## PRP Records

### Probable Primes Top 10000

#### (294113 PRPs in the top)

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) !!!

See the Top discoverers
See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 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

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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