## PRP Records

### Probable Primes Top 10000

#### (293016 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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 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 (2^314740+3642)/2 94746 Stefano Morozzi 09/2020 9252 6^121756-16253 94745 Enzo Doria 02/2013 9253 (5*25^67773-2267)/6 94743 Eric Chen 04/2023 9254 2^314718-112793 94740 Enzo Doria 06/2014 9255 2^314697-1847293 94734 Enzo Doria 07/2015 9256 22836^14065+14065^22836 94727 Hans Havermann 09/2020 9257 2^314548-249 94689 Yves Minet 02/2012 9258 5^135469+42 94689 Lelio R Paula 04/2016 9259 gcd(V(1137755),5*F(227551)*(F(227551)-1)+1) 94676 Serge Batalov 04/2015 9260 25773^4712+4712^25773 94670 Hans Havermann 08/2020 9261 (2^314485+3614)/2 94670 Stefano Morozzi 09/2020 9262 (2*10^94604+547)/9 94604 Robert Price 10/2017 9263 (2^314164+2562)/2 94573 Stefano Morozzi 09/2020 9264 3*2^314152+5 94570 Lelio R Paula 08/2014 9265 2*6^121530-5 94570 Lelio R Paula 10/2014 9266 7*10^94563+87 94564 Robert Price 11/2016 9267 2^314114-109677 94558 Enzo Doria 04/2014 9268 (218389#+240867)/(3*11*811) 94557 Makoto Morimoto 10/2017 9269 2^314059+76583 94542 Enzo Doria 05/2016 9270 2^314041-4035 94536 Lelio R Paula 03/2016 9271 (2^314028+3102)/2 94532 Stefano Morozzi 09/2020 9272 (807*33^62250-7)/32 94529 Eric Chen 05/2023 9273 (2^314012+618)/2 94527 Stefano Morozzi 09/2020 9274 (7*2^314003-11)/15 94524 Renaud Lifchitz 03/2011 9275 11^90760-4710 94517 Enzo Doria 01/2013 9276 21675^21796+21796^21675 94507 Norbert Schneider 04/2020 9277 2^313942+100280245065 94506 Paul Bourdelais 10/2021 9278 (457829*27^66017-385)/26 94499 Eric Chen 02/2023 9279 (7*2^313926-1)/148821 94497 Lelio R Paula 02/2014 9280 94*10^94493-3 94495 Robert Price 11/2016 9281 (1000547^15749+1)/1000548 94492 Faysal YAtim 12/2008 9282 (2^313859+2706)/2 94481 Stefano Morozzi 09/2020 9283 (F(3*75345)^2+L(3*75345)^2)/4 94477 Henri Lifchitz 10/2017 9284 7^111792-32 94476 Lelio R Paula 04/2016 9285 (2^313800+822)/2 94463 Stefano Morozzi 01/2021 9286 9*10^94462-47 94463 Robert Price 11/2021 9287 11*10^94460+3 94462 Robert Price 07/2021 9288 (202*10^94441-1)/3 94443 Robert Price 05/2020 9289 11^90680-5850 94434 Enzo Doria 01/2013 9290 (752^32833-1)/751 94432 Michael Stocker 05/2020 9291 2^313675-110125 94426 Enzo Doria 04/2014 9292 (2999*29^64556-2427)/4 94410 Curtis Bright 05/2015 9293 2^313609-112225 94406 Enzo Doria 06/2014 9294 2^313584+72901 94399 Enzo Doria 04/2016 9295 (2^313567+1310)/2 94393 Stefano Morozzi 02/2021 9296 (2^313562+730)/2 94392 Stefano Morozzi 09/2020 9297 2^313510-112865 94376 Enzo Doria 06/2014 9298 7*10^94373+87 94374 Robert Price 11/2016 9299 (9^98897+8^98897)/17 94371 Robert Price 12/2012 9300 2^313453-114703 94359 Enzo Doria 04/2015 9301 8*10^94357-51 94358 Robert Price 10/2017 9302 25903^4392+4392^25903 94356 Hans Havermann 09/2020 9303 31706^945+945^31706 94340 Hans Havermann 09/2020 9304 (379*10^94337-1)/9 94339 Robert Price 08/2017 9305 2^313344-313344+1 94326 Robert Price 10/2014 9306 (2^313313+3662)/2 94317 Stefano Morozzi 09/2020 9307 20^72481-49 94300 Lelio R Paula 05/2016 9308 (34*10^94293-259)/9 94294 Robert Price 12/2021 9309 44725!2+128 94289 Robert Price 03/2015 9310 4*10^94286+9 94287 Robert Price 05/2015 9311 17^76621+24 94279 Lelio R Paula 07/2016 9312 26274^3875+3875^26274 94279 Hans Havermann 09/2020 9313 4*10^94270-33 94271 Robert Price 04/2021 9314 2^313156-112859 94270 Enzo Doria 06/2014 9315 (49*10^94262-211)/9 94263 Robert Price 06/2022 9316 6^121130-59 94258 Lelio R Paula 05/2016 9317 3^197542+28 94252 Robert Price 11/2013 9318 (2^313076+3550)/2 94245 Stefano Morozzi 09/2020 9319 (3^197521+2)/51655 94237 Lelio R Paula 04/2013 9320 2^313045-5955 94236 Lelio R Paula 03/2016 9321 22099^18358+18358^22099 94227 Hans Havermann 08/2020 9322 (9*33^62046+53831)/16 94218 Eric Chen 05/2023 9323 (67*10^94212+23)/9 94213 Ray Chandler 02/2011 9324 2^312909-1865203 94195 Enzo Doria 03/2016 9325 25013^5830+5830^25013 94191 Hans Havermann 09/2020 9326 2^312848-149 94177 Lelio R Paula 11/2012 9327 (2^312819+3278)/2 94168 Stefano Morozzi 02/2021 9328 4^156403-77597 94164 Mike Oakes 04/2011 9329 18^75004-85 94151 Lelio R Paula 06/2016 9330 (19573*10^94146-7)/9 94150 Patrick De Geest 05/2023 9331 19^73622-48 94145 Lelio R Paula 06/2016 9332 (11^90397-3^90397)/8 94138 Robert Price 04/2011 9333 (3^197287+5)/16 94129 Lelio R Paula 04/2013 9334 (23*10^94123-29)/3 94124 Robert Price 03/2022 9335 24220^7691+7691^24220 94119 Hans Havermann 09/2020 9336 12^87212-37 94118 Lelio R Paula 06/2016 9337 11^90376+76 94117 Lelio R Paula 05/2016 9338 (6^120946-11)/5 94114 Paul Bourdelais 11/2011 9339 (2^312622+534)/2 94109 Stefano Morozzi 09/2020 9340 (10^94096+191)/3 94096 Robert Price 11/2017 9341 23794^9005+9005^23794 94093 Hans Havermann 09/2020 9342 2^312562-112685 94091 Enzo Doria 06/2014 9343 137^44026-2 94072 Lelio R Paula 10/2017 9344 s(164441) 94052 Robert Price 05/2020 9345 2^312404-869688105 94043 Lelio R Paula 09/2016 9346 2^312387+2793533 94038 Enzo Doria 03/2016 9348 10^94016+91 94017 Robert Price 04/2011 9347 (15*2^312325-1)/7201 94017 Lelio R Paula 02/2014 9349 10^94016-188963 94016 Patrick De Geest 08/2013 9350 (17*2^312315-1)/45 94016 Lelio R Paula 02/2014 9351 (401*10^94010+13)/9 94012 Robert Price 09/2021 9352 23866^8691+8691^23866 94010 Hans Havermann 08/2020 9353 6^120802+7661 94003 Mike Oakes 04/2011 9354 (67607*2^312254+1)/177 94001 Lelio R Paula 06/2014 9355 (2^312245+702)/2 93995 Stefano Morozzi 09/2020 9356 (56*10^93993+493)/9 93994 Robert Price 10/2021 9357 (11*2^312207+1)/19 93984 Lelio R Paula 09/2013 9358 2^312201+51 93982 Lelio R Paula 11/2012 9359 (4*6^120749+1)/5 93961 Serge Batalov 10/2014 9360 (781*10^93942-7)/9 93944 Robert Price 12/2021 9361 3^196892+58 93942 Lelio R Paula 05/2016 9362 2^312060+18915 93940 Lelio R Paula 03/2016 9363 42^57867-41 93933 Norbert Schneider 08/2018 9364 8*10^93921+83 93922 Robert Price 11/2021 9365 2^311992-16209 93919 Enzo Doria 04/2013 9366 (85^48677+1)/86 93917 Paul Bourdelais 08/2017 9367 2^311965-39 93911 Lelio R Paula 11/2012 9368 2^311920-111689 93898 Enzo Doria 05/2014 9369 130^44414+129 93889 Norbert Schneider 01/2019 9370 (2^311892+2730)/2 93889 Stefano Morozzi 09/2020 9371 7*10^93887-47 93888 Robert Price 02/2017 9372 9*10^93878-37 93879 Robert Price 06/2021 9373 (28*10^93874+323)/9 93875 Robert Price 10/2021 9374 (2^311778+1530)/2 93855 Stefano Morozzi 09/2020 9375 12^86965-13 93851 Lelio R Paula 06/2016 9376 24862^5953+5953^24862 93848 Hans Havermann 09/2020 9377 22299^16148+16148^22299 93837 Hans Havermann 08/2020 9378 2^311705+16095 93833 Lelio R Paula 03/2016 9379 (2^311701+3002)/2 93832 Stefano Morozzi 09/2020 9380 norm(Mod(x,x^3-x-1)^768329-1) 93831 Paul Vanderveen 09/2022 9382 2^311665-81 93821 Lelio R Paula 11/2012 9381 (2^311665+2654)/2 93821 Stefano Morozzi 09/2020 9383 (2^311648+3058)/2 93816 Stefano Morozzi 09/2020 9384 (2^311639+2738)/2 93813 Stefano Morozzi 01/2021 9385 730^32761+32761^730 93806 Norbert Schneider 09/2017 9386 11^90073+92 93802 Lelio R Paula 05/2016 9387 6*10^93792+41 93793 Robert Price 01/2017 9388 10^93790+64611 93791 Patrick De Geest 04/2020 9391 (2^311580+7)/591329 93790 Lelio R Paula 06/2013 9389 10^93790-123456789 93790 Robert Price 02/2020 9390 10^93790-157517 93790 Patrick De Geest 04/2020 9392 (49*10^93782+293)/9 93783 Robert Price 03/2021 9393 12^86900-77 93781 Lelio R Paula 06/2016 9394 2^311508-109769 93774 Enzo Doria 04/2014 9395 2^311486-1859621 93767 Enzo Doria 03/2016 9396 Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831 93765 Kurt Beschorner 04/2015 9397 (10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831) 93765 Gord Palameta 10/2018 9398 2^311471+311469 93763 Renaud Lifchitz 01/2003 9399 (88*10^93760-1)/3 93762 Robert Price 10/2017 9400 2^311426+79459 93749 Enzo Doria 06/2016 9401 21537^21634+21634^21537 93745 Norbert Schneider 04/2020 9402 2^311409+111546435 93744 Paul Bourdelais 10/2021 9403 (2^311360+3078)/2 93729 Stefano Morozzi 09/2020 9404 (2^311341+2186)/2 93723 Stefano Morozzi 09/2020 9405 (2^311313+774)/2 93715 Stefano Morozzi 09/2020 9407 2^311294+5775 93709 Lelio R Paula 03/2016 9406 25155^5312+5312^25155 93709 Hans Havermann 09/2020 9408 2^311252-1017 93697 Lelio R Paula 03/2016 9409 2^311247-112041 93695 Enzo Doria 06/2014 9410 7*10^93692-83 93693 Robert Price 09/2017 9411 2^311205-109645 93683 Enzo Doria 04/2014 9412 5^134027-84 93681 Lelio R Paula 04/2016 9413 (2^311148-1017)/557 93663 Lelio R Paula 06/2013 9414 (2^311027-2^155514+1)/5 93628 11/2006 9415 26748^3161+3161^26748 93614 Hans Havermann 08/2020 9416 3^196192-28 93608 Robert Price 12/2013 9417 216091#+261433 93606 Makoto Morimoto 12/2015 9418 5^133917+68 93604 Lelio R Paula 04/2016 9419 2^310924-1709 93598 Yves Minet 03/2013 9420 24555^6476+6476^24555 93587 Hans Havermann 08/2020 9421 (2^310867+734)/2 93580 Stefano Morozzi 09/2020 9422 (266*10^93577-11)/3 93579 Robert Price 09/2016 9423 (16*10^93577+161)/3 93578 Robert Price 05/2016 9424 3^196113-56 93570 Lelio R Paula 04/2016 9425 2^310806-110345 93562 Enzo Doria 05/2014 9426 3^196093+86 93561 Lelio R Paula 04/2016 9427 2^310780-2327 93555 Yves Minet 10/2013 9428 30^63332+41 93550 Lelio R Paula 08/2012 9429 (21181*2^310707+1)/21 93536 Lelio R Paula 06/2014 9430 8*5^133807+7 93528 Lelio R Paula 10/2014 9431 2^310686+8193 93526 Lelio R Paula 03/2016 9432 22681^13282+13282^22681 93520 Hans Havermann 09/2020 9433 2^310646+63 93514 Lelio R Paula 11/2012 9434 (77*10^93508+31)/9 93509 Robert Price 10/2015 9435 ((2^103536+1)^3-2)/3 93502 Serge Batalov 03/2023 9436 (1000907^15583+1)/1000908 93499 Faysal YAtim 04/2009 9437 (2*10^93497+7)/9 93497 Erik Branger 03/2011 9438 3^195958-112852 93496 Enzo Doria 07/2014 9439 2^310583+16385 93495 Lelio R Paula 03/2016 9440 (9913*2^310557-1)/35 93490 Lelio R Paula 04/2015 9441 9*7^110614+2 93481 Lelio R Paula 11/2014 9442 (19*10^93467+83)/3 93468 Robert Price 08/2020 9443 2^310469-8295 93461 Lelio R Paula 03/2016 9444 2^310459-1159 93458 Yves Minet 11/2012 9445 6^120075-95 93437 Lelio R Paula 05/2016 9446 (2^310362+1758)/2 93428 Stefano Morozzi 09/2020 9447 256*19^73047+9 93412 Eric Chen 12/2022 9448 148^43041-147 93411 Norbert Schneider 05/2019 9449 2^310289+98327 93407 Yves Minet 11/2010 9450 21769^19510+19510^21769 93395 Hans Havermann 08/2020 9451 2^310217-113143 93385 Enzo Doria 07/2014 9452 7^110494-68 93379 Lelio R Paula 04/2016 9453 2^310184-113093 93375 Enzo Doria 07/2014 9454 2^310180-110417 93374 Enzo Doria 05/2014 9455 gcd(V(1124905),5*F(224981)*(F(224981)-1)+1) 93372 Serge Batalov 04/2015 9456 (2^310173+3150)/2 93372 Stefano Morozzi 09/2020 9457 3^195669+68 93358 Lelio R Paula 04/2016 9458 10^93356+91 93357 Robert Price 04/2011 9459 10^93356-28313 93356 Patrick De Geest 08/2013 9460 (85*10^93346+23)/9 93347 Robert Price 11/2015 9461 (3^195648-5)/3158276 93342 Lelio R Paula 04/2013 9462 10^93333+191061 93334 Patrick De Geest 09/2022 9464 10^93333-4000001 93333 Robert Price 07/2021 9463 10^93333-44807 93333 Patrick De Geest 09/2022 9465 3^195556+8680 93304 Lelio R Paula 04/2016 9466 2^309942-109991 93302 Enzo Doria 04/2014 9467 2^309926-1867301 93298 Enzo Doria 03/2016 9468 2^309924+85951 93297 Yves Minet 03/2011 9469 2^309896-4229 93288 Yves Minet 08/2018 9470 (86*10^93263-77)/9 93264 Robert Price 05/2016 9471 6^119836-125 93251 Lelio R Paula 05/2016 9472 (77*10^93249-257)/9 93250 Robert Price 10/2017 9473 21822^18749+18749^21822 93245 Hans Havermann 09/2020 9474 3^195430-2 93244 Theodore Burton 02/2007 9475 (13*10^93236+47)/3 93237 Robert Price 01/2017 9476 (67*10^93226-7)/3 93228 Robert Price 10/2017 9477 (86*10^93217-221)/9 93218 Robert Price 06/2017 9478 2^309637-16329 93211 Enzo Doria 04/2013 9479 (41*10^93207+49)/9 93208 Robert Price 04/2016 9480 14^81312-57 93194 Lelio R Paula 06/2016 9481 41^57783-40 93192 Theodore Burton 02/2007 9482 3*10^93179-97 93180 Robert Price 08/2017 9483 5*7^110252-4 93175 Lelio R Paula 11/2014 9484 22022^16959+16959^22022 93140 Hans Havermann 08/2020 9485 83061!4-512 93137 Robert Price 11/2019 9486 25169^5016+5016^25169 93135 Hans Havermann 08/2020 9487 (483641^16384+1)/2 93135 Richard Fischer 02/2021 9488 2^309380-27 93133 Lelio R Paula 11/2012 9489 25653^4268+4268^25653 93127 Hans Havermann 08/2020 9490 (2^309355+1826)/2 93125 Stefano Morozzi 02/2021 9491 (2^309334+2710)/2 93119 Stefano Morozzi 09/2020 9492 23*10^93116-7 93118 Robert Price 03/2016 9493 (2^309270+3214)/2 93100 Stefano Morozzi 09/2020 9494 (29*10^93082+1)/3 93083 Robert Price 11/2015 9495 (2^309198+3738)/2 93078 Stefano Morozzi 09/2020 9496 (58*10^93062-13)/9 93063 Robert Price 09/2015 9497 (2^309138+1794)/2 93060 Stefano Morozzi 01/2021 9498 2^309131+1869383 93058 Enzo Doria 05/2016 9499 (2^309114+3610)/2 93053 Stefano Morozzi 09/2020 9500 2^309066-93 93039 Lelio R Paula 11/2012

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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