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 ? |
| 4751 | 5*10^141294-63 | 141295 | Robert Price | 04/2021 |
| 4752 | 3^296115+4 | 141283 | Tyler NeSmith | 01/2021 |
| 4753 | (64*10^141256+161)/9 | 141257 | Robert Price | 08/2022 |
| 4755 | 143^(2^16)+106^(2^16) | 141253 | Valeryi Kuryshev | 02/2011 |
| 4754 | 143^65536+106^65536 | 141253 | Serge Batalov | 03/2018 |
| 4756 | (11*10^141243-23)/3 | 141244 | Robert Price | 09/2021 |
| 4758 | 2^469198+782569 | 141243 | Enzo Doria | 10/2016 |
| 4757 | 38129^5062+5062^38129 | 141243 | Hans Havermann | 05/2021 |
| 4759 | (41^87583-1)/192892799240 | 141242 | Paul Vanderveen | 05/2025 |
| 4760 | 2^469076-2786939 | 141206 | Enzo Doria | 11/2015 |
| 4761 | 38630^4521+4521^38630 | 141202 | Hans Havermann | 05/2021 |
| 4762 | 31755^27836+27836^31755 | 141139 | Hans Havermann | 05/2021 |
| 4763 | 35554^9325+9325^35554 | 141137 | Hans Havermann | 05/2021 |
| 4764 | 2^468804+1874941 | 141125 | Enzo Doria | 06/2016 |
| 4765 | 2^468787+81353 | 141119 | Enzo Doria | 08/2016 |
| 4766 | 30204^31493-31493^30204 | 141091 | Frank Doornink | 06/2024 |
| 4767 | 2^468595-350407 | 141062 | Enzo Doria | 06/2015 |
| 4768 | 2^468564+87855 | 141052 | Lelio R Paula | 01/2016 |
| 4769 | 2^468551-21987 | 141048 | Enzo Doria | 07/2013 |
| 4770 | 2^468523-7 | 141040 | Lelio R Paula | 08/2015 |
| 4771 | (25*10^141019-13)/3 | 141020 | Robert Price | 09/2019 |
| 4772 | 2^468405+87855 | 141004 | Lelio R Paula | 01/2016 |
| 4773 | 39338^3831+3831^39338 | 140961 | Hans Havermann | 05/2021 |
| 4774 | 31458^30239+30239^31458 | 140950 | Hans Havermann | 05/2021 |
| 4775 | 8*10^140932+29 | 140933 | Robert Price | 11/2021 |
| 4776 | 33166^17691+17691^33166 | 140881 | Hans Havermann | 06/2021 |
| 4777 | 2^467978-113051 | 140876 | Enzo Doria | 07/2014 |
| 4778 | 2^467780-344429 | 140816 | Enzo Doria | 07/2015 |
| 4779 | 9*10^140802-89 | 140803 | Robert Price | 04/2020 |
| 4780 | 2^467605-1855603 | 140764 | Enzo Doria | 09/2015 |
| 4781 | (9^147503-5^147503)/4 | 140754 | Jon Grantham | 07/2023 |
| 4782 | 5*10^140744-7 | 140745 | Robert Price | 09/2015 |
| 4783 | (5^201359-1)/4 | 140744 | Paul Bourdelais | 12/2008 |
| 4784 | 2^467401-1850023 | 140702 | Enzo Doria | 08/2015 |
| 4785 | (14*10^140693+13)/9 | 140694 | Tyler Busby | 02/2023 |
| 4786 | (266*10^140681-17)/3 | 140683 | Robert Price | 07/2020 |
| 4787 | (2^467270+78557)/23247 | 140658 | Lelio R Paula | 07/2015 |
| 4788 | 32138^23781+23781^32138 | 140644 | Hans Havermann | 05/2021 |
| 4789 | 31654^27735+27735^31654 | 140640 | Hans Havermann | 05/2021 |
| 4790 | (29*2^467205+1)/2780517107 | 140635 | Lelio R Paula | 08/2015 |
| 4791 | 2^467166-1854941 | 140631 | Enzo Doria | 09/2015 |
| 4792 | (203*10^140615-11)/3 | 140617 | Robert Price | 12/2020 |
| 4793 | (85*10^140609+473)/9 | 140610 | Robert Price | 01/2020 |
| 4794 | (3^672799)%L(672799) | 140607 | Henri Lifchitz | 06/2025 |
| 4795 | 39231^3836+3836^39231 | 140600 | Hans Havermann | 06/2021 |
| 4796 | 5*3^294676+2^294676 | 140597 | Jon Grantham | 08/2023 |
| 4797 | (5^672618)%L(672618) | 140569 | Henri Lifchitz | 07/2025 |
| 4798 | 2^466866-1840571 | 140541 | Enzo Doria | 06/2015 |
| 4799 | 2^466829-459523 | 140530 | Enzo Doria | 05/2015 |
| 4800 | 2^466692-113213 | 140489 | Enzo Doria | 07/2014 |
| 4801 | 23*10^140464-3 | 140466 | Robert Price | 10/2021 |
| 4802 | (2*10^140461-17)/3 | 140461 | Serge Batalov | 11/2022 |
| 4803 | 29^96047-30 | 140459 | Anonymous | 09/2024 |
| 4804 | 31335^30364+30364^31335 | 140455 | Hans Havermann | 05/2021 |
| 4805 | 28511^31524-31524^28511 | 140440 | Frank Doornink | 06/2024 |
| 4806 | 32795^19126+19126^32795 | 140416 | Hans Havermann | 05/2021 |
| 4807 | (44*10^140410-503)/9 | 140411 | Robert Price | 12/2018 |
| 4808 | 28332^31535-31535^28332 | 140403 | Frank Doornink | 06/2024 |
| 4809 | 153^64265-2 | 140400 | Lelio R Paula | 11/2017 |
| 4810 | 30323^31322-31322^30323 | 140379 | Frank Doornink | 06/2024 |
| 4811 | (112*10^140357-1)/3 | 140359 | Serge Batalov | 12/2014 |
| 4812 | (29*10^140337-17)/3 | 140338 | Robert Price | 09/2019 |
| 4813 | 2^466181-112735 | 140335 | Enzo Doria | 07/2014 |
| 4814 | (16*10^140290-37)/3 | 140291 | Robert Price | 05/2021 |
| 4815 | (5*10^140281-119)/3 | 140282 | Robert Price | 03/2018 |
| 4816 | 34568^11415+11415^34568 | 140259 | Hans Havermann | 05/2021 |
| 4817 | (27*2^465872+1)/691 | 140241 | Lelio R Paula | 08/2015 |
| 4818 | 33632^14781+14781^33632 | 140236 | Hans Havermann | 05/2021 |
| 4819 | 31803^25670+25670^31803 | 140233 | Hans Havermann | 05/2021 |
| 4820 | 2^465803-114817 | 140221 | Enzo Doria | 05/2015 |
| 4821 | floor(Pi*10^140344)%10^140165 | 140165 | Serge Batalov | 08/2012 |
| 4822 | 2^465503-112735 | 140131 | Enzo Doria | 07/2014 |
| 4823 | (16*10^140091+167)/3 | 140092 | Robert Price | 06/2019 |
| 4824 | (8*10^140087-137)/3 | 140088 | Robert Price | 03/2022 |
| 4825 | 6^179964+179964^6-1 | 140040 | Robert Price | 04/2014 |
| 4826 | (89*10^140008-179)/9 | 140009 | Robert Price | 12/2019 |
| 4827 | (29*2^465077-1)/9 | 140003 | Lelio R Paula | 08/2015 |
| 4828 | 2^465072-344789 | 140001 | Enzo Doria | 07/2015 |
| 4829 | 34742^10683+10683^34742 | 139965 | Hans Havermann | 05/2021 |
| 4830 | 5*10^139945+81 | 139946 | Robert Price | 03/2019 |
| 4831 | 32648^19335+19335^32648 | 139941 | Hans Havermann | 05/2021 |
| 4832 | 2^464864-17 | 139939 | Lelio R Paula | 09/2017 |
| 4833 | 8*10^139920+51 | 139921 | Robert Price | 08/2019 |
| 4834 | (85*10^139913-1)/3 | 139915 | Robert Price | 02/2020 |
| 4835 | 31203^30436+30436^31203 | 139896 | Hans Havermann | 04/2021 |
| 4836 | 2^464642+22189 | 139872 | Enzo Doria | 09/2023 |
| 4837 | 26138^31663-31663^26138 | 139865 | Frank Doornink | 03/2024 |
| 4838 | (16^116139+619)/5 | 139845 | Anonymous | 08/2022 |
| 4839 | (2^464556+619)/5 | 139845 | Eric Chen | 10/2023 |
| 4840 | 4*10^139839-27 | 139840 | Robert Price | 08/2021 |
| 4841 | 33582^14573+14573^33582 | 139821 | Hans Havermann | 05/2021 |
| 4842 | (17^113621+1)/18 | 139804 | Paul Bourdelais | 09/2011 |
| 4844 | 2*10^139800-21 | 139801 | Robert Price | 09/2020 |
| 4843 | 32628^19261+19261^32628 | 139801 | Hans Havermann | 04/2021 |
| 4845 | (13*10^139782+191)/3 | 139783 | Robert Price | 11/2018 |
| 4846 | (64*10^139776+791)/9 | 139777 | Robert Price | 01/2022 |
| 4847 | (695*10^139772+7)/9 | 139774 | Robert Price | 12/2021 |
| 4848 | (19*2^464312-1)/3 | 139773 | Lelio R Paula | 08/2015 |
| 4849 | (74*10^139723+133)/9 | 139724 | Robert Price | 06/2019 |
| 4850 | 3*10^139722+13 | 139723 | Robert Price | 07/2018 |
| 4851 | 31577^26592+26592^31577 | 139721 | Hans Havermann | 05/2021 |
| 4852 | 77*10^139692+3 | 139694 | Robert Price | 06/2020 |
| 4853 | (31*2^463970+1)/5 | 139670 | Lelio R Paula | 08/2015 |
| 4854 | (18203^(2^15)+(18201)^(2^15))/2 | 139597 | Robert Price | 05/2018 |
| 4855 | 39640^3321+3321^39640 | 139584 | Hans Havermann | 05/2021 |
| 4856 | 36663^6410+6410^36663 | 139571 | Hans Havermann | 05/2021 |
| 4857 | 2^463633-2788423 | 139568 | Enzo Doria | 11/2015 |
| 4858 | 33659^13978+13978^33659 | 139532 | Hans Havermann | 05/2021 |
| 4859 | 31811^24318+24318^31811 | 139521 | Hans Havermann | 04/2021 |
| 4860 | 34149^12172+12172^34149 | 139512 | Hans Havermann | 04/2021 |
| 4861 | (29*10^139476+313)/9 | 139477 | Robert Price | 04/2021 |
| 4862 | 31721^24940+24940^31721 | 139474 | Hans Havermann | 05/2021 |
| 4863 | 32833^17698+17698^32833 | 139473 | Hans Havermann | 05/2021 |
| 4864 | 2^463271-109501 | 139459 | Enzo Doria | 04/2014 |
| 4865 | (5*10^139457+79)/3 | 139458 | Robert Price | 03/2018 |
| 4866 | 2^463237-99 | 139449 | Lelio R Paula | 09/2017 |
| 4867 | (49*10^139442+383)/9 | 139443 | Robert Price | 04/2019 |
| 4868 | 31155^29902+29902^31155 | 139441 | Hans Havermann | 05/2021 |
| 4869 | (7*10^139417-547)/9 | 139417 | Robert Price | 01/2018 |
| 4870 | 29636^31175-31175^29636 | 139409 | Frank Doornink | 05/2024 |
| 4871 | (10^139398+191)/3 | 139398 | Robert Price | 02/2018 |
| 4872 | 23*10^139386-3 | 139388 | Robert Price | 10/2021 |
| 4873 | 2^463019+79463 | 139383 | Enzo Doria | 06/2016 |
| 4874 | 3^292129-112756 | 139381 | Enzo Doria | 07/2014 |
| 4875 | (15*2^462951+1)/527 | 139361 | Lelio R Paula | 08/2015 |
| 4876 | 31922^23205+23205^31922 | 139359 | Hans Havermann | 05/2021 |
| 4877 | (19*10^139336+503)/9 | 139337 | Alfred Reich | 11/2023 |
| 4879 | 2^462855-1865707 | 139334 | Enzo Doria | 02/2016 |
| 4878 | 31237^28876+28876^31237 | 139334 | Hans Havermann | 05/2021 |
| 4880 | (86*10^139315+121)/9 | 139316 | Robert Price | 08/2019 |
| 4881 | 2^462786-292043 | 139313 | Enzo Doria | 08/2015 |
| 4882 | 38915^3798+3798^38915 | 139299 | Hans Havermann | 05/2021 |
| 4884 | (26*10^139289+1)/9 | 139290 | Serge Batalov | 05/2010 |
| 4883 | (17*10^139289+7)/3 | 139290 | Robert Price | 06/2023 |
| 4885 | 34065^12248+12248^34065 | 139260 | Hans Havermann | 05/2021 |
| 4886 | 36425^6654+6654^36425 | 139256 | Hans Havermann | 05/2021 |
| 4887 | 39252^3527+3527^39252 | 139243 | Hans Havermann | 05/2021 |
| 4888 | (17*10^139239+67)/3 | 139240 | Robert Price | 01/2019 |
| 4889 | 31887^23248+23248^31887 | 139231 | Hans Havermann | 05/2021 |
| 4890 | (25*10^139210-97)/9 | 139211 | Robert Price | 01/2022 |
| 4891 | 2^462238-935 | 139148 | Yves Minet | 02/2014 |
| 4892 | (29*10^139134-119)/9 | 139135 | Robert Price | 12/2021 |
| 4893 | U(687859)/4127153 | 139105 | Serge Batalov | 07/2024 |
| 4894 | (109*10^139100-7)/3 | 139102 | Robert Price | 03/2021 |
| 4895 | 38744^3885+3885^38744 | 139068 | Hans Havermann | 05/2021 |
| 4896 | 31112^29499+29499^31112 | 139065 | Hans Havermann | 05/2021 |
| 4897 | 2*10^139043-63 | 139044 | Robert Price | 01/2022 |
| 4898 | 36390^6613+6613^36390 | 139025 | Hans Havermann | 04/2021 |
| 4899 | 30554^30989-30989^30554 | 138988 | Frank Doornink | 05/2024 |
| 4900 | 2*10^138975+33 | 138976 | Robert Price | 11/2021 |
| 4901 | 42437^1882+1882^42437 | 138966 | Hans Havermann | 05/2021 |
| 4902 | 32151^20990+20990^32151 | 138958 | Hans Havermann | 05/2021 |
| 4903 | 32154^20933+20933^32154 | 138933 | Hans Havermann | 04/2021 |
| 4904 | 31082^29499+29499^31082 | 138931 | Hans Havermann | 04/2021 |
| 4905 | 30573^30962-30962^30573 | 138876 | Frank Doornink | 05/2024 |
| 4906 | 2^461228+1870441 | 138844 | Enzo Doria | 05/2016 |
| 4907 | 2^461204-113675 | 138837 | Enzo Doria | 08/2014 |
| 4908 | (397227*29^94935-19)/28 | 138837 | Eric Chen | 06/2025 |
| 4909 | (2^461139-7)/47 | 138815 | Lelio R Paula | 08/2015 |
| 4910 | (17*10^138812-521)/9 | 138813 | Robert Price | 04/2018 |
| 4911 | 3*10^138811-11 | 138812 | Robert Price | 07/2018 |
| 4912 | 29109^31088-31088^29109 | 138778 | Frank Doornink | 05/2024 |
| 4913 | (28*10^138768+173)/3 | 138769 | Robert Price | 12/2019 |
| 4914 | (17*2^460963+1)/124051613 | 138757 | Lelio R Paula | 08/2015 |
| 4915 | (379*10^138737-1)/9 | 138739 | Robert Price | 02/2020 |
| 4916 | (43*10^138648+101)/9 | 138649 | Robert Price | 11/2018 |
| 4917 | 2^460567-113541 | 138645 | Enzo Doria | 08/2014 |
| 4918 | 2^460539+224789 | 138637 | Enzo Doria | 07/2024 |
| 4919 | (10^138622+161)/9 | 138622 | Robert Price | 09/2021 |
| 4920 | 7*10^138604+3 | 138605 | Robert Price | 08/2015 |
| 4921 | (133*10^138600+17)/3 | 138602 | Robert Price | 11/2021 |
| 4922 | 33912^12203+12203^33912 | 138581 | Hans Havermann | 05/2021 |
| 4923 | 2^460330+69 | 138574 | Lelio R Paula | 09/2017 |
| 4924 | (17*10^138569-77)/3 | 138570 | Robert Price | 08/2019 |
| 4925 | 31186^27725+27725^31186 | 138556 | Hans Havermann | 05/2021 |
| 4926 | (41^85909-3^85909)/38 | 138552 | Robert Price | 09/2025 |
| 4927 | (16*10^138545+89)/3 | 138546 | Robert Price | 03/2021 |
| 4928 | 39753^3056+3056^39753 | 138546 | Hans Havermann | 05/2021 |
| 4929 | 31282^26847+26847^31282 | 138545 | Hans Havermann | 05/2021 |
| 4930 | 6*10^138520-37 | 138521 | Robert Price | 02/2021 |
| 4932 | 2^460078-69581 | 138498 | Enzo Doria | 12/2015 |
| 4931 | 31830^22447+22447^31830 | 138498 | Hans Havermann | 05/2021 |
| 4933 | 37384^5065+5065^37384 | 138492 | Hans Havermann | 05/2021 |
| 4934 | 28736^31055-31055^28736 | 138457 | Frank Doornink | 05/2024 |
| 4935 | 34774^9585+9585^34774 | 138456 | Hans Havermann | 05/2021 |
| 4936 | 10^138444-5001 | 138444 | Robert Price | 12/2021 |
| 4937 | 2^459768+1531 | 138404 | Lelio R Paula | 06/2012 |
| 4938 | (266*10^138328-17)/3 | 138330 | Robert Price | 07/2020 |
| 4939 | 27200^31193-31193^27200 | 138328 | Frank Doornink | 01/2024 |
| 4940 | 2024^41836+2025 | 138319 | Henri Lifchitz | 01/2025 |
| 4941 | 28782^31019-31019^28782 | 138318 | Frank Doornink | 05/2024 |
| 4942 | 32963^15696+15696^32963 | 138306 | Hans Havermann | 05/2021 |
| 4943 | 2^459343-113611 | 138277 | Enzo Doria | 08/2014 |
| 4944 | (28*10^138240+113)/3 | 138241 | Robert Price | 03/2020 |
| 4945 | 2^459199+1874393 | 138233 | Enzo Doria | 06/2016 |
| 4946 | 33339^14002+14002^33339 | 138230 | Hans Havermann | 05/2021 |
| 4947 | 30137^30860-30860^30137 | 138226 | Frank Doornink | 05/2024 |
| 4948 | 2^459063-345307 | 138192 | Enzo Doria | 06/2015 |
| 4949 | 2*10^138162-43 | 138163 | Robert Price | 04/2018 |
| 4950 | 2^458927-112747 | 138151 | Enzo Doria | 06/2014 |
| 4951 | 2^458927-69217 | 138151 | Enzo Doria | 11/2015 |
| 4952 | 30907^29458+29458^30907 | 138130 | Hans Havermann | 05/2021 |
| 4953 | 32882^15837+15837^32882 | 138094 | Hans Havermann | 05/2021 |
| 4954 | 39252^3295+3295^39252 | 138083 | Hans Havermann | 05/2021 |
| 4955 | 33789^12190+12190^33789 | 138062 | Hans Havermann | 06/2021 |
| 4956 | 555555*2^458524+1513 | 138036 | Darren Bedwell | 08/2009 |
| 4957 | 28095^31028-31028^28095 | 138033 | Frank Doornink | 05/2024 |
| 4958 | 30931^29002+29002^30931 | 138028 | Hans Havermann | 05/2021 |
| 4959 | 2^458465+2^32+1 | 138012 | T. D. Noe | 06/2007 |
| 4960 | 32206^19275+19275^32206 | 138003 | Hans Havermann | 05/2021 |
| 4961 | 2^458321-113053 | 137969 | Enzo Doria | 07/2014 |
| 4962 | 6^177298+323 | 137965 | Riley Fisher | 03/2023 |
| 4963 | 2^458298+79459 | 137962 | Enzo Doria | 06/2016 |
| 4964 | 30254^30789-30789^30254 | 137959 | Frank Doornink | 05/2024 |
| 4965 | 2^458248-21815 | 137947 | Enzo Doria | 07/2013 |
| 4966 | 2^458194+1876549 | 137931 | Enzo Doria | 07/2016 |
| 4967 | (318259#+325270)/(2^2*5*11*2957) | 137907 | Makoto Morimoto | 10/2017 |
| 4968 | (318259#+2625)/(3^2*5*7^5*22965193) | 137899 | Makoto Morimoto | 06/2019 |
| 4969 | (793*10^137887+53)/9 | 137889 | Robert Price | 01/2022 |
| 4970 | 2^457937+57 | 137853 | Lelio R Paula | 09/2017 |
| 4971 | 28714^30921-30921^28714 | 137849 | Frank Doornink | 05/2024 |
| 4972 | (8*10^137845+13)/3 | 137846 | Robert Price | 06/2018 |
| 4973 | 2^457822+105 | 137819 | Donovan Johnson | 06/2006 |
| 4974 | 2^457754-113711 | 137798 | Enzo Doria | 09/2014 |
| 4975 | 11^132315-360 | 137792 | Enzo Doria | 09/2012 |
| 4976 | (2^659318)%L(659318) | 137787 | Henri Lifchitz | 05/2025 |
| 4977 | 32072^19689+19689^32072 | 137725 | Hans Havermann | 06/2021 |
| 4978 | 26529^31132-31132^26529 | 137720 | Frank Doornink | 03/2024 |
| 4979 | 44592^1225+1225^44592 | 137707 | Hans Havermann | 05/2021 |
| 4980 | 28986^30857-30857^28986 | 137690 | Frank Doornink | 05/2024 |
| 4981 | 2^457347-37 | 137676 | Lelio R Paula | 09/2017 |
| 4982 | 2^457322-2786393 | 137668 | Enzo Doria | 10/2015 |
| 4983 | gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901) | 137664 | Serge Batalov | 04/2015 |
| 4984 | Phi(699340M,10) | 137664 | Anonymous | 03/2025 |
| 4985 | 34015^11134+11134^34015 | 137647 | Hans Havermann | 06/2021 |
| 4986 | 2^457240-59939 | 137643 | Enzo Doria | 10/2015 |
| 4987 | (856*10^137633-1)/9 | 137635 | Robert Price | 03/2020 |
| 4988 | 36232^6289+6289^36232 | 137631 | Hans Havermann | 05/2021 |
| 4989 | 2^457120-21575 | 137607 | Enzo Doria | 07/2013 |
| 4991 | (11*2^456978+1)/15 | 137564 | Lelio R Paula | 07/2015 |
| 4990 | 30963^27722+27722^30963 | 137564 | Hans Havermann | 04/2021 |
| 4992 | 33722^12003+12003^33722 | 137562 | Hans Havermann | 06/2021 |
| 4993 | (7*25^98399+10613)/12 | 137556 | Curtis Bright | 05/2015 |
| 4994 | 41901^1918+1918^41901 | 137555 | Hans Havermann | 06/2021 |
| 4995 | (7*10^137551-1)/3 | 137552 | Robert Price | 08/2022 |
| 4996 | 32930^15021+15021^32930 | 137539 | Hans Havermann | 05/2021 |
| 4997 | 31178^25785+25785^31178 | 137538 | Hans Havermann | 05/2021 |
| 4998 | 419^52446+52446^419 | 137525 | Norbert Schneider | 11/2020 |
| 4999 | 2^456813+214175 | 137515 | Enzo Doria | 10/2023 |
| 5000 | 2^456796-113513 | 137510 | Enzo Doria | 08/2014 |
