## PRP Records

### Probable Primes Top 10000

#### (293510 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 ? 9251 9*2^321336-7 96733 Lelio R Paula 08/2014 9252 (209*10^96722-17)/3 96724 Robert Price 05/2017 9253 (54163^20431-1)/54162 96710 Serge Batalov 06/2022 9254 2^321237-4615 96702 Yves Minet 05/2019 9255 (27273^21799-1)/27272 96691 Serge Batalov 06/2022 9256 2^321187-1159 96687 Yves Minet 11/2012 9257 2^321182-1850081 96686 Enzo Doria 08/2015 9259 23359^13768+13768^23359 96680 Hans Havermann 06/2020 9258 (65630^20071-1)/65629 96680 Serge Batalov 06/2022 9260 2^321116-112829 96666 Enzo Doria 06/2014 9261 2^321108-109499 96664 Enzo Doria 04/2014 9262 2^321098+2793859 96661 Enzo Doria 03/2016 9263 (2^321100+1170)/2 96661 Stefano Morozzi 09/2020 9264 2^321057+4097 96648 Lelio R Paula 06/2016 9265 (4435*29^66081-4)/7 96640 Curtis Bright 05/2015 9266 22743^17750+17750^22743 96640 Hans Havermann 04/2020 9267 22882^16679+16679^22882 96612 Hans Havermann 02/2020 9268 23452^13163+13163^23452 96608 Hans Havermann 02/2020 9269 (1042^32009-1)/1041 96596 Serge Batalov 06/2022 9270 (85*10^96594-373)/9 96595 Robert Price 05/2021 9271 (2^320863+666)/2 96590 Stefano Morozzi 09/2020 9272 p(19849)#/2-64 96581 Robert Price 04/2017 9273 2^320817+189 96576 Lelio R Paula 12/2012 9274 2^320816-4685 96576 Yves Minet 05/2019 9276 (361*10^96567-163)/9 96569 Robert Price 10/2017 9275 (19*10^96568+137)/3 96569 Robert Price 03/2022 9277 2^320788-110327 96567 Enzo Doria 05/2014 9278 (3065^27697-1)/3064 96561 Serge Batalov 06/2022 9279 2^320764+793 96560 Lelio R Paula 02/2013 9280 (2^320752+1842)/2 96556 Stefano Morozzi 02/2021 9281 (48331^20611-1)/48330 96542 Serge Batalov 06/2022 9282 (50595^20521-1)/50594 96529 Serge Batalov 06/2022 9283 (9179*2^320652-1)/221 96528 Lelio R Paula 05/2015 9284 23288^13947+13947^23288 96517 Hans Havermann 07/2020 9286 2^320616-78795 96516 Lelio R Paula 03/2016 9285 (19*10^96520+287)/9/109/409 96516 Alfred Reich 11/2022 9287 2^320612-461939 96514 Enzo Doria 07/2015 9288 (21245^22303-1)/21244 96507 Serge Batalov 06/2022 9289 10^96504+987654321 96505 Robert Price 12/2019 9290 10^96504+71887 96505 Patrick De Geest 02/2020 9291 22654^18195+18195^22654 96505 Hans Havermann 07/2020 9292 10^96504-139277 96504 Patrick De Geest 02/2020 9293 (218^41263-1)/217 96490 Serge Batalov 06/2022 9294 (47220^20641-1)/47219 96474 Serge Batalov 06/2022 9295 5*2^320431+7 96461 Lelio R Paula 08/2014 9296 19^75431-90 96458 Lelio R Paula 06/2016 9297 (11853^23677-1)/11852 96452 Serge Batalov 06/2022 9298 (2^320386+2814)/2 96446 Stefano Morozzi 02/2021 9299 (2^320370+3)/67 96440 Lelio R Paula 10/2013 9300 3*10^96431-17 96432 Robert Price 03/2021 9301 2^320309+1871477 96423 Enzo Doria 05/2016 9302 (10412^24001-1)/10411 96421 Serge Batalov 06/2022 9303 tau(809^6028) 96410 Nik Lygeros / Olivier Rozier / LR team 10/2013 9304 (29*10^96407-23)/3 96408 Robert Price 03/2022 9305 (21*2^320252-1)/1895 96404 Lelio R Paula 02/2014 9306 2^320232-173 96400 Lelio R Paula 12/2012 9307 175^42975-2 96395 Lelio R Paula 10/2017 9308 (2^320170+2718)/2 96381 Stefano Morozzi 09/2020 9309 10^96377+199911 96378 Patrick De Geest 12/2016 9310 10^96377-20001 96377 Robert Price 11/2016 9311 (18079^22639-1)/18078 96374 Serge Batalov 06/2022 9313 2^320124-2790449 96367 Enzo Doria 03/2016 9312 10^96366+19197 96367 Patrick De Geest 08/2021 9315 10^96366-10000000001 96366 Robert Price 04/2021 9314 10^96366-287367 96366 Patrick De Geest 08/2021 9316 (26351^21799-1)/26350 96365 Serge Batalov 06/2022 9317 22488^19255+19255^22488 96351 Hans Havermann 11/2019 9318 23248^13939+13939^23248 96346 Hans Havermann 11/2019 9319 (5928^25537-1)/5927 96345 Serge Batalov 06/2022 9321 2^320043-108775 96343 Enzo Doria 04/2014 9320 24989^7168+7168^24989 96343 Hans Havermann 11/2019 9322 10^96338+424939 96339 Patrick De Geest 03/2016 9323 10^96338-9281 96338 Robert Price 09/2015 9324 (8527^24509-1)/8526 96336 Serge Batalov 06/2022 9325 (3*2^320008+1)/7 96332 Lelio R Paula 09/2013 9326 (2444^28433-1)/2443 96331 Serge Batalov 06/2022 9327 (48690^20551-1)/48689 96327 Serge Batalov 06/2022 9328 (61935^20101-1)/61934 96318 Serge Batalov 06/2022 9329 25699^5596+5596^25699 96317 Hans Havermann 07/2020 9330 (7*10^96312+83)/9 96312 Tyler Busby 01/2023 9331 (11*10^96298+529)/9 96299 Robert Price 09/2021 9333 26502^4297+4297^26502 96287 Hans Havermann 07/2020 9332 (54180^20341-1)/54179 96287 Serge Batalov 06/2022 9334 2^319838+4257 96281 Lelio R Paula 03/2016 9335 2^319830-16995 96279 Lelio R Paula 03/2016 9336 6^123713+143 96268 Lelio R Paula 05/2016 9337 (28*10^96265-97)/3 96266 Robert Price 07/2016 9338 (3799^26893-1)/3798 96265 Serge Batalov 06/2022 9340 103^47825-102 96264 Norbert Schneider 10/2016 9339 (54041^20341-1)/54040 96264 Serge Batalov 06/2022 9341 (2^319777+2082)/2 96263 Stefano Morozzi 09/2020 9342 (2^319771+3686)/2 96261 Stefano Morozzi 09/2020 9343 2^319713-81 96244 Lelio R Paula 11/2012 9344 2^319711+213413 96243 Enzo Doria 09/2023 9345 (55459*2^319706+1)/20167 96242 Lelio R Paula 07/2014 9346 22834^16393+16393^22834 96238 Hans Havermann 05/2020 9347 8*10^96236+27 96237 Robert Price 09/2021 9348 12^89153-43 96213 Lelio R Paula 06/2016 9349 (25048^21871-1)/25047 96202 Serge Batalov 06/2022 9351 (2*10^96195-59)/3 96195 Robert Price 05/2017 9350 9*10^96194-77 96195 Robert Price 08/2020 9352 2^319545+147 96193 Lelio R Paula 11/2012 9353 23357^13128+13128^23357 96189 Hans Havermann 02/2020 9354 (19838^22381-1)/19837 96179 Serge Batalov 06/2022 9355 (221^41023-1)/220 96172 Serge Batalov 06/2022 9356 25952^5073+5073^25952 96160 Hans Havermann 12/2019 9357 (50891^20431-1)/50890 96157 Serge Batalov 06/2022 9358 (50^56597+1)/51 96155 Robert Price 03/2014 9359 22313^20374+20374^22313 96149 Hans Havermann 12/2019 9360 22279^20668+20668^22279 96141 Hans Havermann 11/2019 9361 (41*10^96137-59)/9 96138 Robert Price 10/2017 9362 2^319353-110343 96135 Enzo Doria 05/2014 9363 11^92309-42 96130 Lelio R Paula 05/2016 9364 (21675^22171-1)/21674 96129 Serge Batalov 06/2022 9365 14^83869-13^83869 96125 Jean-Louis Charton 01/2009 9366 (7*10^96112+143)/3 96113 Robert Price 04/2016 9367 26731^3940+3940^26731 96112 Hans Havermann 07/2020 9368 22640^17583+17583^22640 96109 Hans Havermann 07/2020 9369 (19178^22441-1)/19177 96107 Serge Batalov 06/2022 9370 2^319237+65835 96100 Lelio R Paula 03/2016 9371 2^319194-1841 96087 Yves Minet 03/2013 9372 23949^10280+10280^23949 96084 Hans Havermann 07/2020 9373 (1927^29251-1)/1926 96083 Serge Batalov 06/2022 9374 20^73847-31 96078 Lelio R Paula 05/2016 9375 (60229^20101-1)/60228 96075 Serge Batalov 06/2022 9376 (28044^21601-1)/28043 96074 Serge Batalov 06/2022 9377 50^56543-49 96065 Norbert Schneider 09/2018 9378 2^319107-109555 96061 Enzo Doria 04/2014 9379 (3*2^319114-1)/2627 96060 Lelio R Paula 02/2014 9380 2^319098-112157 96059 Enzo Doria 06/2014 9381 15^81673+94 96055 Lelio R Paula 07/2016 9382 (85761^19471-1)/85760 96052 Serge Batalov 06/2022 9383 2^319074+1871749 96051 Enzo Doria 05/2016 9384 25670^5517+5517^25670 96050 Hans Havermann 06/2020 9385 6*10^96037+19 96038 Robert Price 11/2021 9386 2^319007-112111 96031 Enzo Doria 06/2014 9387 (57987^20161-1)/57986 96029 Serge Batalov 06/2022 9389 2^318946-1421 96013 Yves Minet 01/2013 9388 (68310^19861-1)/68309 96013 Serge Batalov 06/2022 9390 (20294^22291-1)/20293 96012 Serge Batalov 06/2022 9391 (304^38669-1)/303 96008 Serge Batalov 06/2022 9392 (1840^29401-1)/1839 95986 Serge Batalov 06/2022 9393 22830^16003+16003^22830 95982 Hans Havermann 02/2020 9394 2^318834-110411 95979 Enzo Doria 05/2014 9395 2^318831-1965 95978 Lelio R Paula 03/2016 9396 (5*10^95976+7)/3 95977 Erik Branger 03/2014 9397 (12797^23369-1)/12796 95975 Serge Batalov 06/2022 9398 (10534^23857-1)/10533 95963 Serge Batalov 06/2022 9399 22871^15696+15696^22871 95962 Hans Havermann 01/2020 9400 (2^318760+858)/2 95957 Stefano Morozzi 02/2021 9401 23167^13860+13860^23167 95953 Hans Havermann 01/2020 9402 (823^32911-1)/822 95946 Serge Batalov 06/2022 9404 5*3^201089-8 95945 Lelio R Paula 08/2014 9403 (81783^19531-1)/81782 95945 Serge Batalov 06/2022 9405 2^318711-139 95942 Lelio R Paula 11/2012 9406 2^318635-1167 95919 Lelio R Paula 03/2016 9407 15^81555+16 95917 Lelio R Paula 07/2016 9408 (37*10^95895+377)/9 95896 Robert Price 10/2017 9409 (22699*2^318527+1)/21 95890 Lelio R Paula 07/2014 9410 2^318496-97305 95877 Lelio R Paula 03/2016 9411 22129^21496+21496^22129 95871 Hans Havermann 07/2020 9413 2^318466+15015 95868 Lelio R Paula 03/2016 9412 24847^7216+7216^24847 95868 Hans Havermann 07/2020 9414 23706^11065+11065^23706 95866 Hans Havermann 07/2020 9415 (2863^27733-1)/2862 95865 Serge Batalov 06/2022 9416 6^123187-173129 95859 Mike Oakes 04/2011 9417 2^318423-487 95855 Yves Minet 03/2012 9418 10^95848+443709 95849 Patrick De Geest 10/2022 9419 10^95848-5000000001 95848 Robert Price 09/2022 9420 10^95848-61971 95848 Patrick De Geest 10/2022 9421 (2^318359+678)/2 95836 Stefano Morozzi 09/2020 9422 (10223*2^318350+1)/1563 95834 Lelio R Paula 07/2014 9423 (8060^24533-1)/8059 95831 Serge Batalov 06/2022 9424 (9853^23993-1)/9852 95814 Serge Batalov 06/2022 9426 (2^318267+2550)/2 95808 Stefano Morozzi 09/2020 9425 (5048^25873-1)/5047 95808 Serge Batalov 06/2022 9428 4*10^95799+13 95800 Robert Price 02/2021 9427 (65533^19891-1)/65532 95800 Serge Batalov 06/2022 9429 2^318203+211343 95789 Enzo Doria 08/2023 9430 45369!2+1024 95787 Robert Price 02/2015 9431 3^200758-86 95786 Lelio R Paula 05/2016 9432 (2^318271+1)/(3*46031404238891*654090604244843) 95781 Gord Palameta 12/2018 9433 (2^318171+2030)/2 95779 Stefano Morozzi 09/2020 9434 3*10^95776-59 95777 Robert Price 10/2017 9435 (82970^19471-1)/82969 95772 Serge Batalov 06/2022 9436 193^41901-2 95768 Lelio R Paula 10/2017 9437 (2^318124+2502)/2 95765 Stefano Morozzi 09/2020 9438 (12900^23297-1)/12899 95761 Serge Batalov 06/2022 9439 4*10^95752-71 95753 Robert Price 11/2017 9440 (16955^22639-1)/16954 95743 Serge Batalov 06/2022 9441 (81795^19489-1)/81794 95740 Serge Batalov 06/2022 9442 (2742^27847-1)/2741 95737 Serge Batalov 06/2022 9443 (6072^25303-1)/6071 95726 Serge Batalov 06/2022 9444 23640^11197+11197^23640 95721 Hans Havermann 12/2019 9445 10^95712+89329 95713 Patrick De Geest 09/2022 9447 10^95712-4000001 95712 Robert Price 07/2021 9446 10^95712-989313 95712 Patrick De Geest 09/2022 9448 (60657^20011-1)/60656 95706 Serge Batalov 06/2022 9449 ((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/9 95704 Hans Havermann 05/2019 9450 (509203*2^317881-1)/52805 95693 Lelio R Paula 04/2015 9451 (26161^21661-1)/26160 95687 Serge Batalov 06/2022 9452 (2^317853+1086)/2 95683 Stefano Morozzi 09/2020 9453 4*10^95672+91 95673 Robert Price 11/2017 9454 6*10^95665+43 95666 Robert Price 07/2020 9455 (20819^22153-1)/20818 95663 Serge Batalov 06/2022 9456 (64464^19891-1)/64463 95658 Serge Batalov 06/2022 9457 (934^32203-1)/933 95652 Serge Batalov 06/2022 9458 (11*10^95641-113)/3 95642 Robert Price 01/2017 9459 (72330^19681-1)/72329 95632 Serge Batalov 06/2022 9460 (13224^23203-1)/13223 95624 Serge Batalov 06/2022 9461 (18211^22441-1)/18210 95602 Serge Batalov 06/2022 9462 (71975^19681-1)/71974 95590 Serge Batalov 06/2022 9463 (13*10^95588+11)/3 95589 Robert Price 05/2015 9464 Phi(191188,10)/191189 95587 Maksym Voznyy 11/2015 9465 (13368^23167-1)/13367 95585 Serge Batalov 06/2022 9466 (25874^21661-1)/25873 95583 Serge Batalov 06/2022 9467 3^200325+70 95580 Lelio R Paula 05/2016 9468 (25*10^95574-7)/9 95575 Robert Price 12/2014 9469 (2^317485-3)/21313 95569 Lelio R Paula 06/2013 9470 2^317464+31 95567 Lelio R Paula 11/2012 9471 (2^317451+2114)/2 95562 Stefano Morozzi 09/2020 9472 7^113073+82 95558 Lelio R Paula 04/2016 9473 (24728^21751-1)/24727 95552 Serge Batalov 06/2022 9474 (49764^20341-1)/49763 95536 Serge Batalov 06/2022 9475 (36155^20959-1)/36154 95531 Serge Batalov 06/2022 9476 (7725^24571-1)/7724 95526 Serge Batalov 06/2022 9477 (20546^22147-1)/20545 95510 Serge Batalov 06/2022 9478 2^317251+465 95503 Lelio R Paula 03/2016 9479 19^74684+58 95503 Lelio R Paula 06/2016 9480 (2^317250-7)/339 95500 Lelio R Paula 07/2013 9481 5*10^95498-21 95499 Robert Price 12/2021 9482 (21615^22031-1)/21614 95495 Serge Batalov 06/2022 9483 6^122718-79 95494 Lelio R Paula 05/2016 9484 22168^20291+20291^22168 95485 Hans Havermann 10/2019 9485 (77427^19531-1)/77426 95481 Serge Batalov 06/2022 9486 (13026^23203-1)/13025 95472 Serge Batalov 06/2022 9487 2^317141-110491 95469 Enzo Doria 05/2014 9488 (2^317097+3014)/2 95456 Stefano Morozzi 09/2020 9489 2^317094+76309 95455 Enzo Doria 05/2016 9490 2^317085+95 95453 Lelio R Paula 11/2012 9491 (17*10^95451-377)/9 95452 Robert Price 11/2017 9492 2^317057-109551 95444 Enzo Doria 04/2014 9493 3^200026+28 95437 Lelio R Paula 05/2016 9494 2^317024+93 95434 Donovan Johnson 06/2008 9495 (86*10^95428-437)/9 95429 Robert Price 03/2021 9496 10^95427+192591 95428 Patrick De Geest 05/2021 9499 2^316999+1605 95427 Lelio R Paula 03/2016 9498 (2^317000+3210)/2 95427 Stefano Morozzi 09/2020 9497 10^95427-10001 95427 Robert Price 02/2021 9500 2^316995-110427 95426 Enzo Doria 05/2014

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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