo Doria | 06/2014 |
9815 | 22730^19389+19389^22730 | 97457 | Hans Havermann | 02/2020 |
9816 | 2^323720-6555 | 97450 | Lelio R Paula | 07/2016 |
9817 | 2^323694-1860401 | 97442 | Enzo Doria | 03/2016 |
9818 | 20^74886+3 | 97429 | Lelio R Paula | 06/2016 |
9819 | 24476^9561+9561^24476 | 97427 | Hans Havermann | 01/2020 |
9820 | (2^323623+1766)/2 | 97420 | Stefano Morozzi | 09/2020 |
9821 | (3250^27739-1)/3249 | 97413 | Serge Batalov | 06/2022 |
9823 | 3*10^97399+73 | 97400 | Robert Price | 04/2016 |
9822 | 7^115252-50 | 97400 | Lelio R Paula | 07/2016 |
9824 | (4715^26513-1)/4714 | 97392 | Serge Batalov | 06/2022 |
9825 | 2^323521+213317 | 97390 | Enzo Doria | 09/2023 |
9826 | 224737#+393581 | 97389 | Nicolas PALAU | 12/2016 |
9827 | (119374^19321-1)/(119374^139-1) | 97386 | Ryan Propper | 11/2023 |
9828 | (2^323468+3186)/2 | 97374 | Stefano Morozzi | 09/2020 |
9829 | (2^323456+538)/2 | 97370 | Stefano Morozzi | 09/2020 |
9830 | 23277^15236+15236^23277 | 97365 | Hans Havermann | 07/2020 |
9832 | (26*10^97353+31)/3 | 97354 | Robert Price | 07/2016 |
9831 | (2^323403+3510)/2 | 97354 | Stefano Morozzi | 09/2020 |
9833 | 23756^12519+12519^23756 | 97342 | Hans Havermann | 07/2020 |
9834 | 10^97335+271641 | 97336 | Patrick De Geest | 09/2022 |
9836 | 10^97335-4000001 | 97335 | Robert Price | 07/2021 |
9835 | 10^97335-98193 | 97335 | Patrick De Geest | 09/2022 |
9837 | (637*10^97331+11)/9 | 97333 | Robert Price | 10/2021 |
9838 | 23991^11402+11402^23991 | 97332 | Hans Havermann | 07/2020 |
9839 | 61^54517-60^54517 | 97331 | Jean-Louis Charton | 09/2005 |
9840 | (38*10^97329+187)/9 | 97330 | Robert Price | 11/2017 |
9841 | (31147^21661-1)/31146 | 97328 | Serge Batalov | 06/2022 |
9842 | 86455!4+8 | 97319 | Robert Price | 09/2019 |
9843 | 22591^20310+20310^22591 | 97316 | Hans Havermann | 06/2020 |
9844 | 2^323261-431173 | 97312 | Harrison Mesh | 06/2022 |
9845 | (3996^27017-1)/3995 | 97302 | Serge Batalov | 06/2022 |
9846 | 25101^7520+7520^25101 | 97297 | Hans Havermann | 05/2020 |
9847 | (233*10^97294+7)/3 | 97296 | Robert Price | 03/2022 |
9848 | p(19982)#/2-1024 | 97293 | Robert Price | 09/2017 |
9849 | (65*10^97288+277)/9 | 97289 | Robert Price | 08/2021 |
9850 | 6^125021-85 | 97286 | Lelio R Paula | 08/2016 |
9851 | 2^323164-47355 | 97283 | Lelio R Paula | 07/2016 |
9852 | (3^203902+4)/36051015157 | 97276 | Lelio R Paula | 09/2013 |
9853 | 2^323054-6555 | 97249 | Lelio R Paula | 07/2016 |
9854 | 22822^18247+18247^22822 | 97249 | Hans Havermann | 02/2020 |
9855 | 9*10^97247-29 | 97248 | Robert Price | 05/2017 |
9856 | 24382^9735+9735^24382 | 97244 | Hans Havermann | 02/2020 |
9857 | (31*10^97242+41)/9 | 97243 | Robert Price | 04/2015 |
9858 | GoldenRatioPrime[97241] | 97241 | Eric W. Weisstein | 06/2009 |
9859 | 12^90098-41 | 97233 | Lelio R Paula | 07/2016 |
9860 | 2^322928-216929 | 97212 | Enzo Doria | 05/2014 |
9861 | (16731^23017-1)/16730 | 97209 | Serge Batalov | 06/2022 |
9862 | 3*10^97205-61 | 97206 | Robert Price | 04/2021 |
9863 | (7*2^322896-1)/57 | 97201 | Lelio R Paula | 02/2014 |
9864 | (35*10^97194-341)/9 | 97195 | Robert Price | 08/2021 |
9865 | (4872^26357-1)/4871 | 97194 | Serge Batalov | 06/2022 |
9866 | (2^322897+5)/3146107489 | 97193 | Lelio R Paula | 10/2013 |
9867 | (796*10^97183-31)/9 | 97185 | Robert Price | 07/2022 |
9868 | (2^322789+2214)/2 | 97169 | Stefano Morozzi | 09/2020 |
9869 | 2^322725+75761 | 97150 | Enzo Doria | 04/2016 |
9870 | (13*2^322686+1)/119 | 97138 | Lelio R Paula | 11/2013 |
9871 | (2175^29101-1)/2174 | 97121 | Serge Batalov | 06/2022 |
9872 | 22402^21639+21639^22402 | 97118 | Hans Havermann | 07/2020 |
9873 | 23399^14128+14128^23399 | 97108 | Hans Havermann | 06/2020 |
9874 | (2892^28057-1)/2891 | 97108 | Serge Batalov | 06/2022 |
9875 | (9578^24391-1)/9577 | 97104 | Serge Batalov | 06/2022 |
9876 | (2^322525+2606)/2 | 97090 | Stefano Morozzi | 09/2020 |
9877 | (9563^24391-1)/9562 | 97087 | Serge Batalov | 06/2022 |
9878 | (41*10^97085+373)/9 | 97086 | Robert Price | 04/2017 |
9879 | (2^322473+854)/2 | 97074 | Stefano Morozzi | 02/2021 |
9880 | 2^322413+77 | 97056 | Lelio R Paula | 12/2012 |
9881 | 2^322406+177 | 97054 | Lelio R Paula | 12/2012 |
9882 | (349^38167-1)/348 | 97050 | Serge Batalov | 06/2022 |
9883 | (14*10^97044+31)/9 | 97045 | Robert Price | 02/2015 |
9884 | 2^322302+255255 | 97023 | Lelio R Paula | 07/2016 |
9885 | 2^322286+212659 | 97018 | Enzo Doria | 09/2023 |
9886 | (1302^31147-1)/1301 | 97008 | Serge Batalov | 06/2022 |
9887 | 2^322196-113093 | 96991 | Enzo Doria | 07/2014 |
9888 | (2^322169+2690)/2 | 96983 | Stefano Morozzi | 09/2020 |
9889 | (49*10^96980+221)/9 | 96981 | Robert Price | 02/2022 |
9890 | 9*10^96968-47 | 96969 | Robert Price | 11/2021 |
9891 | (5895^25717-1)/5894 | 96962 | Serge Batalov | 06/2022 |
9892 | (27473^21841-1)/27472 | 96946 | Serge Batalov | 06/2022 |
9893 | 23109^15668+15668^23109 | 96943 | Hans Havermann | 07/2020 |
9894 | 2^322000-1861469 | 96932 | Enzo Doria | 03/2016 |
9895 | 2^321971-112747 | 96923 | Enzo Doria | 06/2014 |
9896 | 23754^12023+12023^23754 | 96917 | Hans Havermann | 07/2020 |
9897 | 11^93062-92 | 96915 | Lelio R Paula | 06/2016 |
9898 | (37871^21169-1)/37870 | 96914 | Serge Batalov | 06/2022 |
9899 | (2^321922+2214)/2 | 96908 | Stefano Morozzi | 09/2020 |
9900 | (2^321900+2086)/2 | 96902 | Stefano Morozzi | 09/2020 |
9901 | (11*2^321841-7)/15 | 96884 | Renaud Lifchitz | 03/2011 |
9902 | 3^203051+34 | 96880 | Lelio R Paula | 05/2016 |
9903 | 2*10^96867-51 | 96868 | Robert Price | 11/2017 |
9904 | (2^321779+2618)/2 | 96865 | Stefano Morozzi | 09/2020 |
9905 | (64*10^96863-1)/27 | 96864 | Serge Batalov | 05/2010 |
9906 | 2^321716-2786939 | 96847 | Enzo Doria | 03/2016 |
9907 | 22496^20181+20181^22496 | 96844 | Hans Havermann | 03/2020 |
9908 | 2^321701-113053 | 96842 | Enzo Doria | 07/2014 |
9909 | 2^321700-28635 | 96842 | Lelio R Paula | 06/2016 |
9910 | (5*2^321691-1)/27 | 96838 | Lelio R Paula | 02/2014 |
9911 | 6*10^96835+13 | 96836 | Robert Price | 10/2021 |
9912 | 6^124433-124433 | 96828 | Robert Price | 01/2014 |
9913 | 2^321631+69 | 96821 | Lelio R Paula | 12/2012 |
9914 | (27109^21841-1)/27108 | 96820 | Serge Batalov | 06/2022 |
9915 | (13*2^321606+1)/119 | 96813 | Lelio R Paula | 11/2013 |
9916 | (5052^26141-1)/5051 | 96809 | Serge Batalov | 06/2022 |
9917 | (46*10^96798-1)/9 | 96799 | Serge Batalov | 10/2014 |
9918 | (59*10^96798+31)/9 | 96799 | Robert Price | 09/2015 |
9919 | (2^321536+2062)/2 | 96792 | Stefano Morozzi | 09/2020 |
9920 | 223319#+231223 | 96790 | Makoto Morimoto | 02/2016 |
9921 | 2^321519-28635 | 96787 | Lelio R Paula | 06/2016 |
9922 | 2^321487-1867237 | 96778 | Enzo Doria | 03/2016 |
9923 | 2^321461-63 | 96770 | Lelio R Paula | 12/2012 |
9924 | (16053^23011-1)/16052 | 96770 | Serge Batalov | 06/2022 |
9925 | 2^321439+123 | 96763 | Lelio R Paula | 12/2012 |
9926 | 2^321434+709 | 96762 | Lelio R Paula | 02/2013 |
9927 | 2^321419+22703 | 96757 | Enzo Doria | 09/2023 |
9928 | (2^321415+554)/2 | 96756 | Stefano Morozzi | 09/2020 |
9929 | 14^84413+89 | 96749 | Lelio R Paula | 07/2016 |
9930 | (28*10^96743+71)/9 | 96744 | Serge Batalov | 12/2008 |
9931 | 13^86847+96 | 96743 | Lelio R Paula | 06/2016 |
9932 | 9*2^321336-7 | 96733 | Lelio R Paula | 08/2014 |
9933 | (209*10^96722-17)/3 | 96724 | Robert Price | 05/2017 |
9934 | (54163^20431-1)/54162 | 96710 | Serge Batalov | 06/2022 |
9935 | 2^321237-4615 | 96702 | Yves Minet | 05/2019 |
9936 | (27273^21799-1)/27272 | 96691 | Serge Batalov | 06/2022 |
9937 | 2^321187-1159 | 96687 | Yves Minet | 11/2012 |
9938 | 2^321182-1850081 | 96686 | Enzo Doria | 08/2015 |
9940 | 23359^13768+13768^23359 | 96680 | Hans Havermann | 06/2020 |
9939 | (65630^20071-1)/65629 | 96680 | Serge Batalov | 06/2022 |
9941 | 2^321116-112829 | 96666 | Enzo Doria | 06/2014 |
9942 | 2^321108-109499 | 96664 | Enzo Doria | 04/2014 |
9943 | 2^321098+2793859 | 96661 | Enzo Doria | 03/2016 |
9944 | (2^321100+1170)/2 | 96661 | Stefano Morozzi | 09/2020 |
9945 | 2^321057+4097 | 96648 | Lelio R Paula | 06/2016 |
9946 | (4435*29^66081-4)/7 | 96640 | Curtis Bright | 05/2015 |
9947 | 22743^17750+17750^22743 | 96640 | Hans Havermann | 04/2020 |
9948 | 22882^16679+16679^22882 | 96612 | Hans Havermann | 02/2020 |
9949 | 23452^13163+13163^23452 | 96608 | Hans Havermann | 02/2020 |
9950 | (1042^32009-1)/1041 | 96596 | Serge Batalov | 06/2022 |
9951 | (85*10^96594-373)/9 | 96595 | Robert Price | 05/2021 |
9952 | (2^320863+666)/2 | 96590 | Stefano Morozzi | 09/2020 |
9953 | p(19849)#/2-64 | 96581 | Robert Price | 04/2017 |
9954 | 2^320817+189 | 96576 | Lelio R Paula | 12/2012 |
9955 | 2^320816-4685 | 96576 | Yves Minet | 05/2019 |
9957 | (361*10^96567-163)/9 | 96569 | Robert Price | 10/2017 |
9956 | (19*10^96568+137)/3 | 96569 | Robert Price | 03/2022 |
9958 | 2^320788-110327 | 96567 | Enzo Doria | 05/2014 |
9959 | (3065^27697-1)/3064 | 96561 | Serge Batalov | 06/2022 |
9960 | 2^320764+793 | 96560 | Lelio R Paula | 02/2013 |
9961 | (2^320752+1842)/2 | 96556 | Stefano Morozzi | 02/2021 |
9962 | (48331^20611-1)/48330 | 96542 | Serge Batalov | 06/2022 |
9963 | (107746^19321-1)/(107746^139-1) | 96532 | Ryan Propper | 11/2023 |
9964 | (50595^20521-1)/50594 | 96529 | Serge Batalov | 06/2022 |
9965 | (9179*2^320652-1)/221 | 96528 | Lelio R Paula | 05/2015 |
9966 | 23288^13947+13947^23288 | 96517 | Hans Havermann | 07/2020 |
9968 | 2^320616-78795 | 96516 | Lelio R Paula | 03/2016 |
9967 | (19*10^96520+287)/9/109/409 | 96516 | Alfred Reich | 11/2022 |
9969 | 2^320612-461939 | 96514 | Enzo Doria | 07/2015 |
9970 | (21245^22303-1)/21244 | 96507 | Serge Batalov | 06/2022 |
9971 | 10^96504+987654321 | 96505 | Robert Price | 12/2019 |
9972 | 10^96504+71887 | 96505 | Patrick De Geest | 02/2020 |
9973 | 22654^18195+18195^22654 | 96505 | Hans Havermann | 07/2020 |
9974 | 10^96504-139277 | 96504 | Patrick De Geest | 02/2020 |
9975 | (218^41263-1)/217 | 96490 | Serge Batalov | 06/2022 |
9976 | (47220^20641-1)/47219 | 96474 | Serge Batalov | 06/2022 |
9977 | 5*2^320431+7 | 96461 | Lelio R Paula | 08/2014 |
9978 | 19^75431-90 | 96458 | Lelio R Paula | 06/2016 |
9979 | (11853^23677-1)/11852 | 96452 | Serge Batalov | 06/2022 |
9980 | (2^320386+2814)/2 | 96446 | Stefano Morozzi | 02/2021 |
9981 | (2^320370+3)/67 | 96440 | Lelio R Paula | 10/2013 |
9982 | 3*10^96431-17 | 96432 | Robert Price | 03/2021 |
9983 | 2^320309+1871477 | 96423 | Enzo Doria | 05/2016 |
9984 | (10412^24001-1)/10411 | 96421 | Serge Batalov | 06/2022 |
9985 | tau(809^6028) | 96410 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
9986 | (29*10^96407-23)/3 | 96408 | Robert Price | 03/2022 |
9987 | (21*2^320252-1)/1895 | 96404 | Lelio R Paula | 02/2014 |
9988 | 2^320232-173 | 96400 | Lelio R Paula | 12/2012 |
9989 | 175^42975-2 | 96395 | Lelio R Paula | 10/2017 |
9990 | (2^320170+2718)/2 | 96381 | Stefano Morozzi | 09/2020 |
9991 | 10^96377+199911 | 96378 | Patrick De Geest | 12/2016 |
9992 | 10^96377-20001 | 96377 | Robert Price | 11/2016 |
9993 | (18079^22639-1)/18078 | 96374 | Serge Batalov | 06/2022 |
9995 | 2^320124-2790449 | 96367 | Enzo Doria | 03/2016 |
9994 | 10^96366+19197 | 96367 | Patrick De Geest | 08/2021 |
9997 | 10^96366-10000000001 | 96366 | Robert Price | 04/2021 |
9996 | 10^96366-287367 | 96366 | Patrick De Geest | 08/2021 |
9998 | (26351^21799-1)/26350 | 96365 | Serge Batalov | 06/2022 |
9999 | 22488^19255+19255^22488 | 96351 | Hans Havermann | 11/2019 |
10000 | 23248^13939+13939^23248 | 96346 | Hans Havermann | 11/2019 |