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 ? |
| 4751 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
| 4752 | U(1042497) | 145243 | Serge Batalov | 07/2024 |
| 4753 | 2^482386+212419 | 145213 | Enzo Doria | 08/2023 |
| 4754 | 47952^1067+1067^47952 | 145207 | Hans Havermann | 01/2021 |
| 4755 | (2^482333+5)/9287 | 145193 | Lelio R Paula | 09/2015 |
| 4756 | 2^482087+72623 | 145123 | Enzo Doria | 04/2016 |
| 4757 | 2^482016-286565 | 145102 | Enzo Doria | 07/2015 |
| 4758 | (19*10^145093+101)/3 | 145094 | Robert Price | 09/2019 |
| 4759 | 2^481956+121 | 145084 | Stefano Morozzi | 04/2021 |
| 4760 | 27535^32676-32676^27535 | 145078 | Frank Doornink | 06/2024 |
| 4761 | 2^481840+15 | 145049 | Robert Price | 09/2015 |
| 4762 | (23*10^145040+7)/3 | 145041 | Robert Price | 05/2023 |
| 4763 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
| 4764 | 2^481775+1869083 | 145029 | Enzo Doria | 05/2016 |
| 4765 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
| 4766 | 2^481663+1875653 | 144996 | Enzo Doria | 07/2016 |
| 4767 | 8*10^144977+27 | 144978 | Robert Price | 09/2021 |
| 4768 | 29840^32393-32393^29840 | 144953 | Frank Doornink | 06/2024 |
| 4769 | 36486^9379+9379^36486 | 144929 | Hans Havermann | 12/2020 |
| 4770 | 31580^32209-32209^31580 | 144922 | Frank Doornink | 01/2024 |
| 4771 | 35111^13378+13378^35111 | 144882 | Hans Havermann | 01/2021 |
| 4772 | 2^481149-459073 | 144841 | Enzo Doria | 05/2015 |
| 4773 | 2^481113+181419 | 144830 | Boyan Hu | 04/2024 |
| 4774 | 34619^15246+15246^34619 | 144817 | Hans Havermann | 01/2021 |
| 4775 | 2^481045-113215 | 144809 | Enzo Doria | 07/2014 |
| 4776 | (64*10^144797+287)/9 | 144798 | Robert Price | 04/2019 |
| 4777 | 27320^32629-32629^27320 | 144758 | Frank Doornink | 06/2024 |
| 4778 | 2^480859-113695 | 144753 | Enzo Doria | 09/2014 |
| 4779 | (106*10^144744+17)/3 | 144746 | Robert Price | 04/2021 |
| 4780 | 7*10^144742-27 | 144743 | Robert Price | 11/2022 |
| 4781 | 2^480766-2787191 | 144725 | Enzo Doria | 11/2015 |
| 4782 | (21*27^101106-151)/26 | 144720 | Curtis Bright | 05/2015 |
| 4783 | 28915^32438-32438^28915 | 144710 | Frank Doornink | 06/2024 |
| 4784 | 2^480678+1874239 | 144699 | Enzo Doria | 06/2016 |
| 4785 | (8*10^144683+1)/9 | 144683 | Serge Batalov | 05/2010 |
| 4786 | Phi(272901,-7) | 144681 | Henri Lifchitz | 02/2026 |
| 4787 | L(692147) | 144651 | Henri Lifchitz | 10/2008 |
| 4788 | (76*10^144648+77)/9 | 144649 | Robert Price | 10/2019 |
| 4789 | 32672^26721+26721^32672 | 144635 | Hans Havermann | 01/2021 |
| 4790 | 31478^32153-32153^31478 | 144625 | Frank Doornink | 01/2024 |
| 4791 | 2^480417+35 | 144620 | Robert Price | 11/2015 |
| 4792 | 2^480296-59879 | 144584 | Enzo Doria | 10/2015 |
| 4793 | 33157^22878+22878^33157 | 144546 | Hans Havermann | 12/2020 |
| 4794 | 27520^32541-32541^27520 | 144471 | Frank Doornink | 06/2024 |
| 4795 | 45494^1497+1497^45494 | 144454 | Hans Havermann | 12/2020 |
| 4796 | 2^479844+3 | 144448 | Donovan Johnson | 06/2006 |
| 4797 | 33442^20803+20803^33442 | 144407 | Hans Havermann | 01/2021 |
| 4798 | (441*33^95095-3833)/32 | 144405 | Eric Chen | 12/2023 |
| 4799 | 31892^32061-32061^31892 | 144393 | Norbert Schneider | 01/2023 |
| 4800 | (27*2^479642+1)/733 | 144386 | Lelio R Paula | 08/2015 |
| 4801 | (56*10^144380+169)/9 | 144381 | Robert Price | 03/2022 |
| 4802 | 44917^1638+1638^44917 | 144378 | Hans Havermann | 12/2020 |
| 4803 | (21*2^479605-1)/11 | 144376 | Lelio R Paula | 09/2015 |
| 4804 | (11^138641-1)/6631590024336120710 | 144361 | Paul Vanderveen | 05/2025 |
| 4805 | (56*10^144336+583)/9 | 144337 | Robert Price | 08/2021 |
| 4806 | 5*2^479430-3 | 144324 | Jon Grantham | 07/2023 |
| 4807 | 2^479348-2792219 | 144299 | Enzo Doria | 02/2016 |
| 4808 | 31134^32111-32111^31134 | 144283 | Frank Doornink | 01/2024 |
| 4809 | 3^302389-6242 | 144277 | Enzo Doria | 05/2014 |
| 4810 | 31665^32056-32056^31665 | 144271 | Frank Doornink | 01/2024 |
| 4811 | 33778^18641+18641^33778 | 144248 | Hans Havermann | 01/2021 |
| 4812 | 29083^32312-32312^29083 | 144230 | Frank Doornink | 06/2024 |
| 4813 | 2*10^144220-3 | 144221 | Robert Price | 07/2015 |
| 4814 | 25313^32750-32750^25313 | 144210 | Frank Doornink | 01/2024 |
| 4815 | 2^478904-109109 | 144165 | Enzo Doria | 04/2014 |
| 4816 | 43698^1987+1987^43698 | 144125 | Hans Havermann | 12/2020 |
| 4817 | 79^75948+75948 | 144121 | Kellen Shenton | 06/2023 |
| 4818 | 26941^32522-32522^26941 | 144086 | Frank Doornink | 06/2024 |
| 4819 | 36128^9723+9723^36128 | 144072 | Hans Havermann | 01/2021 |
| 4820 | (103301*19^112659-17)/18 | 144067 | Eric Chen | 04/2026 |
| 4821 | 32817^24518+24518^32817 | 144050 | Hans Havermann | 12/2020 |
| 4822 | (772*10^144036-7)/9 | 144038 | Robert Price | 06/2022 |
| 4823 | 34295^15828+15828^34295 | 144020 | Hans Havermann | 01/2021 |
| 4824 | 2^478337-115333 | 143994 | Enzo Doria | 07/2015 |
| 4825 | (7*2^478330-1)/3 | 143993 | Lelio R Paula | 08/2015 |
| 4826 | 88^74047-87^74047 | 143984 | Robert Price | 05/2015 |
| 4827 | 33242^21441+21441^33242 | 143980 | Hans Havermann | 01/2021 |
| 4828 | (19*10^143963+467)/9 | 143964 | Robert Price | 02/2018 |
| 4829 | (71^77761+1)/72 | 143954 | Paul Bourdelais | 09/2017 |
| 4830 | 33490^19859+19859^33490 | 143939 | Hans Havermann | 01/2021 |
| 4831 | (853*10^143931-7)/9 | 143933 | Robert Price | 07/2021 |
| 4832 | 2^478088+27 | 143919 | Robert Price | 11/2015 |
| 4833 | (8*10^143898-137)/3 | 143899 | Robert Price | 03/2022 |
| 4834 | 7*10^143857-93 | 143858 | Robert Price | 08/2020 |
| 4835 | 3*10^143844+61 | 143845 | Robert Price | 09/2020 |
| 4836 | 41358^3005+3005^41358 | 143837 | Hans Havermann | 01/2021 |
| 4837 | 2^477475-22071 | 143735 | Enzo Doria | 07/2013 |
| 4838 | 2^477417-22123 | 143717 | Enzo Doria | 07/2013 |
| 4839 | 2^477359-3577 | 143700 | Yves Minet | 03/2017 |
| 4840 | 39435^4402+4402^39435 | 143688 | Hans Havermann | 01/2021 |
| 4841 | (14*10^143662-71)/3 | 143663 | Robert Price | 12/2018 |
| 4842 | 6^184614+5 | 143658 | Paul Bourdelais | 01/2021 |
| 4843 | 46371^1252+1252^46371 | 143640 | Hans Havermann | 12/2020 |
| 4844 | 34975^12748+12748^34975 | 143588 | Hans Havermann | 01/2021 |
| 4845 | 2^476936-396765 | 143573 | Enzo Doria | 07/2013 |
| 4846 | 2^476888-2791229 | 143558 | Enzo Doria | 01/2016 |
| 4847 | 2^476868-1859939 | 143552 | Enzo Doria | 11/2015 |
| 4848 | 40807^3294+3294^40807 | 143548 | Hans Havermann | 12/2020 |
| 4849 | 755^49878+49878^755 | 143547 | Norbert Schneider | 04/2019 |
| 4850 | (19^112247-4^112247)/15 | 143536 | Robert Price | 03/2021 |
| 4851 | 35561^10872+10872^35561 | 143536 | Hans Havermann | 06/2021 |
| 4852 | 37637^6492+6492^37637 | 143487 | Hans Havermann | 05/2021 |
| 4853 | 61567^214+214^61567 | 143477 | Hans Havermann | 05/2021 |
| 4854 | 25933^32504-32504^25933 | 143468 | Frank Doornink | 03/2024 |
| 4855 | 2^476558-113627 | 143459 | Enzo Doria | 08/2014 |
| 4856 | 2^476478-45 | 143435 | Lelio R Paula | 11/2017 |
| 4857 | 36380^8757+8757^36380 | 143423 | Hans Havermann | 06/2021 |
| 4858 | (7*21^108452+4733)/20 | 143397 | Eric Chen | 03/2026 |
| 4859 | 32510^25707+25707^32510 | 143371 | Hans Havermann | 05/2021 |
| 4860 | 8*10^143361+17 | 143362 | Robert Price | 07/2021 |
| 4861 | (2^475854+9)/73 | 143245 | Lelio R Paula | 08/2015 |
| 4862 | 2^475813-113239 | 143234 | Enzo Doria | 07/2014 |
| 4863 | (19*10^143212+137)/3 | 143213 | Robert Price | 03/2022 |
| 4864 | 32218^27849+27849^32218 | 143203 | Hans Havermann | 04/2021 |
| 4865 | 580*33^94296+19 | 143193 | Eric Chen | 12/2023 |
| 4866 | 2^475624-114059 | 143178 | Enzo Doria | 11/2014 |
| 4867 | (11*2^475553-7)/15 | 143156 | Renaud Lifchitz | 03/2011 |
| 4868 | 2^475480-2786129 | 143134 | Enzo Doria | 10/2015 |
| 4869 | 33912^16621+16621^33912 | 143131 | Hans Havermann | 05/2021 |
| 4870 | (19*10^143129-43)/3 | 143130 | Robert Price | 05/2019 |
| 4871 | 31830^31373+31373^31830 | 143126 | Hans Havermann | 05/2021 |
| 4872 | 2^475392+1334025 | 143108 | Henri Lifchitz | 01/2025 |
| 4873 | 6*10^143105-53 | 143106 | Robert Price | 05/2021 |
| 4874 | (14*10^143097+73)/3 | 143098 | Robert Price | 12/2018 |
| 4875 | 2^475299-111937 | 143080 | Enzo Doria | 05/2014 |
| 4876 | 35488^10753+10753^35488 | 143071 | Hans Havermann | 04/2021 |
| 4877 | 29695^31986-31986^29695 | 143064 | Frank Doornink | 06/2024 |
| 4878 | 2^475160-2797859 | 143038 | Enzo Doria | 04/2016 |
| 4879 | (2^475069+3)/395 | 143008 | Lelio R Paula | 08/2015 |
| 4880 | 2^475027-461437 | 142998 | Enzo Doria | 07/2015 |
| 4881 | (2^474958+78557)/3 | 142977 | Lelio R Paula | 07/2015 |
| 4882 | (8*10^142932+43)/3 | 142933 | Robert Price | 06/2018 |
| 4883 | 35055^11942+11942^35055 | 142922 | Hans Havermann | 05/2021 |
| 4884 | 37650^6239+6239^37650 | 142887 | Hans Havermann | 05/2021 |
| 4885 | (54^82471-1)/53 | 142871 | Paul Bourdelais | 09/2017 |
| 4886 | 31205^31784-31784^31205 | 142845 | Frank Doornink | 01/2024 |
| 4887 | (11*2^474432-1)/95 | 142818 | Lelio R Paula | 09/2015 |
| 4888 | 2^474417-59923 | 142814 | Enzo Doria | 10/2015 |
| 4889 | 4*10^142810-21 | 142811 | Robert Price | 09/2018 |
| 4890 | 32287^26494+26494^32287 | 142811 | Hans Havermann | 06/2021 |
| 4891 | 37162^6965+6965^37162 | 142811 | Hans Havermann | 06/2021 |
| 4892 | (34*10^142805-601)/9 | 142806 | Robert Price | 07/2022 |
| 4893 | 37456^6493+6493^37456 | 142799 | Hans Havermann | 05/2021 |
| 4894 | 35141^11572+11572^35141 | 142793 | Hans Havermann | 05/2021 |
| 4895 | 32231^26908+26908^32231 | 142780 | Hans Havermann | 05/2021 |
| 4896 | (3*2^474166+1)/7 | 142738 | Lelio R Paula | 08/2015 |
| 4897 | 2^474053+2897 | 142705 | Lelio R Paula | 08/2012 |
| 4898 | (10^142699+359)/9 | 142699 | Serge Batalov | 12/2014 |
| 4899 | 26073^32312-32312^26073 | 142696 | Frank Doornink | 03/2024 |
| 4900 | 898^48311-897^48311 | 142676 | Jean-Louis Charton | 12/2012 |
| 4901 | 2^473740-1856639 | 142610 | Enzo Doria | 09/2015 |
| 4902 | (25*10^142573-403)/9 | 142574 | Robert Price | 12/2020 |
| 4903 | 2^473617-114223 | 142573 | Enzo Doria | 12/2014 |
| 4904 | 36115^8856+8856^36115 | 142555 | Hans Havermann | 05/2021 |
| 4905 | fibonacci(682007)+4 | 142531 | Jon Grantham | 08/2023 |
| 4906 | 2^473257+1873217 | 142465 | Enzo Doria | 06/2016 |
| 4907 | (19*2^473242+1)/11 | 142461 | Lelio R Paula | 09/2015 |
| 4908 | 32750^22371+22371^32750 | 142453 | Hans Havermann | 06/2021 |
| 4909 | (61*10^142446-1)/3 | 142448 | Robert Price | 01/2020 |
| 4910 | (14*10^142440+61)/3 | 142441 | Robert Price | 12/2018 |
| 4911 | (10^142425+359)/9 | 142425 | Serge Batalov | 12/2014 |
| 4912 | 2^473101+773027 | 142418 | Enzo Doria | 05/2016 |
| 4913 | (13*2^472838-1)/3 | 142340 | Lelio R Paula | 09/2015 |
| 4914 | (17*2^472789-1)/187347 | 142320 | Lelio R Paula | 09/2015 |
| 4915 | 36915^7162+7162^36915 | 142309 | Hans Havermann | 05/2021 |
| 4916 | 2^472634-109511 | 142278 | Enzo Doria | 04/2014 |
| 4917 | 31870^28997+28997^31870 | 142216 | Hans Havermann | 06/2021 |
| 4918 | (48^84589+1)/49 | 142213 | Robert Price | 01/2014 |
| 4919 | 7*10^142189+87 | 142190 | Robert Price | 07/2019 |
| 4920 | 2^472258+7 | 142164 | Lelio R Paula | 08/2015 |
| 4921 | 40135^3484+3484^40135 | 142162 | Hans Havermann | 05/2021 |
| 4922 | 9*33^93598+26 | 142131 | Eric Chen | 12/2023 |
| 4923 | Phi(585361,-2) | 142125 | Henri Lifchitz | 02/2026 |
| 4924 | (23*10^142105+91)/3 | 142106 | Robert Price | 08/2019 |
| 4925 | tau(317^10330) | 142098 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 4926 | (11*2^471913-1)/21 | 142060 | Lelio R Paula | 09/2015 |
| 4927 | (16*10^142058+197)/3 | 142059 | Robert Price | 04/2019 |
| 4928 | 9*10^142037+91 | 142038 | Robert Price | 10/2020 |
| 4929 | (4*10^142034+17)/3 | 142035 | Tyler Busby | 01/2023 |
| 4930 | 2^471792+1880881 | 142024 | Enzo Doria | 11/2016 |
| 4931 | (509*10^142018+31)/9 | 142020 | Robert Price | 08/2022 |
| 4932 | (31*2^471580-1)/135 | 141960 | Lelio R Paula | 08/2015 |
| 4933 | (4*10^141926-79)/3 | 141927 | Robert Price | 02/2018 |
| 4934 | 2^471464-111546435 | 141925 | Paul Bourdelais | 10/2021 |
| 4935 | (904*19^110984-1)/3 | 141924 | Curtis Bright | 05/2015 |
| 4936 | (14*10^141853+37)/3 | 141854 | Robert Price | 12/2018 |
| 4937 | (12^131449-1)/4199006867 | 141848 | Paul Vanderveen | 06/2025 |
| 4938 | (41*10^141836-59)/9 | 141837 | Robert Price | 10/2018 |
| 4939 | 4*5^202913-9 | 141831 | Lelio R Paula | 04/2015 |
| 4940 | 2*7^167812-3 | 141818 | Lelio R Paula | 12/2014 |
| 4941 | 2^471043+35 | 141799 | Robert Price | 11/2015 |
| 4942 | (11*2^470956-1)/7945 | 141770 | Lelio R Paula | 08/2015 |
| 4943 | 43636^1773+1773^43636 | 141761 | Hans Havermann | 05/2021 |
| 4944 | (2*10^141751-17)/3 | 141751 | Serge Batalov | 11/2022 |
| 4945 | (53*10^141722-611)/9 | 141723 | Robert Price | 02/2022 |
| 4946 | (11*10^141718-131)/3 | 141719 | Robert Price | 09/2018 |
| 4947 | (61*10^141716+47)/9 | 141717 | Robert Price | 07/2022 |
| 4948 | 26057^32088-32088^26057 | 141699 | Frank Doornink | 03/2024 |
| 4949 | 2^470692+76771 | 141693 | Enzo Doria | 05/2016 |
| 4950 | 50160^667+667^50160 | 141659 | Hans Havermann | 05/2021 |
| 4951 | 31522^31181+31181^31522 | 141657 | Hans Havermann | 05/2021 |
| 4952 | 29487^31690-31690^29487 | 141643 | Frank Doornink | 06/2024 |
| 4953 | 33076^19135+19135^33076 | 141626 | Hans Havermann | 04/2021 |
| 4954 | 28237^31818-31818^28237 | 141617 | Frank Doornink | 06/2024 |
| 4955 | Phi(303939,5) | 141617 | Henri Lifchitz | 02/2026 |
| 4956 | (91*10^141610+71)/9 | 141612 | Robert Price | 01/2022 |
| 4957 | (21*2^470391+1)/533 | 141601 | Lelio R Paula | 09/2015 |
| 4958 | (5*10^141594-23)/9 | 141594 | Serge Batalov | 11/2022 |
| 4959 | 31932^27155+27155^31932 | 141582 | Hans Havermann | 05/2021 |
| 4960 | 36449^7660+7660^36449 | 141577 | Hans Havermann | 05/2021 |
| 4961 | 2^470305-459373 | 141576 | Enzo Doria | 05/2015 |
| 4962 | 32195^24936+24936^32195 | 141556 | Hans Havermann | 05/2021 |
| 4963 | 2^470183+72623 | 141540 | Enzo Doria | 04/2016 |
| 4964 | 2^470173-16465 | 141537 | Enzo Doria | 04/2013 |
| 4965 | 37297^6234+6234^37297 | 141534 | Hans Havermann | 05/2021 |
| 4966 | 2^4^117533+117533^4^2 | 141524 | Henri Lifchitz | 03/2025 |
| 4967 | (509*10^141479+13)/9 | 141481 | Robert Price | 05/2022 |
| 4968 | 44*10^141476+9 | 141478 | Robert Price | 10/2020 |
| 4969 | 2^469974-1841 | 141477 | Enzo Doria | 05/2014 |
| 4970 | (23*2^469939+1)/25 | 141466 | Lelio R Paula | 08/2015 |
| 4971 | 312*33^93158+23 | 141465 | Eric Chen | 12/2023 |
| 4972 | 2*10^141448+63 | 141449 | Robert Price | 05/2018 |
| 4973 | 2^469824+43 | 141432 | Lelio R Paula | 09/2017 |
| 4974 | (124750^27751-1)/124749 | 141416 | Anonymous | 09/2025 |
| 4975 | 2*10^141407-27 | 141408 | Robert Price | 05/2018 |
| 4976 | (214*10^141385-1)/3 | 141387 | Robert Price | 01/2021 |
| 4977 | 2^469630-59711 | 141373 | Enzo Doria | 10/2015 |
| 4978 | 35277^10172+10172^35277 | 141370 | Hans Havermann | 04/2021 |
| 4979 | 33397^17100+17100^33397 | 141370 | Hans Havermann | 04/2021 |
| 4980 | (25*10^141366-331)/9 | 141367 | Robert Price | 08/2018 |
| 4981 | 36986^6639+6639^36986 | 141365 | Hans Havermann | 06/2021 |
| 4982 | 34572^12271+12271^34572 | 141361 | Hans Havermann | 06/2021 |
| 4983 | 37179^6338+6338^37179 | 141353 | Hans Havermann | 05/2021 |
| 4984 | (2^469564-3)/611 | 141351 | Lelio R Paula | 08/2015 |
| 4985 | 197^61601+2 | 141342 | Lelio R Paula | 08/2017 |
| 4986 | 33420^16951+16951^33420 | 141340 | Hans Havermann | 05/2021 |
| 4987 | 31623^29458+29458^31623 | 141330 | Hans Havermann | 05/2021 |
| 4988 | 48112^865+865^48112 | 141306 | Hans Havermann | 05/2021 |
| 4989 | 2^469372-112949 | 141296 | Enzo Doria | 07/2014 |
| 4990 | 5*10^141294-63 | 141295 | Robert Price | 04/2021 |
| 4991 | 3^296115+4 | 141283 | Tyler NeSmith | 01/2021 |
| 4992 | (64*10^141256+161)/9 | 141257 | Robert Price | 08/2022 |
| 4993 | 143^(2^16)+106^(2^16) | 141253 | Valeryi Kuryshev | 02/2011 |
| 4994 | 143^65536+106^65536 | 141253 | Serge Batalov | 03/2018 |
| 4995 | (11*10^141243-23)/3 | 141244 | Robert Price | 09/2021 |
| 4997 | 2^469198+782569 | 141243 | Enzo Doria | 10/2016 |
| 4996 | 38129^5062+5062^38129 | 141243 | Hans Havermann | 05/2021 |
| 4998 | (41^87583-1)/192892799240 | 141242 | Paul Vanderveen | 05/2025 |
| 4999 | 2^469076-2786939 | 141206 | Enzo Doria | 11/2015 |
| 5000 | 38630^4521+4521^38630 | 141202 | Hans Havermann | 05/2021 |
