## PRP Records

### Probable Primes Top 10000

#### (295765 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) !!!

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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 ? 9251 (26*10^100566+49)/3 100567 Robert Price 08/2019 9252 (21*2^334050+1)/935 100558 Lelio R Paula 12/2013 9253 24885^10984+10984^24885 100555 Hans Havermann 07/2018 9254 (1351^32119-1)/1350 100551 Serge Batalov 06/2022 9255 (78557*2^334018+1)/4326021 100548 Lelio R Paula 07/2014 9256 (35*10^100542+1)/9 100543 Serge Batalov 11/2010 9257 23578^18367+18367^23578 100538 Hans Havermann 07/2018 9258 13^90251+24 100535 Lelio R Paula 10/2016 9259 2^333963+789 100533 Lelio R Paula 08/2011 9260 2^333919-1840087 100520 Enzo Doria 06/2015 9261 (2^333916+1698)/2 100519 Stefano Morozzi 09/2020 9262 2^333911+72623 100518 Enzo Doria 04/2016 9263 24605^12168+12168^24605 100517 Hans Havermann 08/2018 9264 66*10^100502+7 100504 Robert Price 07/2020 9265 18^80064-67 100503 Lelio R Paula 10/2016 9266 (13*10^100487+137)/3 100488 Robert Price 06/2021 9267 23034^23034-12085^12085 100483 Serge Batalov 04/2024 9268 5^143742-48 100472 Lelio R Paula 10/2016 9269 24095^14784+14784^24095 100472 Hans Havermann 08/2018 9270 2^333757-112123 100471 Enzo Doria 06/2014 9271 (7953^25759-1)/7952 100470 Serge Batalov 06/2022 9272 23030^23030-7401^7401 100464 Serge Batalov 04/2024 9273 7*10^100457-57 100458 Robert Price 06/2020 9274 27358^4693+4693^27358 100444 Hans Havermann 07/2018 9275 8*10^100439-51 100440 Robert Price 08/2019 9276 2^333603-108861 100425 Enzo Doria 03/2014 9277 9*7^118818-2 100414 Lelio R Paula 11/2014 9278 2^333546-17097 100408 Enzo Doria 05/2013 9279 (19*10^100403+287)/9/3 100403 Alfred Reich 11/2022 9280 17^81597+72 100401 Lelio R Paula 10/2016 9281 (3613^28219-1)/3612 100396 Serge Batalov 06/2022 9282 p(20559)#/2+8 100384 Robert Price 01/2017 9283 11^96390-24 100380 Lelio R Paula 10/2016 9284 23011^23011+18846^18846 100373 Serge Batalov 04/2024 9285 (2^333385+2730)/2 100359 Stefano Morozzi 09/2020 9286 4832563059*2^333333+30029 100353 Donovan Johnson 01/2008 9287 23565^18136+18136^23565 100353 Hans Havermann 07/2018 9288 2^333354+763 100350 Lelio R Paula 08/2011 9289 (1608961*2^333333+1)/3 100349 Alex_soldier 09/2022 9290 (424517*2^333333+1)/5 100349 Alex_soldier 09/2022 9291 (887087*2^333333+1)/5 100349 Alex_soldier 09/2022 9292 (1159703*2^333333+1)/7 100349 Alex_soldier 09/2022 9293 (25*10^100343-67)/3 100344 Robert Price 06/2019 9294 V(486482)/9729641 100343 Serge Batalov 07/2024 9295 2^333289-109483 100330 Enzo Doria 04/2014 9296 (194^43853-1)/193 100325 Anonymous 06/2024 9297 2^333240-2790209 100316 Enzo Doria 03/2016 9298 23601^17798+17798^23601 100314 Hans Havermann 05/2018 9300 (2^333227-2^166614+1)/5 100311 11/2006 9299 2^333225+719 100311 Lelio R Paula 08/2011 9301 2^333221-2785333 100310 Enzo Doria 10/2015 9302 76^53332-75 100308 Norbert Schneider 02/2015 9303 (29*10^100302+583)/9 100303 Robert Price 06/2021 9304 6^128892-17573 100298 Enzo Doria 03/2013 9305 (47*10^100283-119)/9 100284 Robert Price 05/2019 9306 2^333105-113215 100275 Enzo Doria 07/2014 9307 (31*2^333102+1)/2375 100272 Lelio R Paula 11/2013 9308 4*10^100257-83 100258 Robert Price 10/2018 9309 17^81476-74 100253 Lelio R Paula 10/2016 9310 23392^19207+19207^23392 100199 Hans Havermann 06/2018 9311 (2^332830+750)/2 100192 Stefano Morozzi 09/2020 9312 (206*10^100189-17)/9 100191 Robert Price 01/2020 9313 17^81417-16 100180 Theodore Burton 11/2005 9314 (2^332773+590)/2 100175 Stefano Morozzi 09/2020 9315 2*23^73562+215 100172 Eric Chen 08/2023 9317 2^332739-113215 100165 Enzo Doria 07/2014 9316 (19*31^67163-199)/30 100165 Eric Chen 04/2024 9318 2^332730-1865621 100162 Enzo Doria 03/2016 9319 91^51127-2 100160 Lelio R Paula 09/2013 9320 15^85159-32 100155 Lelio R Paula 10/2016 9321 22963^22963+4620^4620 100143 Serge Batalov 04/2024 9322 22960^22960+9991^9991 100128 Serge Batalov 04/2024 9323 6^128661+97 100118 Lelio R Paula 10/2016 9324 19^78285+40 100108 Lelio R Paula 07/2016 9325 6^128640+5 100102 Lelio R Paula 11/2014 9326 10^100095+89973 100096 Patrick De Geest 10/2022 9327 10^100095-400001 100095 Robert Price 09/2021 9328 10^100095-203693 100095 Patrick De Geest 10/2022 9329 22779^22970-22970^22779 100093 Norbert Schneider 08/2020 9330 (2^332468+3130)/2 100083 Stefano Morozzi 09/2020 9331 (14*10^100075+61)/3 100076 Robert Price 12/2018 9332 (2^332435+3098)/2 100073 Stefano Morozzi 09/2020 9333 28562^3189+3189^28562 100072 Hans Havermann 05/2018 9334 10^100053+56193 100054 Alexander Weiss 04/2024 9335 6^128565-127 100044 Lelio R Paula 08/2016 9336 (2^332317+2106)/2 100038 Stefano Morozzi 09/2020 9338 2^332309-133 100035 Lelio R Paula 02/2011 9339 2^332307+731 100035 Lelio R Paula 07/2011 9337 937^33662-33662^937 100035 Norbert Schneider 05/2023 9340 2^332301+12927 100033 Lelio R Paula 04/2013 9341 17025^23642-23642^17025 100032 Norbert Schneider 04/2024 9342 23406^18781+18781^23406 100031 Hans Havermann 04/2018 9343 2^332277-4573 100026 Yves Minet 03/2019 9344 12^92684-13 100023 Lelio R Paula 07/2016 9345 70^54207-54207^70 100018 Norbert Schneider 04/2023 9346 78557*2^332193+55669 100005 Jorge Menendez 04/2019 9347 78557*2^332192+72689 100005 Jorge Menendez 04/2019 9348 10^100003+45799 100004 Stefano Morozzi 04/2019 9349 10^100003+155461 100004 Stefano Morozzi 04/2019 9350 10^100003+211389 100004 Stefano Morozzi 04/2019 9351 10^100003+381027 100004 Stefano Morozzi 04/2019 9352 10^100003+540703 100004 Stefano Morozzi 04/2019 9353 10^100003+823977 100004 Stefano Morozzi 04/2019 9365 10^100002+236023 100003 Stefano Morozzi 05/2018 9366 10^100002+433741 100003 Stefano Morozzi 05/2018 9354 2^332202+104659 100003 Stefano Morozzi 04/2019 9355 2^332202+857539 100003 Stefano Morozzi 04/2019 9356 2^332202+181773 100003 Stefano Morozzi 04/2019 9357 2^332202+687543 100003 Stefano Morozzi 04/2019 9358 2^332202+941595 100003 Stefano Morozzi 04/2019 9359 2^332202+445813 100003 Stefano Morozzi 04/2019 9360 2^332202+1599727 100003 Stefano Morozzi 04/2019 9361 2^332202+1389567 100003 Stefano Morozzi 04/2019 9362 2^332202+1206315 100003 Stefano Morozzi 04/2019 9363 2^332202+1958647 100003 Stefano Morozzi 04/2019 9364 10^100003-562857 100003 Patrick De Geest 07/2019 9367 (10^100002-1)/9-10^33441 100002 Akihiko Yoshida 03/2018 9368 (10^100002-1)/9-10^44692 100002 Akihiko Yoshida 03/2018 9369 10^100002-249519 100002 Patrick De Geest 07/2018 9370 10^100001+314199 100002 Patrick De Geest 07/2018 9421 25206!+p(4114) 100001 Henri Lifchitz 09/2005 9422 25206!-p(5447) 100001 Henri Lifchitz 10/2005 9423 25206!-p(12402) 100001 Henri Lifchitz 04/2006 9424 25206!-p(16290) 100001 Henri Lifchitz 09/2006 9425 25206!-p(19647) 100001 Henri Lifchitz 02/2007 9426 2^332194+11473 100001 Henri Lifchitz 03/2007 9416 10^100000+342909 100001 Milton L. Brown 12/2007 9417 10^100000+346579 100001 Robert Price 04/2012 9418 10^100000+829767 100001 Robert Price 05/2012 9419 10^100000+871899 100001 Robert Price 05/2012 9420 10^100000+1475997 100001 Robert Price 07/2012 9409 10^100000+1751769 100001 Robert Price 08/2012 9410 10^100000+2155489 100001 Robert Price 10/2012 9411 10^100000+2483527 100001 Robert Price 12/2012 9412 10^100000+2503087 100001 Robert Price 12/2012 9413 10^100000+2686179 100001 Robert Price 12/2012 9414 10^100000+2688933 100001 Robert Price 12/2012 9415 10^100000+3667159 100001 Robert Price 08/2013 9390 10^100000+3938473 100001 Robert Price 05/2015 9391 10^100000+3979761 100001 Robert Price 05/2015 9392 10^100000+4293973 100001 Robert Price 09/2015 9387 10^100000+4858267 100001 Robert Price 12/2015 9388 10^100000+5113299 100001 Robert Price 02/2016 9389 10^100000+5169411 100001 Robert Price 02/2016 9379 10^100000+5354043 100001 Robert Price 05/2016 9380 10^100000+5717979 100001 Robert Price 05/2016 9381 10^100000+6080631 100001 Robert Price 07/2016 9382 10^100000+6308469 100001 Robert Price 07/2016 9383 10^100000+6512023 100001 Robert Price 08/2016 9384 10^100000+6596557 100001 Robert Price 08/2016 9385 10^100000+7115409 100001 Robert Price 10/2016 9386 10^100000+7235803 100001 Robert Price 10/2016 9396 10^100000+7867333 100001 Robert Price 12/2016 9397 10^100000+8743093 100001 Robert Price 02/2017 9398 10^100000+8955391 100001 Robert Price 03/2017 9399 10^100000+9180019 100001 Robert Price 03/2017 9400 10^100000+9225987 100001 Robert Price 04/2017 9401 10^100000+9265587 100001 Robert Price 04/2017 9402 10^100000+9287049 100001 Robert Price 04/2017 9403 10^100000+9425053 100001 Robert Price 05/2017 9404 10^100000+9450769 100001 Robert Price 05/2017 9405 10^100000+9528747 100001 Robert Smith 05/2017 9406 10^100000+9548071 100001 Robert Price 06/2017 9407 10^100000+10064287 100001 Robert Price 08/2017 9408 10^100000+10229569 100001 Robert Price 10/2017 9371 10^100000+11187931 100001 Robert Price 03/2018 9372 10^100000+11264721 100001 Robert Price 04/2018 9373 10^100000+11477661 100001 Robert Price 05/2018 9374 10^100000+11644653 100001 Robert Price 07/2018 9375 10^100001-431439 100001 Patrick De Geest 07/2018 9376 10^100000+11769399 100001 Robert Price 08/2018 9377 10^100000+11848159 100001 Robert Price 08/2018 9378 10^100000+11863467 100001 Robert Price 08/2018 9393 10^100000+11992051 100001 Robert Price 09/2018 9394 2^332196-1-2*29696 100001 Matt Stath 11/2018 9395 10^100000+12363957 100001 Robert Price 11/2018 9427 2^332196+1+2*17152 100001 Matt Stath 12/2018 9428 10^100000+12778033 100001 Robert Price 02/2019 9429 10^100000+13581679 100001 Robert Price 05/2019 9430 10^100000+13613199 100001 Robert Price 05/2019 9431 10^100000+13752327 100001 Robert Price 05/2019 9432 10^100000+14139243 100001 Robert Price 06/2019 9433 10^100000+14151057 100001 Robert Price 06/2019 9434 10^100000+14218923 100001 Robert Price 06/2019 9435 10^100000+24543147 100001 Robert Price 08/2021 9436 10^100000+24781659 100001 Robert Price 08/2021 9437 10^100000+24906153 100001 Robert Price 08/2021 9438 10^100000+25682679 100001 Robert Price 10/2021 9439 10^100000+25905301 100001 Robert Price 10/2021 9440 10^100000+25923967 100001 Robert Price 10/2021 9441 10^100000+26061691 100001 Robert Price 10/2021 9442 10^100000+26173351 100001 Robert Price 11/2021 9443 10^100000+26673487 100001 Robert Price 11/2021 9444 10^100000+26849359 100001 Robert Price 12/2021 9445 10^100000+26893887 100001 Robert Price 12/2021 9446 10^100000+26954551 100001 Robert Price 12/2021 9447 10^100000+27024543 100001 Robert Price 12/2021 9448 10^100000+27060877 100001 Robert Price 12/2021 9449 10^100000+27617577 100001 Robert Price 03/2022 9450 10^100000+27869671 100001 Robert Price 03/2022 9451 10^100000+27956481 100001 Robert Price 03/2022 9452 10^100000+28078261 100001 Robert Price 03/2022 9453 10^100000+28150203 100001 Robert Price 03/2022 9454 10^100000+28626021 100001 Robert Price 05/2022 9455 10^100000+28649299 100001 Robert Price 05/2022 9456 10^100000+29409799 100001 Robert Price 06/2022 9457 10^100000+29415577 100001 Robert Price 06/2022 9458 10^100000+29424201 100001 Robert Price 06/2022 9459 10^100000+29610153 100001 Robert Price 07/2022 9460 10^100000+30166789 100001 Robert Price 07/2022 9461 10^100000+30338259 100001 Robert Price 07/2022 9462 10^100000+30540031 100001 Robert Price 07/2022 9463 10^100000+30635157 100001 Robert Price 07/2022 9464 10^100000+30762711 100001 Robert Price 07/2022 9465 10^100000+30862057 100001 Robert Price 07/2022 9466 10^100000+30998953 100001 Robert Price 07/2022 9467 10^100000+31405203 100001 Robert Price 07/2022 9468 10^100000+40159119 100001 Robert Price 07/2022 9469 10^100000+40181863 100001 Robert Price 07/2022 9470 10^100000+40277131 100001 Robert Price 07/2022 9471 10^100000+40326061 100001 Robert Price 07/2022 9472 10^100000+40417411 100001 Robert Price 07/2022 9473 10^100000+50049909 100001 Robert Price 07/2022 9474 10^100000+50510163 100001 Robert Price 07/2022 9475 10^100000+50591583 100001 Robert Price 07/2022 9476 10^100000+50850357 100001 Robert Price 07/2022 9477 10^100000+50974641 100001 Robert Price 07/2022 9478 10^100000+51046671 100001 Robert Price 07/2022 9479 10^100000+51459657 100001 Robert Price 07/2022 9480 10^100000+70081471 100001 Robert Price 07/2022 9481 10^100000+70159557 100001 Robert Price 07/2022 9482 10^100000+70262479 100001 Robert Price 07/2022 9483 10^100000+70417521 100001 Robert Price 07/2022 9484 10^100000+70476531 100001 Robert Price 07/2022 9485 10^100000+70534627 100001 Robert Price 07/2022 9486 10^100000+70873077 100001 Robert Price 07/2022 9487 10^100000+71114643 100001 Robert Price 07/2022 9488 10^100000+71272539 100001 Robert Price 07/2022 9489 10^100000+80025337 100001 Robert Price 07/2022 9490 10^100000+71580817 100001 Robert Price 07/2022 9491 10^100000+80270349 100001 Robert Price 07/2022 9492 10^100000+29831551 100001 Robert Price 07/2022 9493 10^100000+29955417 100001 Robert Price 08/2022 9494 479072067*10^99992+1+2*1779 100001 Matt Stath 12/2022 9495 10^100000+90000000+851439 100001 Robert Price 04/2023 9496 10^100000+90000000+1088017 100001 Robert Price 04/2023 9497 10^100000+90000000+1288173 100001 Robert Price 04/2023 9498 10^100000+90000000+1324549 100001 Robert Price 04/2023 9499 10^100000+90000000+3643869 100001 Robert Price 04/2023 9500 10^100000+110000000+60221 100001 Robert Price 04/2023

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2024 17:43 (Time in France)

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