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 ? |
| 4501 | (865*10^149737-1)/9 | 149739 | Robert Price | 04/2020 |
| 4502 | 10^149695-7000001 | 149695 | Robert Price | 06/2021 |
| 4503 | 38237^8214+8214^38237 | 149681 | Hans Havermann | 09/2020 |
| 4504 | Phi(745791,2)/1491583 | 149664 | Anonymous | 03/2025 |
| 4505 | (497167*2^497167-1)/70975 | 149664 | Anonymous | 04/2025 |
| 4506 | (23*10^149655+19)/3 | 149656 | Robert Price | 07/2019 |
| 4507 | 2^497068-113579 | 149633 | Enzo Doria | 08/2014 |
| 4508 | 2^497037+73727 | 149624 | Enzo Doria | 04/2016 |
| 4509 | 11*10^149618+3 | 149620 | Robert Price | 07/2021 |
| 4510 | 34942^19067+19067^34942 | 149562 | Hans Havermann | 09/2020 |
| 4511 | 33696^27449+27449^33696 | 149561 | Hans Havermann | 09/2020 |
| 4512 | 2^496773+77747 | 149544 | Enzo Doria | 05/2016 |
| 4513 | 29937^33400-33400^29937 | 149506 | Frank Doornink | 06/2024 |
| 4514 | (7*10^149483-493)/9 | 149483 | Robert Price | 04/2021 |
| 4515 | (206*10^149459+7)/3 | 149461 | Robert Price | 07/2020 |
| 4516 | 34589^20940+20940^34589 | 149459 | Hans Havermann | 09/2020 |
| 4517 | 2^496477-113485 | 149455 | Enzo Doria | 08/2014 |
| 4518 | (496423*2^496423-1)/223573 | 149439 | Anonymous | 04/2025 |
| 4519 | 3*2^496411-5 | 149436 | Jon Grantham | 07/2023 |
| 4520 | ((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9 | 149410 | Hans Havermann | 09/2019 |
| 4521 | 2^496270-49451 | 149393 | Enzo Doria | 10/2015 |
| 4522 | 2^496238-1865081 | 149383 | Enzo Doria | 01/2016 |
| 4523 | 33831^26030+26030^33831 | 149380 | Hans Havermann | 09/2020 |
| 4524 | 34131^23780+23780^34131 | 149365 | Hans Havermann | 09/2020 |
| 4525 | (5*10^149335-53)/3 | 149336 | Robert Price | 09/2020 |
| 4526 | 26043^33818-33818^26043 | 149330 | Frank Doornink | 03/2024 |
| 4527 | 2^495968-1853699 | 149302 | Enzo Doria | 09/2015 |
| 4528 | 2^495935-4117 | 149292 | Yves Minet | 02/2018 |
| 4529 | 5*2^495930+3 | 149291 | Jon Grantham | 07/2023 |
| 4530 | 35816^14709+14709^35816 | 149267 | Hans Havermann | 09/2020 |
| 4531 | (10^149264+7)/191/2683/80557 | 149254 | Alfred Reich | 07/2021 |
| 4532 | 3^312800+6560 | 149244 | Alfred Reich | 04/2026 |
| 4533 | 10^149240-40000001 | 149240 | Robert Price | 07/2022 |
| 4534 | 10^149240-10809 | 149240 | Alfred Reich | 08/2024 |
| 4535 | 2^495712-396765 | 149225 | Enzo Doria | 07/2013 |
| 4536 | (21*2^495676-1)/4835 | 149211 | Lelio R Paula | 10/2015 |
| 4537 | 2^495420+1880701 | 149137 | Enzo Doria | 10/2016 |
| 4538 | 25646^33823-33823^25646 | 149127 | Frank Doornink | 02/2024 |
| 4539 | 2^495337-1847293 | 149112 | Enzo Doria | 07/2015 |
| 4540 | (2^495193-7)/5 | 149068 | Lelio R Paula | 10/2015 |
| 4541 | 2^495163+111546435 | 149059 | Paul Bourdelais | 10/2021 |
| 4542 | 33282^30097+30097^33282 | 149055 | Hans Havermann | 09/2020 |
| 4543 | 37384^9705+9705^37384 | 149050 | Hans Havermann | 09/2020 |
| 4544 | 34808^19143+19143^34808 | 149049 | Hans Havermann | 09/2020 |
| 4545 | 413^56963-412^56963 | 149013 | Jean-Louis Charton | 08/2012 |
| 4546 | 30657^33212-33212^30657 | 149007 | Frank Doornink | 06/2024 |
| 4547 | 47^89113-46^89113 | 149006 | Robert Price | 10/2012 |
| 4548 | V(891190) | 148997 | Serge Batalov | 07/2024 |
| 4549 | 2^494916+87855 | 148985 | Lelio R Paula | 01/2016 |
| 4550 | 6*10^148982+73 | 148983 | Robert Price | 04/2019 |
| 4551 | 3^312155-4 | 148936 | Anonymous | 02/2023 |
| 4552 | 10^148934+1530019 | 148935 | Patrick De Geest | 02/2021 |
| 4553 | 10^148934-1000000001 | 148934 | Robert Price | 11/2020 |
| 4554 | 10^148934-512057 | 148934 | Patrick De Geest | 02/2021 |
| 4555 | 39000^6571+6571^39000 | 148888 | Hans Havermann | 10/2020 |
| 4556 | 2^494586-2791991 | 148886 | Enzo Doria | 02/2016 |
| 4557 | Phi(117375,3^5) | 148862 | Henri Lifchitz | 12/2025 |
| 4558 | 8*10^148860-3 | 148861 | Ray Chandler | 04/2011 |
| 4559 | 38262^7769+7769^38262 | 148854 | Hans Havermann | 10/2020 |
| 4560 | 10^148816-500001 | 148816 | Robert Price | 03/2022 |
| 4561 | (53*10^148811-287)/9 | 148812 | Robert Price | 02/2022 |
| 4562 | 2^494333-286183 | 148810 | Enzo Doria | 06/2015 |
| 4563 | 2^494144-264119 | 148753 | Enzo Doria | 05/2014 |
| 4564 | 6*10^148734+47 | 148735 | Robert Price | 06/2022 |
| 4565 | 28724^33353-33353^28724 | 148696 | Frank Doornink | 06/2024 |
| 4566 | 36502^11823+11823^36502 | 148663 | Hans Havermann | 11/2020 |
| 4567 | (5*2^493838-1)/3721 | 148658 | Lelio R Paula | 10/2015 |
| 4568 | 64239^206+206^64239 | 148641 | Hans Havermann | 10/2020 |
| 4569 | (23*2^493761-1)/555 | 148636 | Lelio R Paula | 10/2015 |
| 4570 | (23*10^148627-137)/3 | 148628 | Robert Price | 08/2021 |
| 4571 | (151*10^148601-1)/3 | 148603 | Robert Price | 03/2020 |
| 4572 | 2^493636+82081 | 148600 | Enzo Doria | 09/2016 |
| 4573 | ((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 | 148593 | Serge Batalov | 07/2016 |
| 4574 | 27134^33509-33509^27134 | 148563 | Frank Doornink | 01/2024 |
| 4575 | 177487#+(519643#)/(177487#) | 148558 | Makoto Morimoto | 11/2017 |
| 4576 | (2*10^148460-23)/3 | 148460 | Robert Price | 04/2018 |
| 4577 | (28*10^148445+101)/3 | 148446 | Robert Price | 09/2020 |
| 4578 | 2^493065+225 | 148428 | Henri Lifchitz | 11/2024 |
| 4579 | 36203^12556+12556^36203 | 148391 | Hans Havermann | 10/2020 |
| 4580 | 33912^23749+23749^33912 | 148387 | Hans Havermann | 10/2020 |
| 4581 | (8*10^148328+1)/9 | 148328 | Serge Batalov | 05/2010 |
| 4582 | 34294^21117+21117^34294 | 148309 | Hans Havermann | 10/2020 |
| 4583 | (71*10^148306-539)/9 | 148307 | Robert Price | 07/2019 |
| 4584 | 30814^33039-33039^30814 | 148304 | Frank Doornink | 06/2024 |
| 4585 | 38042^7875+7875^38042 | 148222 | Hans Havermann | 10/2020 |
| 4586 | 5^211959-12874 | 148153 | Enzo Doria | 05/2014 |
| 4587 | 34142^21831+21831^34142 | 148145 | Hans Havermann | 10/2020 |
| 4588 | (288*21^112023-13)/5 | 148121 | Eric Chen | 03/2026 |
| 4589 | 10^148112+34059 | 148113 | Patrick De Geest | 05/2021 |
| 4590 | 10^148112-70000001 | 148112 | Robert Price | 03/2021 |
| 4591 | 10^148112-106593 | 148112 | Patrick De Geest | 05/2021 |
| 4592 | 36303^12016+12016^36303 | 148108 | Hans Havermann | 10/2020 |
| 4593 | (77*10^148089-149)/9 | 148090 | Robert Price | 03/2022 |
| 4594 | (16*10^148071+41)/3 | 148072 | Robert Price | 03/2019 |
| 4595 | 187^65175-2 | 148068 | Lelio R Paula | 11/2017 |
| 4596 | 2^491851+1871453 | 148062 | Enzo Doria | 05/2016 |
| 4597 | (68*10^148060-257)/9 | 148061 | Robert Price | 07/2019 |
| 4598 | Phi(162903,-5#) | 148043 | Henri Lifchitz | 12/2025 |
| 4599 | (151*10^148020-1)/3 | 148022 | Robert Price | 03/2020 |
| 4600 | 39153^6032+6032^39153 | 148017 | Hans Havermann | 10/2020 |
| 4601 | 36798^10507+10507^36798 | 147983 | Hans Havermann | 12/2020 |
| 4602 | (26*10^147973-23)/3 | 147974 | Robert Price | 12/2019 |
| 4603 | Phi(65997,11#) | 147973 | Henri Lifchitz | 12/2025 |
| 4604 | 2^491521-1865323 | 147963 | Enzo Doria | 02/2016 |
| 4605 | (2^491476+7)/71 | 147948 | Lelio R Paula | 10/2015 |
| 4606 | 2*10^147928+47 | 147929 | Robert Price | 12/2021 |
| 4607 | 2^491391-7807 | 147924 | Lelio R Paula | 01/2013 |
| 4608 | 2^491384+236221 | 147922 | Enzo Doria | 05/2025 |
| 4609 | 39736^5279+5279^39736 | 147920 | Hans Havermann | 11/2020 |
| 4610 | 2^491370-113297 | 147918 | Enzo Doria | 07/2014 |
| 4611 | (3^707753)%F(707753) | 147912 | Henri Lifchitz | 06/2025 |
| 4612 | (32760^32760+32759^32759)/95546586737133567708319 | 147900 | Robert Price | 07/2016 |
| 4613 | 44368^2155+2155^44368 | 147899 | Hans Havermann | 12/2020 |
| 4614 | (17*10^147890+79)/3 | 147891 | Robert Price | 04/2019 |
| 4615 | 94*10^147871-3 | 147873 | Robert Price | 05/2020 |
| 4616 | 10^147843+620967 | 147844 | Patrick De Geest | 05/2021 |
| 4617 | 10^147843-50000000001 | 147843 | Robert Price | 12/2020 |
| 4618 | 10^147843-182891 | 147843 | Patrick De Geest | 05/2021 |
| 4619 | 35805^13346+13346^35805 | 147709 | Hans Havermann | 11/2020 |
| 4620 | 2^490672+255255 | 147707 | Paul Bourdelais | 10/2021 |
| 4621 | 2^490660-17 | 147704 | Lelio R Paula | 12/2017 |
| 4622 | (229*10^147699-1)/3 | 147701 | Robert Price | 07/2020 |
| 4623 | 40656^4289+4289^40656 | 147678 | Hans Havermann | 11/2020 |
| 4624 | (85*10^147676-31)/9 | 147677 | Rytis Slatkevicius | 12/2024 |
| 4625 | 2^490550+1179439 | 147671 | Enzo Doria | 06/2016 |
| 4626 | 27249^33292-33292^27249 | 147662 | Frank Doornink | 06/2024 |
| 4627 | (23*10^147649-59)/9 | 147650 | Robert Price | 05/2018 |
| 4628 | 2^490303+2793653 | 147596 | Enzo Doria | 03/2016 |
| 4629 | 2^490266+255255 | 147585 | Paul Bourdelais | 10/2021 |
| 4630 | 199^64181-2 | 147543 | Lelio R Paula | 11/2017 |
| 4631 | 32849^30958+30958^32849 | 147518 | Hans Havermann | 11/2020 |
| 4632 | 2^489871-286987 | 147466 | Enzo Doria | 07/2015 |
| 4633 | 2^489864-351899 | 147464 | Enzo Doria | 07/2015 |
| 4634 | 175^65724-2 | 147422 | Lelio R Paula | 11/2017 |
| 4635 | 2^489712+1874851 | 147419 | Enzo Doria | 06/2016 |
| 4636 | 34473^18830+18830^34473 | 147367 | Hans Havermann | 11/2020 |
| 4637 | 63^81896-2 | 147359 | Lelio R Paula | 10/2017 |
| 4638 | 34580^18237+18237^34580 | 147344 | Hans Havermann | 11/2020 |
| 4639 | (11*10^147313-107)/3 | 147314 | Robert Price | 09/2018 |
| 4640 | (397*10^147310+17)/9 | 147312 | Robert Price | 03/2022 |
| 4641 | 2^489305-59815 | 147296 | Enzo Doria | 10/2015 |
| 4642 | (2^489280-7)/6381 | 147285 | Lelio R Paula | 09/2015 |
| 4643 | 2*10^147264-61 | 147265 | Robert Price | 10/2021 |
| 4644 | 2*10^147260+29 | 147261 | Robert Price | 02/2021 |
| 4645 | 33556^24457+24457^33556 | 147258 | Hans Havermann | 11/2020 |
| 4646 | 12^136450-11 | 147255 | Riley Fisher | 12/2024 |
| 4647 | 2^489125+80357 | 147242 | Enzo Doria | 06/2016 |
| 4648 | 10^147240-40000001 | 147240 | Robert Price | 07/2022 |
| 4649 | 10^147240-371331 | 147240 | Alfred Reich | 09/2024 |
| 4650 | 10^147240-464727 | 147240 | Alfred Reich | 09/2024 |
| 4651 | 32835^30452+30452^32835 | 147220 | Hans Havermann | 12/2020 |
| 4652 | (19*10^147213-97)/3 | 147214 | Robert Price | 10/2021 |
| 4653 | 27123^33190-33190^27123 | 147143 | Frank Doornink | 01/2024 |
| 4654 | (148*10^147139-1)/3 | 147141 | Robert Price | 03/2020 |
| 4655 | 34338^19255+19255^34338 | 147123 | Hans Havermann | 11/2020 |
| 4656 | 2^488648-112799 | 147098 | Enzo Doria | 07/2014 |
| 4657 | 2^488627-350317 | 147092 | Enzo Doria | 06/2015 |
| 4658 | 33432^25075+25075^33432 | 147076 | Hans Havermann | 12/2020 |
| 4659 | (2^488441-1)/(61543567*30051203516986199) | 147012 | Dario Alpern | 12/2014 |
| 4660 | 2^488280-2165 | 146987 | Yves Minet | 07/2014 |
| 4661 | 2^488278+45 | 146987 | Lelio R Paula | 12/2017 |
| 4662 | (3^834646)/(2^834646) | 146974 | Henri Lifchitz | 06/2025 |
| 4663 | 32568^32568+32561^32561 | 146973 | Henri Lifchitz | 08/2024 |
| 4664 | 2^487927-39 | 146881 | Lelio R Paula | 12/2017 |
| 4665 | (7*10^146860-13)/3 | 146861 | Robert Price | 07/2018 |
| 4666 | (26*10^146856-77)/3 | 146857 | Robert Price | 11/2019 |
| 4667 | 32948^28611+28611^32948 | 146834 | Hans Havermann | 11/2020 |
| 4668 | 42596^2799+2799^42596 | 146829 | Hans Havermann | 12/2020 |
| 4669 | 2^487726-1863341 | 146821 | Enzo Doria | 12/2015 |
| 4670 | 43838^2229+2229^43838 | 146775 | Hans Havermann | 11/2020 |
| 4671 | 35005^15594+15594^35005 | 146775 | Hans Havermann | 11/2020 |
| 4672 | (167*10^146764+7)/3 | 146766 | Robert Price | 04/2021 |
| 4673 | 53^85114+85114 | 146761 | Kellen Shenton | 05/2022 |
| 4674 | (59*10^146738+157)/9 | 146739 | Robert Price | 12/2021 |
| 4675 | ((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9 | 146728 | Hans Havermann | 09/2019 |
| 4676 | 32963^28234+28234^32963 | 146711 | Hans Havermann | 12/2020 |
| 4677 | (22*10^146661-19)/3 | 146662 | Robert Price | 04/2019 |
| 4678 | 33958^20825+20825^33958 | 146651 | Hans Havermann | 12/2020 |
| 4679 | 26289^33178-33178^26289 | 146640 | Frank Doornink | 03/2024 |
| 4680 | 2^487121-39523 | 146639 | Enzo Doria | 09/2015 |
| 4681 | 61063^252+252^61063 | 146637 | Hans Havermann | 12/2020 |
| 4682 | (7*2^486967+1)/39 | 146591 | Lelio R Paula | 09/2015 |
| 4683 | 34099^19900+19900^34099 | 146587 | Hans Havermann | 11/2020 |
| 4684 | (10^146606+1)/2931129793051428557705609 | 146582 | Anonymous | 03/2026 |
| 4685 | 2^486893-79 | 146570 | Yves Minet | 09/2017 |
| 4686 | 36818^9567+9567^36818 | 146565 | Hans Havermann | 12/2020 |
| 4687 | 2^486840+1879141 | 146554 | Enzo Doria | 08/2016 |
| 4688 | 2^486774-87 | 146534 | Lelio R Paula | 12/2017 |
| 4689 | 38655^6176+6176^38655 | 146530 | Hans Havermann | 11/2020 |
| 4690 | 8*10^146522-81 | 146523 | Robert Price | 02/2021 |
| 4691 | 32820^29059+29059^32820 | 146485 | Hans Havermann | 12/2020 |
| 4692 | 37261^8530+8530^37261 | 146472 | Hans Havermann | 12/2020 |
| 4693 | 66953^154+154^66953 | 146462 | Hans Havermann | 12/2020 |
| 4694 | 96^73877-95^73877 | 146445 | Robert Price | 10/2015 |
| 4695 | 8*10^146421+81 | 146422 | Robert Price | 08/2019 |
| 4696 | 33153^26090+26090^33153 | 146420 | Hans Havermann | 11/2020 |
| 4697 | 2^486275+23961 | 146384 | Enzo Doria | 10/2023 |
| 4698 | (12^135607-1)/18437127731 | 146335 | Paul Vanderveen | 06/2025 |
| 4699 | (52^85259+1)/53 | 146304 | Paul Bourdelais | 09/2017 |
| 4700 | 179^64935+2 | 146290 | Lelio R Paula | 10/2017 |
| 4701 | 32595^30758+30758^32595 | 146285 | Hans Havermann | 11/2020 |
| 4702 | 34972^15157+15157^34972 | 146205 | Hans Havermann | 12/2020 |
| 4703 | (16*10^146200+131)/3 | 146201 | Robert Price | 03/2022 |
| 4704 | (19*10^146181-49)/3 | 146182 | Robert Price | 05/2019 |
| 4705 | 2^485531-114621 | 146160 | Enzo Doria | 05/2015 |
| 4706 | 2^485473-933075 | 146142 | Paul Bourdelais | 06/2021 |
| 4707 | (2^485461-9)/4249 | 146135 | Lelio R Paula | 09/2015 |
| 4708 | (22*10^146130-193)/9 | 146131 | Robert Price | 07/2022 |
| 4709 | 2^485389+81887 | 146117 | Enzo Doria | 08/2016 |
| 4710 | 32554^30773+30773^32554 | 146108 | Hans Havermann | 11/2020 |
| 4711 | 28075^32844-32844^28075 | 146101 | Frank Doornink | 06/2024 |
| 4712 | (10^146063+71)/9 | 146063 | Serge Batalov | 07/2015 |
| 4713 | 2*10^146051-63 | 146052 | Robert Price | 01/2022 |
| 4714 | (2^485119+7)/2745 | 146032 | Lelio R Paula | 09/2015 |
| 4715 | (22*10^146029+257)/9 | 146030 | Robert Price | 06/2018 |
| 4716 | 7*10^145982-53 | 145983 | Robert Price | 06/2020 |
| 4717 | 2^484743+1872923 | 145923 | Enzo Doria | 05/2016 |
| 4718 | 33140^25287+25287^33140 | 145913 | Hans Havermann | 01/2021 |
| 4719 | 37875^7112+7112^37875 | 145895 | Hans Havermann | 01/2021 |
| 4720 | 30542^32529-32529^30542 | 145890 | Frank Doornink | 06/2024 |
| 4721 | Phi(193945,-9) | 145885 | Henri Lifchitz | 12/2025 |
| 4722 | 32862^27473+27473^32862 | 145872 | Hans Havermann | 01/2021 |
| 4723 | V(1046652)/2093303 | 145817 | Serge Batalov | 07/2024 |
| 4724 | 32836^27587+27587^32836 | 145815 | Hans Havermann | 01/2021 |
| 4725 | 2^484341+1879157 | 145802 | Enzo Doria | 08/2016 |
| 4726 | 2*10^145784-91 | 145785 | Robert Price | 04/2020 |
| 4727 | 2^484271-51 | 145781 | Lelio R Paula | 11/2017 |
| 4728 | (188*10^145750-11)/3 | 145752 | Robert Price | 02/2022 |
| 4729 | 70^78989-69^78989 | 145743 | Robert Price | 01/2014 |
| 4730 | 51^85334+2 | 145714 | Robert Price | 07/2015 |
| 4731 | 10^2^72843+72843^2^10 | 145687 | Henri Lifchitz | 03/2025 |
| 4732 | 2^483886-1857101 | 145665 | Enzo Doria | 10/2015 |
| 4733 | 29312^32607-32607^29312 | 145657 | Frank Doornink | 06/2024 |
| 4734 | 33350^23307+23307^33350 | 145656 | Hans Havermann | 01/2021 |
| 4735 | (19*10^145585+131)/3 | 145586 | Robert Price | 06/2020 |
| 4736 | 31815^32332-32332^31815 | 145580 | Frank Doornink | 01/2024 |
| 4737 | 2^483563-1863457 | 145567 | Enzo Doria | 12/2015 |
| 4738 | 4*10^145563-69 | 145564 | Robert Price | 01/2022 |
| 4739 | 2^483516-1861409 | 145553 | Enzo Doria | 11/2015 |
| 4740 | 2^483384-115019 | 145514 | Enzo Doria | 06/2015 |
| 4741 | (259*10^145501-1)/3 | 145503 | Robert Price | 12/2020 |
| 4742 | (19*10^145499-61)/3 | 145500 | Robert Price | 05/2019 |
| 4743 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
| 4744 | (23*10^145463+61)/3 | 145464 | Robert Price | 01/2022 |
| 4745 | 35523^12434+12434^35523 | 145453 | Hans Havermann | 01/2021 |
| 4746 | (29121^32761-1)/(29121^181-1) | 145444 | Ryan Propper | 11/2023 |
| 4747 | 2^483046+1874029 | 145412 | Enzo Doria | 06/2016 |
| 4748 | 2^482991-2789317 | 145395 | Enzo Doria | 12/2015 |
| 4749 | 2^482978-2789711 | 145391 | Enzo Doria | 12/2015 |
| 4750 | 2^482966-2789711 | 145388 | Enzo Doria | 12/2015 |
