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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 5751 | 2^425808-459959 | 128181 | Enzo Doria | 06/2015 |
| 5752 | 30632^15291+15291^30632 | 128178 | Hans Havermann | 04/2021 |
| 5753 | U(623603) | 128177 | Serge Batalov | 07/2024 |
| 5754 | 35981^3648+3648^35981 | 128167 | Hans Havermann | 04/2021 |
| 5755 | 2^425627-113605 | 128127 | Enzo Doria | 08/2014 |
| 5756 | (4*10^128109+119)/3 | 128110 | Robert Price | 12/2021 |
| 5757 | (22*10^128094+53)/3 | 128095 | Robert Price | 07/2019 |
| 5758 | (86*10^128086-221)/9 | 128087 | Robert Price | 09/2019 |
| 5759 | 18565^30002-30002^18565 | 128070 | Norbert Schneider | 01/2015 |
| 5760 | (2^425287-9)/2737 | 128021 | Lelio R Paula | 05/2015 |
| 5761 | (3*2^425233-1)/25 | 128007 | Lelio R Paula | 05/2014 |
| 5762 | Phi(149401,10)/30037901719561 | 128003 | Makoto Kamada | 07/2022 |
| 5763 | 2^425205+4911 | 128000 | Marek Hubal | 02/2017 |
| 5764 | 29241^23836+23836^29241 | 127995 | Hans Havermann | 04/2021 |
| 5765 | 2^425118-113663 | 127974 | Enzo Doria | 08/2014 |
| 5766 | (86*10^127967-329)/9 | 127968 | Robert Price | 01/2020 |
| 5767 | 2^425061+1869761 | 127957 | Enzo Doria | 05/2016 |
| 5768 | 746^44541+44541^746 | 127955 | Norbert Schneider | 07/2019 |
| 5769 | 30236^17043+17043^30236 | 127946 | Hans Havermann | 03/2021 |
| 5770 | 2^424938+212419 | 127920 | Enzo Doria | 08/2023 |
| 5771 | 2^424918-21141 | 127914 | Enzo Doria | 07/2013 |
| 5772 | Phi(274823,-3) | 127907 | Henri Lifchitz | 12/2025 |
| 5773 | (62*10^127903+91)/9 | 127904 | Robert Price | 07/2021 |
| 5774 | 2^424864-29489 | 127897 | Enzo Doria | 08/2015 |
| 5775 | 30438^15893+15893^30438 | 127877 | Hans Havermann | 02/2021 |
| 5776 | (97*10^127858-1)/3 | 127860 | Serge Batalov | 12/2014 |
| 5777 | 28929^26258+26258^28929 | 127845 | Hans Havermann | 03/2021 |
| 5778 | 30563^15220+15220^30563 | 127828 | Hans Havermann | 03/2021 |
| 5779 | 2^424632-2786639 | 127827 | Enzo Doria | 03/2016 |
| 5780 | 10^127821-700001 | 127821 | Robert Price | 08/2021 |
| 5781 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
| 5782 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
| 5783 | (56*10^127752+691)/9 | 127753 | Robert Price | 05/2019 |
| 5784 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
| 5785 | 22*10^127645+3 | 127647 | Robert Price | 01/2020 |
| 5786 | 28715^27844+27844^28715 | 127631 | Hans Havermann | 03/2021 |
| 5787 | (56*10^127612+187)/9 | 127613 | Robert Price | 10/2021 |
| 5788 | (5*36^81995+821)/7 | 127609 | Eric Chen | 01/2021 |
| 5789 | 4*10^127562-39 | 127563 | Robert Price | 09/2020 |
| 5790 | 32595^8186+8186^32595 | 127547 | Hans Havermann | 03/2021 |
| 5791 | 2^423696-21429 | 127546 | Enzo Doria | 07/2013 |
| 5792 | 2^423664-1864559 | 127536 | Enzo Doria | 03/2016 |
| 5793 | 37889^2322+2322^37889 | 127530 | Hans Havermann | 03/2021 |
| 5794 | 37668^2429+2429^37668 | 127523 | Hans Havermann | 03/2021 |
| 5795 | 3^267267-4 | 127519 | Henri Lifchitz | 10/2014 |
| 5796 | fibonacci(610144)-2 | 127513 | Jon Grantham | 08/2023 |
| 5797 | 26253^28852-28852^26253 | 127503 | Frank Doornink | 03/2024 |
| 5798 | (103*10^127491+17)/3 | 127493 | Robert Price | 08/2020 |
| 5799 | 29376^21869+21869^29376 | 127487 | Hans Havermann | 03/2021 |
| 5800 | 31186^12241+12241^31186 | 127483 | Hans Havermann | 02/2021 |
| 5801 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
| 5802 | 27069^28754-28754^27069 | 127452 | Frank Doornink | 01/2024 |
| 5803 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
| 5804 | 30594^14645+14645^30594 | 127446 | Hans Havermann | 03/2021 |
| 5805 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
| 5806 | (67*10^127413-7)/3 | 127415 | Robert Price | 01/2020 |
| 5807 | (5*34^83193+700233)/11 | 127408 | Eric Chen | 08/2023 |
| 5808 | (2*10^127407+73)/3 | 127407 | Robert Price | 09/2020 |
| 5809 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
| 5810 | (7726^32768+1)/13917994151414876602369 | 127379 | Kellen Shenton | 04/2021 |
| 5811 | (4*10^127349+17)/3 | 127350 | Tyler Busby | 01/2023 |
| 5812 | 29512^20647+20647^29512 | 127341 | Hans Havermann | 03/2021 |
| 5813 | 2^422987-3001935 | 127332 | Paul Bourdelais | 07/2023 |
| 5814 | (112*10^127324+17)/3 | 127326 | Robert Price | 03/2020 |
| 5816 | 29565^20252+20252^29565 | 127321 | Hans Havermann | 03/2021 |
| 5815 | 232^232^232+1831^1831 | 127321 | Henri Lifchitz | 03/2025 |
| 5817 | fibonacci(609165)-3 | 127308 | Jon Grantham | 08/2023 |
| 5819 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
| 5818 | (5^182099-3^182099)/2 | 127282 | Kellen Shenton | 05/2022 |
| 5820 | (16*10^127259+197)/3 | 127260 | Robert Price | 04/2019 |
| 5821 | (26*10^127240+61)/3 | 127241 | Robert Price | 10/2019 |
| 5822 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
| 5823 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
| 5824 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
| 5825 | 31678^10343+10343^31678 | 127176 | Hans Havermann | 03/2021 |
| 5826 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
| 5827 | 34947^4352+4352^34947 | 127162 | Hans Havermann | 03/2021 |
| 5828 | 6*10^127158+19 | 127159 | Robert Price | 11/2021 |
| 5829 | 30469^14902+14902^30469 | 127155 | Hans Havermann | 03/2021 |
| 5830 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
| 5831 | 29941^17620+17620^29941 | 127130 | Hans Havermann | 02/2021 |
| 5832 | 31607^10516+10516^31607 | 127119 | Hans Havermann | 03/2021 |
| 5833 | (19*10^127118-97)/3 | 127119 | Robert Price | 10/2021 |
| 5834 | (29*10^127111+691)/9 | 127112 | Robert Price | 08/2021 |
| 5835 | 736^44335+44335^736 | 127104 | Norbert Schneider | 07/2019 |
| 5836 | 33040^7023+7023^33040 | 127090 | Hans Havermann | 03/2021 |
| 5837 | (4*10^127081+167)/9 | 127081 | Robert Price | 03/2022 |
| 5838 | 29748^18661+18661^29748 | 127052 | Hans Havermann | 03/2021 |
| 5839 | 27905^28578-28578^27905 | 127049 | Frank Doornink | 03/2024 |
| 5840 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
| 5841 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
| 5842 | (14*10^127014-137)/3 | 127015 | Robert Price | 04/2021 |
| 5843 | 31436^10965+10965^31436 | 127002 | Hans Havermann | 03/2021 |
| 5844 | 28905^24758+24758^28905 | 127001 | Hans Havermann | 03/2021 |
| 5845 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
| 5846 | (10^127030+7)/81234833/9230384921/6092460488946445358851 | 126991 | Alfred Reich | 07/2021 |
| 5847 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
| 5848 | 26268^28729-28729^26268 | 126966 | Frank Doornink | 03/2024 |
| 5849 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
| 5850 | (56*10^126935+187)/9 | 126936 | Robert Price | 10/2021 |
| 5851 | 28915^24538+24538^28915 | 126933 | Hans Havermann | 03/2021 |
| 5852 | (29*10^126928-77)/3 | 126929 | Robert Price | 02/2020 |
| 5853 | (259*10^126919-1)/3 | 126921 | Robert Price | 12/2020 |
| 5854 | 10^126919+204567 | 126920 | Patrick De Geest | 05/2021 |
| 5855 | (2^421617+100280245065) | 126920 | Paul Bourdelais | 05/2022 |
| 5856 | 10^126919-100001 | 126919 | Robert Price | 07/2020 |
| 5857 | 28340^28503+28503^28340 | 126907 | Norbert Schneider | 02/2021 |
| 5858 | 2^421534-3001935 | 126895 | Paul Bourdelais | 07/2023 |
| 5859 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
| 5860 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
| 5861 | Phi(47471,561) | 126871 | Henri Lifchitz | 12/2025 |
| 5862 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
| 5863 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
| 5864 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
| 5865 | 37938^2203+2203^37938 | 126828 | Hans Havermann | 03/2021 |
| 5866 | (13*10^126819+77)/9 | 126820 | Robert Price | 07/2022 |
| 5867 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
| 5869 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
| 5868 | 2^421169-3001935 | 126785 | Paul Bourdelais | 07/2023 |
| 5870 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
| 5871 | 26733^28628-28628^26733 | 126738 | Frank Doornink | 03/2024 |
| 5872 | (106*10^126726+17)/3 | 126728 | Robert Price | 04/2021 |
| 5873 | 30718^13347+13347^30718 | 126724 | Hans Havermann | 03/2021 |
| 5874 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
| 5875 | 11*23^93048+356 | 126708 | Eric Chen | 08/2023 |
| 5876 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
| 5877 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
| 5878 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
| 5879 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
| 5880 | (167*10^126637-17)/3 | 126639 | Robert Price | 03/2020 |
| 5881 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
| 5882 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
| 5883 | 7*10^126600-99 | 126601 | Robert Price | 06/2019 |
| 5884 | U(655247)/250330563881/206066063082749 | 126596 | Serge Batalov | 07/2024 |
| 5885 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
| 5886 | 28717^25534+25534^28717 | 126560 | Hans Havermann | 03/2021 |
| 5887 | (86*10^126542+103)/9 | 126543 | Robert Price | 12/2021 |
| 5888 | (19*10^126517-7)/3 | 126518 | Robert Price | 12/2023 |
| 5889 | 2026^38261-2025^38261 | 126516 | Henri Lifchitz | 12/2025 |
| 5890 | 28922^23655+23655^28922 | 126503 | Hans Havermann | 03/2021 |
| 5891 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
| 5892 | 25982^28643-28643^25982 | 126450 | Frank Doornink | 03/2024 |
| 5893 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
| 5894 | 8*10^126408+71 | 126409 | Robert Price | 05/2022 |
| 5895 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
| 5896 | 29315^20484+20484^29315 | 126390 | Hans Havermann | 03/2021 |
| 5897 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
| 5898 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
| 5899 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
| 5900 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
| 5901 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
| 5902 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
| 5903 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
| 5904 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
| 5905 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
| 5906 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
| 5907 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
| 5908 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
| 5909 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
| 5910 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
| 5911 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
| 5912 | Phi(267889,3) | 126161 | Henri Lifchitz | 12/2025 |
| 5913 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
| 5914 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
| 5915 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
| 5916 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
| 5917 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
| 5918 | 4*10^126064-69 | 126065 | Robert Price | 01/2022 |
| 5919 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
| 5920 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
| 5921 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
| 5922 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
| 5923 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
| 5924 | 25134^28625-28625^25134 | 125958 | Frank Doornink | 12/2023 |
| 5925 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
| 5926 | (23*35^81566-144013)/34 | 125944 | Eric Chen | 05/2025 |
| 5927 | 26197^28502-28502^26197 | 125930 | Frank Doornink | 03/2024 |
| 5928 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
| 5929 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
| 5930 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
| 5931 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
| 5932 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
| 5933 | 10^(2*62938+1)-7*10^62938-1 | 125877 | Robert Price | 07/2023 |
| 5934 | 55*10^125847+9 | 125849 | Robert Price | 03/2022 |
| 5935 | 4*10^125832+57 | 125833 | Robert Price | 05/2022 |
| 5936 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
| 5937 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
| 5938 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
| 5939 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
| 5940 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
| 5941 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
| 5942 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
| 5943 | 30455^13464+13464^30455 | 125754 | Hans Havermann | 03/2021 |
| 5944 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
| 5945 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
| 5946 | 29755^16816+16816^29755 | 125737 | Hans Havermann | 03/2021 |
| 5947 | (22*10^125734+203)/9 | 125735 | Robert Price | 10/2021 |
| 5948 | 29918^15915+15915^29918 | 125710 | Hans Havermann | 03/2021 |
| 5949 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
| 5950 | 28531^25368+25368^28531 | 125659 | Hans Havermann | 03/2021 |
| 5951 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
| 5952 | (46*10^125642+593)/9 | 125643 | Robert Price | 04/2022 |
| 5953 | 2^417315+213953 | 125625 | Enzo Doria | 10/2023 |
| 5954 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
| 5955 | 30638^12537+12537^30638 | 125561 | Hans Havermann | 03/2021 |
| 5956 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
| 5957 | 30162^14525+14525^30162 | 125538 | Hans Havermann | 03/2021 |
| 5958 | (56*10^125535+583)/9 | 125536 | Robert Price | 08/2021 |
| 5959 | (23*10^125517-179)/3 | 125518 | Robert Price | 06/2022 |
| 5960 | 9*10^125516+29 | 125517 | Robert Price | 03/2022 |
| 5961 | 404*35^81280+23 | 125505 | Eric Chen | 05/2025 |
| 5962 | (88*10^125492-637)/9 | 125493 | Robert Price | 11/2020 |
| 5963 | 28958^21525+21525^28958 | 125474 | Hans Havermann | 02/2021 |
| 5966 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
| 5964 | (10^125482+7)/162685667/1639829194459 | 125462 | Alfred Reich | 07/2021 |
| 5965 | 26078^28409-28409^26078 | 125462 | Frank Doornink | 03/2024 |
| 5967 | 33889^5032+5032^33889 | 125449 | Hans Havermann | 03/2021 |
| 5968 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
| 5969 | (2861^36481+1)/(2861^191+1) | 125438 | Martin Hopf | 12/2023 |
| 5970 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
| 5971 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
| 5972 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
| 5973 | 33392^5697+5697^33392 | 125409 | Hans Havermann | 03/2021 |
| 5974 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
| 5975 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
| 5976 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
| 5977 | 27953^28198+28198^27953 | 125381 | Norbert Schneider | 01/2021 |
| 5978 | 31074^10837+10837^31074 | 125381 | Hans Havermann | 03/2021 |
| 5979 | 33745^5194+5194^33745 | 125380 | Hans Havermann | 03/2021 |
| 5980 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
| 5981 | 28360^26331+26331^28360 | 125365 | Hans Havermann | 03/2021 |
| 5982 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
| 5983 | 25805^28412-28412^25805 | 125346 | Frank Doornink | 03/2024 |
| 5984 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
| 5985 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
| 5986 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
| 5987 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
| 5988 | (599*10^125224+13)/9 | 125226 | Robert Price | 02/2022 |
| 5989 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
| 5990 | 30054^14657+14657^30054 | 125207 | Hans Havermann | 03/2021 |
| 5991 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
| 5992 | 2^415884-933075 | 125194 | Paul Bourdelais | 06/2021 |
| 5993 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
| 5994 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
| 5995 | 10^125166-5001 | 125166 | Robert Price | 12/2021 |
| 5996 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
| 5997 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
| 5998 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
| 5999 | (11*10^125054+73)/3 | 125055 | Robert Price | 08/2021 |
| 6000 | Phi(251979,-9) | 125044 | Henri Lifchitz | 02/2026 |
