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 ? |
| 4251 | 2^469974-1841 | 141477 | Enzo Doria | 05/2014 |
| 4252 | (23*2^469939+1)/25 | 141466 | Lelio R Paula | 08/2015 |
| 4253 | 312*33^93158+23 | 141465 | Eric Chen | 12/2023 |
| 4254 | 2*10^141448+63 | 141449 | Robert Price | 05/2018 |
| 4255 | 2^469824+43 | 141432 | Lelio R Paula | 09/2017 |
| 4256 | 2*10^141407-27 | 141408 | Robert Price | 05/2018 |
| 4257 | (214*10^141385-1)/3 | 141387 | Robert Price | 01/2021 |
| 4258 | 2^469630-59711 | 141373 | Enzo Doria | 10/2015 |
| 4259 | 35277^10172+10172^35277 | 141370 | Hans Havermann | 04/2021 |
| 4260 | 33397^17100+17100^33397 | 141370 | Hans Havermann | 04/2021 |
| 4261 | (25*10^141366-331)/9 | 141367 | Robert Price | 08/2018 |
| 4262 | 36986^6639+6639^36986 | 141365 | Hans Havermann | 06/2021 |
| 4263 | 34572^12271+12271^34572 | 141361 | Hans Havermann | 06/2021 |
| 4264 | 37179^6338+6338^37179 | 141353 | Hans Havermann | 05/2021 |
| 4265 | (2^469564-3)/611 | 141351 | Lelio R Paula | 08/2015 |
| 4266 | 197^61601+2 | 141342 | Lelio R Paula | 08/2017 |
| 4267 | 33420^16951+16951^33420 | 141340 | Hans Havermann | 05/2021 |
| 4268 | 31623^29458+29458^31623 | 141330 | Hans Havermann | 05/2021 |
| 4269 | 48112^865+865^48112 | 141306 | Hans Havermann | 05/2021 |
| 4270 | 2^469372-112949 | 141296 | Enzo Doria | 07/2014 |
| 4271 | 5*10^141294-63 | 141295 | Robert Price | 04/2021 |
| 4272 | 3^296115+4 | 141283 | Tyler NeSmith | 01/2021 |
| 4273 | (64*10^141256+161)/9 | 141257 | Robert Price | 08/2022 |
| 4274 | 143^(2^16)+106^(2^16) | 141253 | Valeryi Kuryshev | 02/2011 |
| 4275 | 143^65536+106^65536 | 141253 | Serge Batalov | 03/2018 |
| 4276 | (11*10^141243-23)/3 | 141244 | Robert Price | 09/2021 |
| 4278 | 2^469198+782569 | 141243 | Enzo Doria | 10/2016 |
| 4277 | 38129^5062+5062^38129 | 141243 | Hans Havermann | 05/2021 |
| 4279 | 2^469076-2786939 | 141206 | Enzo Doria | 11/2015 |
| 4280 | 38630^4521+4521^38630 | 141202 | Hans Havermann | 05/2021 |
| 4281 | 31755^27836+27836^31755 | 141139 | Hans Havermann | 05/2021 |
| 4282 | 35554^9325+9325^35554 | 141137 | Hans Havermann | 05/2021 |
| 4283 | 2^468804+1874941 | 141125 | Enzo Doria | 06/2016 |
| 4284 | 2^468787+81353 | 141119 | Enzo Doria | 08/2016 |
| 4285 | 30204^31493-31493^30204 | 141091 | Frank Doornink | 06/2024 |
| 4286 | 2^468595-350407 | 141062 | Enzo Doria | 06/2015 |
| 4287 | 2^468564+87855 | 141052 | Lelio R Paula | 01/2016 |
| 4288 | 2^468551-21987 | 141048 | Enzo Doria | 07/2013 |
| 4289 | 2^468523-7 | 141040 | Lelio R Paula | 08/2015 |
| 4290 | (25*10^141019-13)/3 | 141020 | Robert Price | 09/2019 |
| 4291 | 2^468405+87855 | 141004 | Lelio R Paula | 01/2016 |
| 4292 | 39338^3831+3831^39338 | 140961 | Hans Havermann | 05/2021 |
| 4293 | 31458^30239+30239^31458 | 140950 | Hans Havermann | 05/2021 |
| 4294 | 8*10^140932+29 | 140933 | Robert Price | 11/2021 |
| 4295 | 33166^17691+17691^33166 | 140881 | Hans Havermann | 06/2021 |
| 4296 | 2^467978-113051 | 140876 | Enzo Doria | 07/2014 |
| 4297 | 2^467780-344429 | 140816 | Enzo Doria | 07/2015 |
| 4298 | 9*10^140802-89 | 140803 | Robert Price | 04/2020 |
| 4299 | 2^467605-1855603 | 140764 | Enzo Doria | 09/2015 |
| 4300 | (9^147503-5^147503)/4 | 140754 | Jon Grantham | 07/2023 |
| 4301 | 5*10^140744-7 | 140745 | Robert Price | 09/2015 |
| 4302 | (5^201359-1)/4 | 140744 | Paul Bourdelais | 12/2008 |
| 4303 | 2^467401-1850023 | 140702 | Enzo Doria | 08/2015 |
| 4304 | (14*10^140693+13)/9 | 140694 | Tyler Busby | 02/2023 |
| 4305 | (266*10^140681-17)/3 | 140683 | Robert Price | 07/2020 |
| 4306 | (2^467270+78557)/23247 | 140658 | Lelio R Paula | 07/2015 |
| 4307 | 32138^23781+23781^32138 | 140644 | Hans Havermann | 05/2021 |
| 4308 | 31654^27735+27735^31654 | 140640 | Hans Havermann | 05/2021 |
| 4309 | (29*2^467205+1)/2780517107 | 140635 | Lelio R Paula | 08/2015 |
| 4310 | 2^467166-1854941 | 140631 | Enzo Doria | 09/2015 |
| 4311 | (203*10^140615-11)/3 | 140617 | Robert Price | 12/2020 |
| 4312 | (85*10^140609+473)/9 | 140610 | Robert Price | 01/2020 |
| 4313 | 39231^3836+3836^39231 | 140600 | Hans Havermann | 06/2021 |
| 4314 | 5*3^294676+2^294676 | 140597 | Jon Grantham | 08/2023 |
| 4315 | 2^466866-1840571 | 140541 | Enzo Doria | 06/2015 |
| 4316 | 2^466829-459523 | 140530 | Enzo Doria | 05/2015 |
| 4317 | 2^466692-113213 | 140489 | Enzo Doria | 07/2014 |
| 4318 | 23*10^140464-3 | 140466 | Robert Price | 10/2021 |
| 4319 | (2*10^140461-17)/3 | 140461 | Serge Batalov | 11/2022 |
| 4320 | 29^96047-30 | 140459 | Anonymous | 09/2024 |
| 4321 | 31335^30364+30364^31335 | 140455 | Hans Havermann | 05/2021 |
| 4322 | 28511^31524-31524^28511 | 140440 | Frank Doornink | 06/2024 |
| 4323 | 32795^19126+19126^32795 | 140416 | Hans Havermann | 05/2021 |
| 4324 | (44*10^140410-503)/9 | 140411 | Robert Price | 12/2018 |
| 4325 | 28332^31535-31535^28332 | 140403 | Frank Doornink | 06/2024 |
| 4326 | 153^64265-2 | 140400 | Lelio R Paula | 11/2017 |
| 4327 | 30323^31322-31322^30323 | 140379 | Frank Doornink | 06/2024 |
| 4328 | (112*10^140357-1)/3 | 140359 | Serge Batalov | 12/2014 |
| 4329 | (29*10^140337-17)/3 | 140338 | Robert Price | 09/2019 |
| 4330 | 2^466181-112735 | 140335 | Enzo Doria | 07/2014 |
| 4331 | (16*10^140290-37)/3 | 140291 | Robert Price | 05/2021 |
| 4332 | (5*10^140281-119)/3 | 140282 | Robert Price | 03/2018 |
| 4333 | 34568^11415+11415^34568 | 140259 | Hans Havermann | 05/2021 |
| 4334 | (27*2^465872+1)/691 | 140241 | Lelio R Paula | 08/2015 |
| 4335 | 33632^14781+14781^33632 | 140236 | Hans Havermann | 05/2021 |
| 4336 | 31803^25670+25670^31803 | 140233 | Hans Havermann | 05/2021 |
| 4337 | 2^465803-114817 | 140221 | Enzo Doria | 05/2015 |
| 4338 | floor(Pi*10^140344)%10^140165 | 140165 | Serge Batalov | 08/2012 |
| 4339 | 2^465503-112735 | 140131 | Enzo Doria | 07/2014 |
| 4340 | (16*10^140091+167)/3 | 140092 | Robert Price | 06/2019 |
| 4341 | (8*10^140087-137)/3 | 140088 | Robert Price | 03/2022 |
| 4342 | 6^179964+179964^6-1 | 140040 | Robert Price | 04/2014 |
| 4343 | (89*10^140008-179)/9 | 140009 | Robert Price | 12/2019 |
| 4344 | (29*2^465077-1)/9 | 140003 | Lelio R Paula | 08/2015 |
| 4345 | 2^465072-344789 | 140001 | Enzo Doria | 07/2015 |
| 4346 | 34742^10683+10683^34742 | 139965 | Hans Havermann | 05/2021 |
| 4347 | 5*10^139945+81 | 139946 | Robert Price | 03/2019 |
| 4348 | 32648^19335+19335^32648 | 139941 | Hans Havermann | 05/2021 |
| 4349 | 2^464864-17 | 139939 | Lelio R Paula | 09/2017 |
| 4350 | 8*10^139920+51 | 139921 | Robert Price | 08/2019 |
| 4351 | (85*10^139913-1)/3 | 139915 | Robert Price | 02/2020 |
| 4352 | 31203^30436+30436^31203 | 139896 | Hans Havermann | 04/2021 |
| 4353 | 2^464642+22189 | 139872 | Enzo Doria | 09/2023 |
| 4354 | 26138^31663-31663^26138 | 139865 | Frank Doornink | 03/2024 |
| 4355 | (16^116139+619)/5 | 139845 | Anonymous | 08/2022 |
| 4356 | (2^464556+619)/5 | 139845 | Eric Chen | 10/2023 |
| 4357 | 4*10^139839-27 | 139840 | Robert Price | 08/2021 |
| 4358 | 33582^14573+14573^33582 | 139821 | Hans Havermann | 05/2021 |
| 4359 | (17^113621+1)/18 | 139804 | Paul Bourdelais | 09/2011 |
| 4361 | 2*10^139800-21 | 139801 | Robert Price | 09/2020 |
| 4360 | 32628^19261+19261^32628 | 139801 | Hans Havermann | 04/2021 |
| 4362 | (13*10^139782+191)/3 | 139783 | Robert Price | 11/2018 |
| 4363 | (64*10^139776+791)/9 | 139777 | Robert Price | 01/2022 |
| 4364 | (695*10^139772+7)/9 | 139774 | Robert Price | 12/2021 |
| 4365 | (19*2^464312-1)/3 | 139773 | Lelio R Paula | 08/2015 |
| 4366 | (74*10^139723+133)/9 | 139724 | Robert Price | 06/2019 |
| 4367 | 3*10^139722+13 | 139723 | Robert Price | 07/2018 |
| 4368 | 31577^26592+26592^31577 | 139721 | Hans Havermann | 05/2021 |
| 4369 | 77*10^139692+3 | 139694 | Robert Price | 06/2020 |
| 4370 | (31*2^463970+1)/5 | 139670 | Lelio R Paula | 08/2015 |
| 4371 | (18203^(2^15)+(18201)^(2^15))/2 | 139597 | Robert Price | 05/2018 |
| 4372 | 39640^3321+3321^39640 | 139584 | Hans Havermann | 05/2021 |
| 4373 | 36663^6410+6410^36663 | 139571 | Hans Havermann | 05/2021 |
| 4374 | 2^463633-2788423 | 139568 | Enzo Doria | 11/2015 |
| 4375 | 33659^13978+13978^33659 | 139532 | Hans Havermann | 05/2021 |
| 4376 | 31811^24318+24318^31811 | 139521 | Hans Havermann | 04/2021 |
| 4377 | 34149^12172+12172^34149 | 139512 | Hans Havermann | 04/2021 |
| 4378 | (29*10^139476+313)/9 | 139477 | Robert Price | 04/2021 |
| 4379 | 31721^24940+24940^31721 | 139474 | Hans Havermann | 05/2021 |
| 4380 | 32833^17698+17698^32833 | 139473 | Hans Havermann | 05/2021 |
| 4381 | 2^463271-109501 | 139459 | Enzo Doria | 04/2014 |
| 4382 | (5*10^139457+79)/3 | 139458 | Robert Price | 03/2018 |
| 4383 | 2^463237-99 | 139449 | Lelio R Paula | 09/2017 |
| 4384 | (49*10^139442+383)/9 | 139443 | Robert Price | 04/2019 |
| 4385 | 31155^29902+29902^31155 | 139441 | Hans Havermann | 05/2021 |
| 4386 | (7*10^139417-547)/9 | 139417 | Robert Price | 01/2018 |
| 4387 | 29636^31175-31175^29636 | 139409 | Frank Doornink | 05/2024 |
| 4388 | (10^139398+191)/3 | 139398 | Robert Price | 02/2018 |
| 4389 | 23*10^139386-3 | 139388 | Robert Price | 10/2021 |
| 4390 | 2^463019+79463 | 139383 | Enzo Doria | 06/2016 |
| 4391 | 3^292129-112756 | 139381 | Enzo Doria | 07/2014 |
| 4392 | (15*2^462951+1)/527 | 139361 | Lelio R Paula | 08/2015 |
| 4393 | 31922^23205+23205^31922 | 139359 | Hans Havermann | 05/2021 |
| 4394 | (19*10^139336+503)/9 | 139337 | Alfred Reich | 11/2023 |
| 4396 | 2^462855-1865707 | 139334 | Enzo Doria | 02/2016 |
| 4395 | 31237^28876+28876^31237 | 139334 | Hans Havermann | 05/2021 |
| 4397 | (86*10^139315+121)/9 | 139316 | Robert Price | 08/2019 |
| 4398 | 2^462786-292043 | 139313 | Enzo Doria | 08/2015 |
| 4399 | 38915^3798+3798^38915 | 139299 | Hans Havermann | 05/2021 |
| 4401 | (26*10^139289+1)/9 | 139290 | Serge Batalov | 05/2010 |
| 4400 | (17*10^139289+7)/3 | 139290 | Robert Price | 06/2023 |
| 4402 | 34065^12248+12248^34065 | 139260 | Hans Havermann | 05/2021 |
| 4403 | 36425^6654+6654^36425 | 139256 | Hans Havermann | 05/2021 |
| 4404 | 39252^3527+3527^39252 | 139243 | Hans Havermann | 05/2021 |
| 4405 | (17*10^139239+67)/3 | 139240 | Robert Price | 01/2019 |
| 4406 | 31887^23248+23248^31887 | 139231 | Hans Havermann | 05/2021 |
| 4407 | (25*10^139210-97)/9 | 139211 | Robert Price | 01/2022 |
| 4408 | 2^462238-935 | 139148 | Yves Minet | 02/2014 |
| 4409 | (29*10^139134-119)/9 | 139135 | Robert Price | 12/2021 |
| 4410 | U(687859)/4127153 | 139105 | Serge Batalov | 07/2024 |
| 4411 | (109*10^139100-7)/3 | 139102 | Robert Price | 03/2021 |
| 4412 | 38744^3885+3885^38744 | 139068 | Hans Havermann | 05/2021 |
| 4413 | 31112^29499+29499^31112 | 139065 | Hans Havermann | 05/2021 |
| 4414 | 2*10^139043-63 | 139044 | Robert Price | 01/2022 |
| 4415 | 36390^6613+6613^36390 | 139025 | Hans Havermann | 04/2021 |
| 4416 | 30554^30989-30989^30554 | 138988 | Frank Doornink | 05/2024 |
| 4417 | 2*10^138975+33 | 138976 | Robert Price | 11/2021 |
| 4418 | 42437^1882+1882^42437 | 138966 | Hans Havermann | 05/2021 |
| 4419 | 32151^20990+20990^32151 | 138958 | Hans Havermann | 05/2021 |
| 4420 | 32154^20933+20933^32154 | 138933 | Hans Havermann | 04/2021 |
| 4421 | 31082^29499+29499^31082 | 138931 | Hans Havermann | 04/2021 |
| 4422 | 30573^30962-30962^30573 | 138876 | Frank Doornink | 05/2024 |
| 4423 | 2^461228+1870441 | 138844 | Enzo Doria | 05/2016 |
| 4424 | 2^461204-113675 | 138837 | Enzo Doria | 08/2014 |
| 4425 | (2^461139-7)/47 | 138815 | Lelio R Paula | 08/2015 |
| 4426 | (17*10^138812-521)/9 | 138813 | Robert Price | 04/2018 |
| 4427 | 3*10^138811-11 | 138812 | Robert Price | 07/2018 |
| 4428 | 29109^31088-31088^29109 | 138778 | Frank Doornink | 05/2024 |
| 4429 | (28*10^138768+173)/3 | 138769 | Robert Price | 12/2019 |
| 4430 | (17*2^460963+1)/124051613 | 138757 | Lelio R Paula | 08/2015 |
| 4431 | (379*10^138737-1)/9 | 138739 | Robert Price | 02/2020 |
| 4432 | (43*10^138648+101)/9 | 138649 | Robert Price | 11/2018 |
| 4433 | 2^460567-113541 | 138645 | Enzo Doria | 08/2014 |
| 4434 | 2^460539+224789 | 138637 | Enzo Doria | 07/2024 |
| 4435 | (10^138622+161)/9 | 138622 | Robert Price | 09/2021 |
| 4436 | 7*10^138604+3 | 138605 | Robert Price | 08/2015 |
| 4437 | (133*10^138600+17)/3 | 138602 | Robert Price | 11/2021 |
| 4438 | 33912^12203+12203^33912 | 138581 | Hans Havermann | 05/2021 |
| 4439 | 2^460330+69 | 138574 | Lelio R Paula | 09/2017 |
| 4440 | (17*10^138569-77)/3 | 138570 | Robert Price | 08/2019 |
| 4441 | 31186^27725+27725^31186 | 138556 | Hans Havermann | 05/2021 |
| 4442 | (16*10^138545+89)/3 | 138546 | Robert Price | 03/2021 |
| 4443 | 39753^3056+3056^39753 | 138546 | Hans Havermann | 05/2021 |
| 4444 | 31282^26847+26847^31282 | 138545 | Hans Havermann | 05/2021 |
| 4445 | 6*10^138520-37 | 138521 | Robert Price | 02/2021 |
| 4447 | 2^460078-69581 | 138498 | Enzo Doria | 12/2015 |
| 4446 | 31830^22447+22447^31830 | 138498 | Hans Havermann | 05/2021 |
| 4448 | 37384^5065+5065^37384 | 138492 | Hans Havermann | 05/2021 |
| 4449 | 28736^31055-31055^28736 | 138457 | Frank Doornink | 05/2024 |
| 4450 | 34774^9585+9585^34774 | 138456 | Hans Havermann | 05/2021 |
| 4451 | 10^138444-5001 | 138444 | Robert Price | 12/2021 |
| 4452 | 2^459768+1531 | 138404 | Lelio R Paula | 06/2012 |
| 4453 | (266*10^138328-17)/3 | 138330 | Robert Price | 07/2020 |
| 4454 | 27200^31193-31193^27200 | 138328 | Frank Doornink | 01/2024 |
| 4455 | 2024^41836+2025 | 138319 | Henri Lifchitz | 01/2025 |
| 4456 | 28782^31019-31019^28782 | 138318 | Frank Doornink | 05/2024 |
| 4457 | 32963^15696+15696^32963 | 138306 | Hans Havermann | 05/2021 |
| 4458 | 2^459343-113611 | 138277 | Enzo Doria | 08/2014 |
| 4459 | (28*10^138240+113)/3 | 138241 | Robert Price | 03/2020 |
| 4460 | 2^459199+1874393 | 138233 | Enzo Doria | 06/2016 |
| 4461 | 33339^14002+14002^33339 | 138230 | Hans Havermann | 05/2021 |
| 4462 | 30137^30860-30860^30137 | 138226 | Frank Doornink | 05/2024 |
| 4463 | 2^459063-345307 | 138192 | Enzo Doria | 06/2015 |
| 4464 | 2*10^138162-43 | 138163 | Robert Price | 04/2018 |
| 4465 | 2^458927-112747 | 138151 | Enzo Doria | 06/2014 |
| 4466 | 2^458927-69217 | 138151 | Enzo Doria | 11/2015 |
| 4467 | 30907^29458+29458^30907 | 138130 | Hans Havermann | 05/2021 |
| 4468 | 32882^15837+15837^32882 | 138094 | Hans Havermann | 05/2021 |
| 4469 | 39252^3295+3295^39252 | 138083 | Hans Havermann | 05/2021 |
| 4470 | 33789^12190+12190^33789 | 138062 | Hans Havermann | 06/2021 |
| 4471 | 555555*2^458524+1513 | 138036 | Darren Bedwell | 08/2009 |
| 4472 | 28095^31028-31028^28095 | 138033 | Frank Doornink | 05/2024 |
| 4473 | 30931^29002+29002^30931 | 138028 | Hans Havermann | 05/2021 |
| 4474 | 2^458465+2^32+1 | 138012 | T. D. Noe | 06/2007 |
| 4475 | 32206^19275+19275^32206 | 138003 | Hans Havermann | 05/2021 |
| 4476 | 2^458321-113053 | 137969 | Enzo Doria | 07/2014 |
| 4477 | 6^177298+323 | 137965 | Riley Fisher | 03/2023 |
| 4478 | 2^458298+79459 | 137962 | Enzo Doria | 06/2016 |
| 4479 | 30254^30789-30789^30254 | 137959 | Frank Doornink | 05/2024 |
| 4480 | 2^458248-21815 | 137947 | Enzo Doria | 07/2013 |
| 4481 | 2^458194+1876549 | 137931 | Enzo Doria | 07/2016 |
| 4482 | (318259#+325270)/(2^2*5*11*2957) | 137907 | Makoto Morimoto | 10/2017 |
| 4483 | (318259#+2625)/(3^2*5*7^5*22965193) | 137899 | Makoto Morimoto | 06/2019 |
| 4484 | (793*10^137887+53)/9 | 137889 | Robert Price | 01/2022 |
| 4485 | 2^457937+57 | 137853 | Lelio R Paula | 09/2017 |
| 4486 | 28714^30921-30921^28714 | 137849 | Frank Doornink | 05/2024 |
| 4487 | (8*10^137845+13)/3 | 137846 | Robert Price | 06/2018 |
| 4488 | 2^457822+105 | 137819 | Donovan Johnson | 06/2006 |
| 4489 | 2^457754-113711 | 137798 | Enzo Doria | 09/2014 |
| 4490 | 11^132315-360 | 137792 | Enzo Doria | 09/2012 |
| 4491 | 32072^19689+19689^32072 | 137725 | Hans Havermann | 06/2021 |
| 4492 | 26529^31132-31132^26529 | 137720 | Frank Doornink | 03/2024 |
| 4493 | 44592^1225+1225^44592 | 137707 | Hans Havermann | 05/2021 |
| 4494 | 28986^30857-30857^28986 | 137690 | Frank Doornink | 05/2024 |
| 4495 | 2^457347-37 | 137676 | Lelio R Paula | 09/2017 |
| 4496 | 2^457322-2786393 | 137668 | Enzo Doria | 10/2015 |
| 4497 | 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 |
| 4498 | Phi(699340M,10) | 137664 | Anonymous | 03/2025 |
| 4499 | 34015^11134+11134^34015 | 137647 | Hans Havermann | 06/2021 |
| 4500 | 2^457240-59939 | 137643 | Enzo Doria | 10/2015 |
