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
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
4251 | fibonacci(610144)-2 | 127513 | Jon Grantham | 08/2023 |
4252 | (103*10^127491+17)/3 | 127493 | Robert Price | 08/2020 |
4253 | 29376^21869+21869^29376 | 127487 | Hans Havermann | 03/2021 |
4254 | 31186^12241+12241^31186 | 127483 | Hans Havermann | 02/2021 |
4255 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
4256 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
4257 | 30594^14645+14645^30594 | 127446 | Hans Havermann | 03/2021 |
4258 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
4259 | (67*10^127413-7)/3 | 127415 | Robert Price | 01/2020 |
4260 | (5*34^83193+700233)/11 | 127408 | Eric Chen | 08/2023 |
4261 | (2*10^127407+73)/3 | 127407 | Robert Price | 09/2020 |
4262 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
4263 | (7726^32768+1)/13917994151414876602369 | 127379 | Kellen Shenton | 04/2021 |
4264 | (4*10^127349+17)/3 | 127350 | Tyler Busby | 01/2023 |
4265 | 29512^20647+20647^29512 | 127341 | Hans Havermann | 03/2021 |
4266 | 2^422987-3001935 | 127332 | Paul Bourdelais | 07/2023 |
4267 | (112*10^127324+17)/3 | 127326 | Robert Price | 03/2020 |
4268 | 29565^20252+20252^29565 | 127321 | Hans Havermann | 03/2021 |
4269 | fibonacci(609165)-3 | 127308 | Jon Grantham | 08/2023 |
4271 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
4270 | (5^182099-3^182099)/2 | 127282 | Kellen Shenton | 05/2022 |
4272 | (16*10^127259+197)/3 | 127260 | Robert Price | 04/2019 |
4273 | (26*10^127240+61)/3 | 127241 | Robert Price | 10/2019 |
4274 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
4275 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
4276 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
4277 | 31678^10343+10343^31678 | 127176 | Hans Havermann | 03/2021 |
4278 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
4279 | 34947^4352+4352^34947 | 127162 | Hans Havermann | 03/2021 |
4280 | 6*10^127158+19 | 127159 | Robert Price | 11/2021 |
4281 | 30469^14902+14902^30469 | 127155 | Hans Havermann | 03/2021 |
4282 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
4283 | 29941^17620+17620^29941 | 127130 | Hans Havermann | 02/2021 |
4284 | 31607^10516+10516^31607 | 127119 | Hans Havermann | 03/2021 |
4285 | (19*10^127118-97)/3 | 127119 | Robert Price | 10/2021 |
4286 | (29*10^127111+691)/9 | 127112 | Robert Price | 08/2021 |
4287 | 736^44335+44335^736 | 127104 | Norbert Schneider | 07/2019 |
4288 | 33040^7023+7023^33040 | 127090 | Hans Havermann | 03/2021 |
4289 | (4*10^127081+167)/9 | 127081 | Robert Price | 03/2022 |
4290 | 29748^18661+18661^29748 | 127052 | Hans Havermann | 03/2021 |
4291 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
4292 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
4293 | (14*10^127014-137)/3 | 127015 | Robert Price | 04/2021 |
4294 | 31436^10965+10965^31436 | 127002 | Hans Havermann | 03/2021 |
4295 | 28905^24758+24758^28905 | 127001 | Hans Havermann | 03/2021 |
4296 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
4297 | (10^127030+7)/81234833/9230384921/6092460488946445358851 | 126991 | Alfred Reich | 07/2021 |
4298 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
4299 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
4300 | (56*10^126935+187)/9 | 126936 | Robert Price | 10/2021 |
4301 | 28915^24538+24538^28915 | 126933 | Hans Havermann | 03/2021 |
4302 | (29*10^126928-77)/3 | 126929 | Robert Price | 02/2020 |
4303 | (259*10^126919-1)/3 | 126921 | Robert Price | 12/2020 |
4304 | 10^126919+204567 | 126920 | Patrick De Geest | 05/2021 |
4305 | (2^421617+100280245065) | 126920 | Paul Bourdelais | 05/2022 |
4306 | 10^126919-100001 | 126919 | Robert Price | 07/2020 |
4307 | 28340^28503+28503^28340 | 126907 | Norbert Schneider | 02/2021 |
4308 | 2^421534-3001935 | 126895 | Paul Bourdelais | 07/2023 |
4309 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
4310 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
4311 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
4312 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
4313 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
4314 | 37938^2203+2203^37938 | 126828 | Hans Havermann | 03/2021 |
4315 | (13*10^126819+77)/9 | 126820 | Robert Price | 07/2022 |
4316 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
4318 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
4317 | 2^421169-3001935 | 126785 | Paul Bourdelais | 07/2023 |
4319 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
4320 | (106*10^126726+17)/3 | 126728 | Robert Price | 04/2021 |
4321 | 30718^13347+13347^30718 | 126724 | Hans Havermann | 03/2021 |
4322 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
4323 | 11*23^93048+356 | 126708 | Eric Chen | 08/2023 |
4324 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
4325 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
4326 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
4327 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
4328 | (167*10^126637-17)/3 | 126639 | Robert Price | 03/2020 |
4329 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
4330 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
4331 | 7*10^126600-99 | 126601 | Robert Price | 06/2019 |
4332 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
4333 | 28717^25534+25534^28717 | 126560 | Hans Havermann | 03/2021 |
4334 | (86*10^126542+103)/9 | 126543 | Robert Price | 12/2021 |
4335 | (19*10^126517-7)/3 | 126518 | Robert Price | 12/2023 |
4336 | 28922^23655+23655^28922 | 126503 | Hans Havermann | 03/2021 |
4337 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
4338 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
4339 | 8*10^126408+71 | 126409 | Robert Price | 05/2022 |
4340 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
4341 | 29315^20484+20484^29315 | 126390 | Hans Havermann | 03/2021 |
4342 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
4343 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
4344 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
4345 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
4346 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
4347 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
4348 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
4349 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
4350 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
4351 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
4352 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
4353 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
4354 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
4355 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
4356 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
4357 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
4358 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
4359 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
4360 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
4361 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
4362 | 4*10^126064-69 | 126065 | Robert Price | 01/2022 |
4363 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
4364 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
4365 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
4366 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
4367 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
4368 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
4369 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
4370 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
4371 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
4372 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
4373 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
4374 | 10^(2*62938+1)-7*10^62938-1 | 125877 | Robert Price | 07/2023 |
4375 | 55*10^125847+9 | 125849 | Robert Price | 03/2022 |
4376 | 4*10^125832+57 | 125833 | Robert Price | 05/2022 |
4377 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
4378 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
4379 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
4380 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
4381 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
4382 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
4383 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
4384 | 30455^13464+13464^30455 | 125754 | Hans Havermann | 03/2021 |
4385 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
4386 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
4387 | 29755^16816+16816^29755 | 125737 | Hans Havermann | 03/2021 |
4388 | (22*10^125734+203)/9 | 125735 | Robert Price | 10/2021 |
4389 | 29918^15915+15915^29918 | 125710 | Hans Havermann | 03/2021 |
4390 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
4391 | 28531^25368+25368^28531 | 125659 | Hans Havermann | 03/2021 |
4392 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
4393 | (46*10^125642+593)/9 | 125643 | Robert Price | 04/2022 |
4394 | 2^417315+213953 | 125625 | Enzo Doria | 10/2023 |
4395 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
4396 | 30638^12537+12537^30638 | 125561 | Hans Havermann | 03/2021 |
4397 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
4398 | 30162^14525+14525^30162 | 125538 | Hans Havermann | 03/2021 |
4399 | (56*10^125535+583)/9 | 125536 | Robert Price | 08/2021 |
4400 | (23*10^125517-179)/3 | 125518 | Robert Price | 06/2022 |
4401 | 9*10^125516+29 | 125517 | Robert Price | 03/2022 |
4402 | (88*10^125492-637)/9 | 125493 | Robert Price | 11/2020 |
4403 | 28958^21525+21525^28958 | 125474 | Hans Havermann | 02/2021 |
4405 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
4404 | (10^125482+7)/162685667/1639829194459 | 125462 | Alfred Reich | 07/2021 |
4406 | 33889^5032+5032^33889 | 125449 | Hans Havermann | 03/2021 |
4407 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
4408 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
4409 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
4410 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
4411 | 33392^5697+5697^33392 | 125409 | Hans Havermann | 03/2021 |
4412 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
4413 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
4414 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
4415 | 27953^28198+28198^27953 | 125381 | Norbert Schneider | 01/2021 |
4416 | 31074^10837+10837^31074 | 125381 | Hans Havermann | 03/2021 |
4417 | 33745^5194+5194^33745 | 125380 | Hans Havermann | 03/2021 |
4418 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
4419 | 28360^26331+26331^28360 | 125365 | Hans Havermann | 03/2021 |
4420 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
4421 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
4422 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
4423 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
4424 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
4425 | (599*10^125224+13)/9 | 125226 | Robert Price | 02/2022 |
4426 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
4427 | 30054^14657+14657^30054 | 125207 | Hans Havermann | 03/2021 |
4428 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
4429 | 2^415884-933075 | 125194 | Paul Bourdelais | 06/2021 |
4430 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
4431 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
4432 | 10^125166-5001 | 125166 | Robert Price | 12/2021 |
4433 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
4434 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
4435 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
4436 | (11*10^125054+73)/3 | 125055 | Robert Price | 08/2021 |
4437 | (29*10^125021-113)/3 | 125022 | Robert Price | 10/2019 |
4438 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
4439 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
4440 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
4441 | (67*10^124990+77)/9 | 124991 | Robert Price | 10/2021 |
4442 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
4443 | 2^415092+111546435 | 124956 | Paul Bourdelais | 10/2021 |
4444 | 31936^8173+8173^31936 | 124946 | Hans Havermann | 03/2021 |
4445 | 5^178715-4 | 124916 | Tyler NeSmith | 07/2021 |
4446 | 29767^15700+15700^29767 | 124900 | Hans Havermann | 03/2021 |
4447 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
4448 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
4449 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
4450 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
4451 | (29*10^124765-71)/3 | 124766 | Robert Price | 07/2021 |
4452 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
4453 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
4454 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
4455 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
4456 | (23*10^124690+37)/3 | 124691 | Robert Price | 02/2022 |
4457 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
4458 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
4460 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
4459 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
4461 | 37373^2158+2158^37373 | 124604 | Hans Havermann | 03/2021 |
4462 | 29811^15112+15112^29811 | 124590 | Hans Havermann | 03/2021 |
4463 | 2^413781-2023 | 124561 | Riley Fisher | 09/2023 |
4464 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
4465 | 29757^15296+15296^29757 | 124521 | Hans Havermann | 03/2021 |
4466 | 35056^3561+3561^35056 | 124504 | Hans Havermann | 03/2021 |
4467 | 40588^1167+1167^40588 | 124487 | Hans Havermann | 02/2021 |
4468 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
4469 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
4470 | 35016^3581+3581^35016 | 124448 | Hans Havermann | 03/2021 |
4471 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
4472 | 28749^21298+21298^28749 | 124436 | Hans Havermann | 03/2021 |
4473 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
4474 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
4475 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
4476 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |
4477 | (68*10^124392-329)/9 | 124393 | Robert Price | 03/2021 |
4478 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
4479 | 10^124383+58407 | 124384 | Patrick De Geest | 08/2021 |
4481 | 10^124383-8000001 | 124383 | Robert Price | 04/2021 |
4480 | 10^124383-5801 | 124383 | Patrick De Geest | 08/2021 |
4482 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
4483 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
4484 | 34716^3811+3811^34716 | 124320 | Hans Havermann | 03/2021 |
4485 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
4486 | 10^124248+899089 | 124249 | Patrick De Geest | 05/2021 |
4488 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
4487 | 10^124248-501903 | 124248 | Patrick De Geest | 05/2021 |
4489 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
4490 | 29901^14272+14272^29901 | 124224 | Hans Havermann | 03/2021 |
4491 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
4492 | 29837^14500+14500^29837 | 124163 | Hans Havermann | 03/2021 |
4493 | 28074^26455+26455^28074 | 124158 | Hans Havermann | 03/2021 |
4494 | 2^412285+213317 | 124111 | Enzo Doria | 09/2023 |
4495 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
4496 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
4497 | (455*10^124093+31)/9 | 124095 | Robert Price | 06/2021 |
4498 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
4499 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
4500 | 28132^25735+25735^28132 | 124077 | Hans Havermann | 03/2021 |