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 ? |
| 5501 | 2^438774-2786411 | 132085 | Enzo Doria | 03/2016 |
| 5502 | 2^438755-1848205 | 132079 | Enzo Doria | 07/2015 |
| 5503 | 30502^21381+21381^30502 | 132075 | Hans Havermann | 04/2021 |
| 5504 | 2^438739-112087 | 132074 | Enzo Doria | 06/2014 |
| 5505 | (588859*29^90289-19)/28 | 132043 | Eric Chen | 06/2025 |
| 5506 | (2^438438+100280245065) | 131983 | Paul Bourdelais | 05/2022 |
| 5507 | 35872^4777+4777^35872 | 131979 | Hans Havermann | 04/2021 |
| 5508 | 31198^16945+16945^31198 | 131938 | Hans Havermann | 03/2021 |
| 5509 | 13907#+(318259#)/(13907#) | 131923 | Makoto Morimoto | 10/2017 |
| 5510 | L(631181) | 131910 | Henri Lifchitz | 09/2008 |
| 5511 | (47*10^131886-119)/9 | 131887 | Robert Price | 05/2019 |
| 5512 | 5*2^438096-3 | 131881 | Jon Grantham | 07/2023 |
| 5513 | (3*2^438121+1)/4308193883 | 131879 | Lelio R Paula | 06/2015 |
| 5514 | 2^438079-1863877 | 131875 | Enzo Doria | 03/2016 |
| 5515 | (16*10^131872-37)/3 | 131873 | Robert Price | 05/2021 |
| 5516 | (2^438067+5)/329 | 131869 | Lelio R Paula | 06/2015 |
| 5517 | 2^437908-113855 | 131824 | Enzo Doria | 09/2014 |
| 5518 | 2^437884-286349 | 131817 | Enzo Doria | 07/2015 |
| 5519 | 15^112072+14 | 131807 | Alfred Reich | 10/2023 |
| 5520 | 5^188558+4 | 131797 | Tyler NeSmith | 05/2021 |
| 5521 | (11*10^131784-17)/3 | 131785 | Robert Price | 06/2018 |
| 5522 | (166^59357-1)/165 | 131777 | Anonymous | 06/2024 |
| 5523 | 4*10^131719-93 | 131720 | Robert Price | 07/2020 |
| 5524 | 31629^14606+14606^31629 | 131720 | Hans Havermann | 04/2021 |
| 5525 | 3^276062-112292 | 131716 | Enzo Doria | 07/2014 |
| 5526 | 2^437539+2025 | 131713 | Henri Lifchitz | 01/2025 |
| 5527 | 11*31^88313+322688 | 131708 | Eric Chen | 05/2024 |
| 5528 | (7*10^131682+89)/3 | 131683 | Robert Price | 08/2020 |
| 5529 | 29512^28969+28969^29512 | 131681 | Hans Havermann | 03/2021 |
| 5530 | 2^437343+75953 | 131654 | Enzo Doria | 04/2016 |
| 5531 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
| 5532 | (28*10^131586+59)/3 | 131587 | Robert Price | 05/2021 |
| 5533 | (59*10^131575+391)/9 | 131576 | Robert Price | 03/2021 |
| 5534 | Phi(51051,-17#) | 131513 | Henri Lifchitz | 12/2025 |
| 5535 | 39984^1945+1945^39984 | 131505 | Hans Havermann | 03/2021 |
| 5536 | 25842^29801-29801^25842 | 131492 | Frank Doornink | 03/2024 |
| 5537 | 28592^29505-29505^28592 | 131482 | Frank Doornink | 05/2024 |
| 5538 | 25647^29818-29818^25647 | 131469 | Frank Doornink | 02/2024 |
| 5539 | (203*10^131457+1)/3 | 131459 | Robert Price | 03/2020 |
| 5540 | 7*10^131421-41 | 131422 | Robert Price | 08/2021 |
| 5541 | 87309^32+32^87309 | 131414 | Hans Havermann | 03/2021 |
| 5542 | (68^71713+1)/69 | 131413 | Paul Bourdelais | 09/2017 |
| 5543 | 2^436521+224885 | 131406 | Enzo Doria | 07/2024 |
| 5544 | (650*10^131391+43)/9 | 131393 | Tyler Busby | 01/2023 |
| 5545 | 2^436451+1884713 | 131385 | Enzo Doria | 03/2017 |
| 5546 | 2^436365+35 | 131359 | Robert Price | 11/2015 |
| 5548 | 2^436300+1866871 | 131340 | Enzo Doria | 03/2016 |
| 5547 | (7*10^131339+179)/3 | 131340 | Robert Price | 09/2018 |
| 5549 | 14^114592-3 | 131338 | Paul Bourdelais | 12/2020 |
| 5550 | 36197^4236+4236^36197 | 131285 | Hans Havermann | 04/2021 |
| 5551 | (37*10^131270+341)/9 | 131271 | Robert Price | 08/2018 |
| 5552 | 29863^24790+24790^29863 | 131227 | Hans Havermann | 03/2021 |
| 5553 | (5*10^131223-29)/3 | 131224 | Robert Price | 03/2018 |
| 5554 | 29524^27825+27825^29524 | 131218 | Hans Havermann | 03/2021 |
| 5555 | (23*2^435891-1)/699 | 131215 | Lelio R Paula | 07/2015 |
| 5556 | (11*2^435879+1)/3337 | 131211 | Lelio R Paula | 06/2015 |
| 5557 | 30639^19136+19136^30639 | 131192 | Hans Havermann | 04/2021 |
| 5558 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
| 5559 | (2^435808+1)/4294967297 | 131182 | Serge Batalov | 12/2016 |
| 5560 | 2^435773+1875557 | 131181 | Enzo Doria | 06/2016 |
| 5562 | (16*10^131180+167)/3 | 131181 | Robert Price | 06/2019 |
| 5561 | (26*10^131180-77)/3 | 131181 | Robert Price | 11/2019 |
| 5563 | (25*10^131144-7)/9 | 131145 | Robert Price | 05/2018 |
| 5564 | 29299^29358-29358^29299 | 131138 | Norbert Schneider | 03/2022 |
| 5565 | 2^435612-2789939 | 131133 | Enzo Doria | 12/2015 |
| 5566 | 33976^7231+7231^33976 | 131121 | Hans Havermann | 03/2021 |
| 5567 | 33715^7746+7746^33715 | 131121 | Hans Havermann | 03/2021 |
| 5568 | 66^72047-65^72047 | 131093 | Robert Price | 09/2013 |
| 5569 | (5*10^131090+37)/3 | 131091 | Robert Price | 03/2018 |
| 5570 | 2^435468+75631 | 131089 | Enzo Doria | 04/2016 |
| 5571 | 37^83588-2 | 131083 | Lelio R Paula | 08/2015 |
| 5572 | (4^217720+11)/3 | 131081 | Robert Price | 02/2017 |
| 5573 | 30407^20448+20448^30407 | 131074 | Hans Havermann | 04/2021 |
| 5574 | (22*10^131070+179)/3 | 131071 | Robert Price | 02/2022 |
| 5575 | 28831^29388-29388^28831 | 131067 | Frank Doornink | 05/2024 |
| 5576 | 29487^27836+27836^29487 | 131059 | Hans Havermann | 04/2021 |
| 5577 | 29962^23615+23615^29962 | 131030 | Hans Havermann | 03/2021 |
| 5578 | 2^435202-113193 | 131009 | Enzo Doria | 07/2014 |
| 5579 | 41705^1384+1384^41705 | 131002 | Hans Havermann | 04/2021 |
| 5580 | 9*10^130998-19 | 130999 | Robert Price | 07/2019 |
| 5581 | 36243^4108+4108^36243 | 130969 | Hans Havermann | 04/2021 |
| 5582 | (445^49433+1)/446 | 130914 | Jinyuan Wang | 05/2024 |
| 5583 | floor((sqrt(5)-1)/2*10^130911) | 130911 | Serge Batalov | 06/2017 |
| 5584 | 2^434835-111937 | 130899 | Enzo Doria | 05/2014 |
| 5585 | (62*10^130895-629)/9 | 130896 | Robert Price | 07/2021 |
| 5586 | 2^434807+225 | 130890 | Henri Lifchitz | 11/2024 |
| 5587 | 2^434685+72257 | 130854 | Enzo Doria | 04/2016 |
| 5588 | Phi(64497,-1105) | 130853 | Henri Lifchitz | 12/2025 |
| 5589 | (7*10^130825+113)/3 | 130826 | Robert Price | 02/2018 |
| 5590 | 2^434539-29317 | 130810 | Enzo Doria | 07/2015 |
| 5591 | (74*10^130791+637)/9 | 130792 | Robert Price | 01/2022 |
| 5592 | 2^434469-114259 | 130789 | Enzo Doria | 01/2015 |
| 5593 | (5*10^130763+103)/9 | 130763 | Robert Price | 04/2022 |
| 5594 | 2^434246+33 | 130722 | Robert Price | 11/2015 |
| 5595 | 30156^21599+21599^30156 | 130710 | Hans Havermann | 04/2021 |
| 5596 | (41^81041-3^81041)/38 | 130701 | Robert Price | 09/2025 |
| 5597 | (17*10^130695-161)/9 | 130696 | Robert Price | 02/2021 |
| 5598 | 30513^19148+19148^30513 | 130661 | Hans Havermann | 03/2021 |
| 5599 | 29736^24761+24761^29736 | 130654 | Hans Havermann | 04/2021 |
| 5600 | 9*10^130638+41 | 130639 | Robert Price | 08/2020 |
| 5601 | 2^433911-91 | 130621 | Lelio R Paula | 06/2017 |
| 5602 | 30786^17449+17449^30786 | 130588 | Hans Havermann | 03/2021 |
| 5603 | 2^433744-114419 | 130570 | Enzo Doria | 02/2015 |
| 5605 | 2^433708+1869451 | 130560 | Enzo Doria | 05/2016 |
| 5604 | 2^433710+93 | 130560 | Lelio R Paula | 06/2017 |
| 5606 | 7*10^130535-27 | 130536 | Robert Price | 11/2022 |
| 5607 | (17^130533)%(10^130533) | 130533 | Henri Lifchitz | 05/2025 |
| 5608 | (9629^32768+1)/120501441265666 | 130520 | Kellen Shenton | 05/2021 |
| 5609 | 804*34^85220+713 | 130516 | Eric Chen | 08/2023 |
| 5610 | (29*2^433547-1)/27 | 130511 | Lelio R Paula | 06/2015 |
| 5611 | 3^273521+10 | 130503 | Tyler NeSmith | 01/2021 |
| 5612 | 41659^1356+1356^41659 | 130487 | Hans Havermann | 03/2021 |
| 5613 | 4*10^130480+9 | 130481 | Robert Price | 05/2015 |
| 5614 | (23*2^433449-1)/75 | 130481 | Lelio R Paula | 06/2015 |
| 5615 | 3*2^433422+5 | 130474 | Jon Grantham | 07/2023 |
| 5616 | (23*2^433334-1)/3731 | 130445 | Lelio R Paula | 06/2015 |
| 5617 | (31*10^130414-49)/9 | 130415 | Robert Price | 11/2021 |
| 5618 | 26462^29485-29485^26462 | 130402 | Frank Doornink | 03/2024 |
| 5619 | 33481^7848+7848^33481 | 130401 | Hans Havermann | 03/2021 |
| 5620 | (17*10^130393+7)/3 | 130394 | Robert Price | 06/2023 |
| 5621 | (22*10^130392+203)/9 | 130393 | Robert Price | 10/2021 |
| 5622 | 29773^23950+23950^29773 | 130386 | Hans Havermann | 04/2021 |
| 5623 | 2^433023-113497 | 130353 | Enzo Doria | 08/2014 |
| 5624 | 31175^15178+15178^31175 | 130350 | Hans Havermann | 04/2021 |
| 5625 | 2^433002+1179379 | 130347 | Enzo Doria | 06/2016 |
| 5626 | 2^432974+19 | 130339 | Robert Price | 08/2015 |
| 5627 | 31903^12168+12168^31903 | 130331 | Hans Havermann | 04/2021 |
| 5628 | 2^432917+22217 | 130322 | Enzo Doria | 09/2023 |
| 5629 | 29387^27112+27112^29387 | 130278 | Hans Havermann | 04/2021 |
| 5630 | 2^432768+213181 | 130277 | Enzo Doria | 09/2023 |
| 5631 | 29577^25370+25370^29577 | 130267 | Hans Havermann | 04/2021 |
| 5632 | 31738^12685+12685^31738 | 130231 | Hans Havermann | 03/2021 |
| 5633 | 44235^878+878^44235 | 130206 | Hans Havermann | 04/2021 |
| 5634 | 32160^11171+11171^32160 | 130187 | Hans Havermann | 04/2021 |
| 5635 | 29489^25956+25956^29489 | 130172 | Hans Havermann | 04/2021 |
| 5636 | (2^432457-1)/1672739247834685086279697 | 130159 | Tony Prest / Never Odd Or Even | 09/2013 |
| 5637 | 33005^8766+8766^33005 | 130133 | Hans Havermann | 04/2021 |
| 5638 | (35*10^130132-611)/9 | 130133 | Robert Price | 02/2022 |
| 5639 | (444^49408+1)/(444^256+1) | 130125 | Martin Hopf | 12/2023 |
| 5640 | 2^432217+41 | 130111 | Lelio R Paula | 06/2017 |
| 5641 | (2^216089*(2^216091-1)-339)/25 | 130098 | Makoto Morimoto | 03/2017 |
| 5642 | ((2^216091+1066)^2+(2^216091+1066)+41)/47/2069 | 130095 | Makoto Morimoto | 05/2016 |
| 5643 | 97^65480-2 | 130094 | Lelio R Paula | 05/2017 |
| 5644 | 36007^4102+4102^36007 | 130094 | Hans Havermann | 04/2021 |
| 5645 | 4*10^130088-89 | 130089 | Robert Price | 11/2018 |
| 5646 | 2^432117-113215 | 130081 | Enzo Doria | 07/2014 |
| 5647 | (4*10^130080+41)/9 | 130080 | Serge Batalov | 11/2022 |
| 5648 | 9583*29^88890+736 | 129997 | Eric Chen | 06/2025 |
| 5649 | 2^431804+72511 | 129986 | Enzo Doria | 04/2016 |
| 5650 | 27902^29237-29237^27902 | 129978 | Frank Doornink | 03/2024 |
| 5651 | 33^85579+32 | 129953 | Alfred Reich | 10/2025 |
| 5652 | (2313^38809-1)/(2313^197-1) | 129898 | Ryan Propper | 11/2023 |
| 5653 | (13*10^129896+137)/3 | 129897 | Robert Price | 06/2021 |
| 5654 | (13*10^129890+71)/3 | 129891 | Robert Price | 06/2021 |
| 5655 | 29048^29101-29101^29048 | 129882 | Norbert Schneider | 03/2022 |
| 5656 | 37832^2709+2709^37832 | 129871 | Hans Havermann | 04/2021 |
| 5657 | 31055^15184+15184^31055 | 129853 | Hans Havermann | 04/2021 |
| 5659 | (3^272141-3^136071+1)/7 | 129844 | Serge Batalov | 03/2014 |
| 5658 | Phi(1632846L,3) | 129844 | Anonymous | 03/2025 |
| 5660 | 31385^13702+13702^31385 | 129833 | Hans Havermann | 04/2021 |
| 5661 | (13*10^129826+41)/9 | 129827 | Tyler Busby | 02/2023 |
| 5662 | 28901^29102-29102^28901 | 129822 | Norbert Schneider | 03/2022 |
| 5663 | (47*10^129789-119)/9 | 129790 | Robert Price | 05/2019 |
| 5664 | (9*2^431141+1)/17 | 129787 | Lelio R Paula | 06/2015 |
| 5665 | 25999^29384-29384^25999 | 129730 | Frank Doornink | 03/2024 |
| 5666 | 25771^29408-29408^25771 | 129723 | Frank Doornink | 02/2024 |
| 5667 | (166*10^129712+17)/3 | 129714 | Robert Price | 07/2022 |
| 5668 | (29*2^430881-1)/21 | 129709 | Lelio R Paula | 06/2015 |
| 5669 | 2^430807+1869563 | 129686 | Enzo Doria | 05/2016 |
| 5670 | 2^430721-21429 | 129660 | Enzo Doria | 07/2013 |
| 5671 | Phi(326081,3) | 129648 | Henri Lifchitz | 12/2025 |
| 5672 | (4*10^129618+89)/3 | 129619 | Robert Price | 08/2021 |
| 5673 | (142^60223-1)/141 | 129616 | Anonymous | 06/2024 |
| 5674 | (10^129587-7^129587)/3 | 129587 | Jon Grantham | 07/2023 |
| 5675 | 2^430415-276271 | 129568 | Enzo Doria | 07/2015 |
| 5676 | 32282^10311+10311^32282 | 129558 | Hans Havermann | 04/2021 |
| 5677 | 29486^24741+24741^29486 | 129545 | Hans Havermann | 04/2021 |
| 5678 | (29*10^129543+313)/9 | 129544 | Robert Price | 04/2021 |
| 5679 | 37095^3104+3104^37095 | 129533 | Hans Havermann | 04/2021 |
| 5680 | 31132^14459+14459^31132 | 129514 | Hans Havermann | 04/2021 |
| 5681 | 32582^9435+9435^32582 | 129506 | Hans Havermann | 03/2021 |
| 5682 | 30442^17953+17953^30442 | 129505 | Hans Havermann | 03/2021 |
| 5683 | (199*10^129487-7)/3 | 129489 | Robert Price | 05/2020 |
| 5684 | 2^430142-2791721 | 129486 | Enzo Doria | 03/2016 |
| 5685 | (7*10^129472-13)/3 | 129473 | Robert Price | 07/2018 |
| 5686 | (8*10^129469+79)/3 | 129470 | Robert Price | 10/2020 |
| 5687 | 31678^12213+12213^31678 | 129463 | Hans Havermann | 04/2021 |
| 5688 | 10620^32143-10619^32143 | 129412 | Norbert Schneider | 08/2023 |
| 5689 | (772*10^129406-7)/9 | 129408 | Robert Price | 06/2022 |
| 5690 | (535^47431-1)/534 | 129406 | Tom Wu | 09/2024 |
| 5691 | ((3*20425-8193)*F(618977)-(20425-8193)*L(618977))/2 | 129363 | Yaroslav Berezhko | 03/2025 |
| 5692 | 31100^14439+14439^31100 | 129362 | Hans Havermann | 04/2021 |
| 5693 | 33009^8288+8288^33009 | 129345 | Hans Havermann | 04/2021 |
| 5694 | 25895^29306-29306^25895 | 129334 | Frank Doornink | 03/2024 |
| 5695 | (44^78697+43^78697)/87 | 129333 | Aurel Gibier | 11/2023 |
| 5696 | 29675^22804+22804^29675 | 129324 | Hans Havermann | 04/2021 |
| 5697 | 29068^28099+28099^29068 | 129315 | Hans Havermann | 04/2021 |
| 5698 | 2^429568-21017 | 129313 | Enzo Doria | 07/2013 |
| 5699 | (10^129295+83)/3 | 129295 | Robert Price | 08/2021 |
| 5700 | (853*10^129274-7)/9 | 129276 | Robert Price | 07/2021 |
| 5701 | 998^43100+997 | 129263 | Alfred Reich | 03/2026 |
| 5702 | 30958^14961+14961^30958 | 129249 | Hans Havermann | 04/2021 |
| 5703 | (11*10^129239-179)/3 | 129240 | Robert Price | 09/2018 |
| 5704 | 28659^28988+28988^28659 | 129208 | Norbert Schneider | 02/2021 |
| 5705 | 29423^24616+24616^29423 | 129203 | Hans Havermann | 03/2021 |
| 5706 | 2^429194-112685 | 129201 | Enzo Doria | 06/2014 |
| 5707 | 31*35^83672+17398 | 129197 | Eric Chen | 05/2025 |
| 5708 | 2^429145-2780449 | 129186 | Enzo Doria | 04/2016 |
| 5709 | 32500^9427+9427^32500 | 129168 | Hans Havermann | 04/2021 |
| 5710 | 33577^7014+7014^33577 | 129136 | Hans Havermann | 03/2021 |
| 5711 | 2^428892-113453 | 129110 | Enzo Doria | 07/2014 |
| 5712 | (11*2^428881-7)/15 | 129106 | Renaud Lifchitz | 03/2011 |
| 5713 | 2^428727-113959 | 129060 | Enzo Doria | 10/2014 |
| 5714 | (7*2^428725-1)/13 | 129059 | Lelio R Paula | 05/2014 |
| 5715 | (10^129051-31)/3 | 129051 | Serge Batalov | 12/2014 |
| 5716 | (3^732836)/(2^732836) | 129047 | Henri Lifchitz | 05/2025 |
| 5717 | (134*10^129038+7)/3 | 129040 | Robert Price | 02/2020 |
| 5718 | 2^428564+71161 | 129011 | Enzo Doria | 04/2016 |
| 5719 | 28781^28930+28930^28781 | 129002 | Norbert Schneider | 02/2021 |
| 5720 | 29065^27424+27424^29065 | 128995 | Hans Havermann | 04/2021 |
| 5721 | 2^428502-113285 | 128992 | Enzo Doria | 07/2014 |
| 5722 | 2^428421-21373 | 128968 | Enzo Doria | 06/2013 |
| 5723 | L(616787) | 128901 | Henri Lifchitz | 09/2008 |
| 5724 | (765^44701-1)/764 | 128900 | Tom Wu | 07/2024 |
| 5725 | 20^99055-3 | 128874 | Paul Bourdelais | 12/2020 |
| 5726 | 91^65772-2 | 128851 | Lelio R Paula | 05/2017 |
| 5727 | 2^428022+43 | 128848 | Lelio R Paula | 05/2017 |
| 5728 | 2^427999-459397 | 128841 | Enzo Doria | 05/2015 |
| 5729 | 2^427993+76847 | 128839 | Enzo Doria | 05/2016 |
| 5730 | 31059^14060+14060^31059 | 128833 | Hans Havermann | 03/2021 |
| 5731 | 10^128805+152871 | 128806 | Patrick De Geest | 05/2021 |
| 5732 | 10^128805-10001 | 128805 | Robert Price | 02/2021 |
| 5733 | 2^427824-1851507 | 128788 | Enzo Doria | 08/2015 |
| 5734 | 2^427807-21469 | 128783 | Enzo Doria | 07/2013 |
| 5735 | 29082^26783+26783^29082 | 128772 | Hans Havermann | 04/2021 |
| 5736 | 40055^1638+1638^40055 | 128750 | Hans Havermann | 04/2021 |
| 5737 | (923^43411-1)/922 | 128720 | Tom Wu | 07/2024 |
| 5738 | 11^123594-240 | 128710 | Enzo Doria | 09/2012 |
| 5739 | 2^427504-21503 | 128692 | Enzo Doria | 07/2013 |
| 5740 | 37727^2574+2574^37727 | 128673 | Hans Havermann | 04/2021 |
| 5741 | 29686^21591+21591^29686 | 128668 | Hans Havermann | 04/2021 |
| 5742 | 10^128668-70000000001 | 128668 | Robert Price | 08/2021 |
| 5743 | 10^128668-350729 | 128668 | Alfred Reich | 08/2024 |
| 5744 | Phi(57476,13#) | 128668 | Henri Lifchitz | 12/2025 |
| 5745 | 2^427420+91 | 128667 | Lelio R Paula | 05/2017 |
| 5746 | 8*10^128651-37 | 128652 | Robert Price | 03/2022 |
| 5747 | (68*10^128645-257)/9 | 128646 | Robert Price | 07/2019 |
| 5748 | Phi(236553,7) | 128631 | Henri Lifchitz | 12/2025 |
| 5749 | 2^427269-113635 | 128621 | Enzo Doria | 08/2014 |
| 5750 | 136^60270+135 | 128589 | Alfred Reich | 03/2026 |
