## PRP Records

### Probable Primes Top 10000

#### (295756 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 ? 4751 11^123594-240 128710 Enzo Doria 09/2012 4752 2^427504-21503 128692 Enzo Doria 07/2013 4753 37727^2574+2574^37727 128673 Hans Havermann 04/2021 4754 29686^21591+21591^29686 128668 Hans Havermann 04/2021 4755 10^128668-70000000001 128668 Robert Price 08/2021 4756 10^128668-350729 128668 Alfred Reich 08/2024 4757 2^427420+91 128667 Lelio R Paula 05/2017 4758 8*10^128651-37 128652 Robert Price 03/2022 4759 (68*10^128645-257)/9 128646 Robert Price 07/2019 4760 2^427269-113635 128621 Enzo Doria 08/2014 4761 2^427130+1877569 128579 Enzo Doria 08/2016 4762 2^427068+20011 128561 Enzo Doria 06/2023 4763 2^427016-115349 128545 Enzo Doria 07/2015 4764 (4*10^128510+137)/3 128511 Robert Price 03/2018 4765 2^426889-112879 128507 Enzo Doria 06/2014 4766 2^426804+1869931 128481 Enzo Doria 05/2016 4767 2^426750+77635 128465 Enzo Doria 05/2016 4768 27708^28913-28913^27708 128450 Frank Doornink 03/2024 4769 36988^2969+2969^36988 128445 Hans Havermann 03/2021 4770 36664^3185+3185^36664 128439 Hans Havermann 03/2021 4771 32618^8649+8649^32618 128416 Hans Havermann 04/2021 4772 28883^27874+27874^28883 128391 Hans Havermann 04/2021 4773 2^426425-91 128367 Lelio R Paula 05/2017 4774 (15*2^426398-1)/11 128359 Lelio R Paula 05/2014 4775 2^426352+74971 128345 Enzo Doria 04/2016 4776 (199*10^128343-7)/3 128345 Robert Price 05/2020 4777 4*10^128343-21 128344 Robert Price 09/2018 4778 (65*10^128338+493)/9 128339 Robert Price 08/2021 4779 35632^3997+3997^35632 128337 Hans Havermann 04/2021 4780 2^426300-1863689 128330 Enzo Doria 03/2016 4781 2^426293+1881017 128327 Enzo Doria 11/2016 4782 (88*10^128324-637)/9 128325 Robert Price 11/2020 4783 (491*10^128285+31)/9 128287 Robert Price 04/2022 4784 39103^1908+1908^39103 128281 Hans Havermann 04/2021 4785 2^426043+35 128252 Robert Price 11/2015 4786 (4*10^128244-19)/3 128245 Robert Price 03/2018 4787 26220^29021-29021^26220 128234 Frank Doornink 03/2024 4788 35489^4102+4102^35489 128222 Hans Havermann 04/2021 4789 34721^4926+4926^34721 128208 Hans Havermann 04/2021 4790 (305*10^128198+1)/9 128200 Robert Price 02/2020 4791 2^425808-459959 128181 Enzo Doria 06/2015 4792 30632^15291+15291^30632 128178 Hans Havermann 04/2021 4793 U(623603) 128177 Serge Batalov 07/2024 4794 35981^3648+3648^35981 128167 Hans Havermann 04/2021 4795 2^425627-113605 128127 Enzo Doria 08/2014 4796 (4*10^128109+119)/3 128110 Robert Price 12/2021 4797 (22*10^128094+53)/3 128095 Robert Price 07/2019 4798 (86*10^128086-221)/9 128087 Robert Price 09/2019 4799 18565^30002-30002^18565 128070 Norbert Schneider 01/2015 4800 (2^425287-9)/2737 128021 Lelio R Paula 05/2015 4801 (3*2^425233-1)/25 128007 Lelio R Paula 05/2014 4802 Phi(149401,10)/30037901719561 128003 Makoto Kamada 07/2022 4803 2^425205+4911 128000 Marek Hubal 02/2017 4804 29241^23836+23836^29241 127995 Hans Havermann 04/2021 4805 2^425118-113663 127974 Enzo Doria 08/2014 4806 (86*10^127967-329)/9 127968 Robert Price 01/2020 4807 2^425061+1869761 127957 Enzo Doria 05/2016 4808 746^44541+44541^746 127955 Norbert Schneider 07/2019 4809 30236^17043+17043^30236 127946 Hans Havermann 03/2021 4810 2^424938+212419 127920 Enzo Doria 08/2023 4811 2^424918-21141 127914 Enzo Doria 07/2013 4812 (62*10^127903+91)/9 127904 Robert Price 07/2021 4813 2^424864-29489 127897 Enzo Doria 08/2015 4814 30438^15893+15893^30438 127877 Hans Havermann 02/2021 4815 (97*10^127858-1)/3 127860 Serge Batalov 12/2014 4816 28929^26258+26258^28929 127845 Hans Havermann 03/2021 4817 30563^15220+15220^30563 127828 Hans Havermann 03/2021 4818 2^424632-2786639 127827 Enzo Doria 03/2016 4819 10^127821-700001 127821 Robert Price 08/2021 4820 2^424577-113755 127811 Enzo Doria 09/2014 4821 (7*2^424512-1)/3 127792 Lelio R Paula 05/2014 4822 (56*10^127752+691)/9 127753 Robert Price 05/2019 4823 11^122629-720 127705 Enzo Doria 11/2012 4824 22*10^127645+3 127647 Robert Price 01/2020 4825 28715^27844+27844^28715 127631 Hans Havermann 03/2021 4826 (56*10^127612+187)/9 127613 Robert Price 10/2021 4827 (5*36^81995+821)/7 127609 Eric Chen 01/2021 4828 4*10^127562-39 127563 Robert Price 09/2020 4829 32595^8186+8186^32595 127547 Hans Havermann 03/2021 4830 2^423696-21429 127546 Enzo Doria 07/2013 4831 2^423664-1864559 127536 Enzo Doria 03/2016 4832 37889^2322+2322^37889 127530 Hans Havermann 03/2021 4833 37668^2429+2429^37668 127523 Hans Havermann 03/2021 4834 3^267267-4 127519 Henri Lifchitz 10/2014 4835 fibonacci(610144)-2 127513 Jon Grantham 08/2023 4836 26253^28852-28852^26253 127503 Frank Doornink 03/2024 4837 (103*10^127491+17)/3 127493 Robert Price 08/2020 4838 29376^21869+21869^29376 127487 Hans Havermann 03/2021 4839 31186^12241+12241^31186 127483 Hans Havermann 02/2021 4840 (19^99689+5^99689)/24 127477 Robert Price 09/2013 4841 27069^28754-28754^27069 127452 Frank Doornink 01/2024 4842 (21*2^423372+1)/101 127447 Lelio R Paula 05/2014 4843 30594^14645+14645^30594 127446 Hans Havermann 03/2021 4844 2^423328-21537 127435 Enzo Doria 07/2013 4845 (67*10^127413-7)/3 127415 Robert Price 01/2020 4846 (5*34^83193+700233)/11 127408 Eric Chen 08/2023 4847 (2*10^127407+73)/3 127407 Robert Price 09/2020 4848 (2^423165-7)/25 127384 Lelio R Paula 05/2015 4849 (7726^32768+1)/13917994151414876602369 127379 Kellen Shenton 04/2021 4850 (4*10^127349+17)/3 127350 Tyler Busby 01/2023 4851 29512^20647+20647^29512 127341 Hans Havermann 03/2021 4852 2^422987-3001935 127332 Paul Bourdelais 07/2023 4853 (112*10^127324+17)/3 127326 Robert Price 03/2020 4854 29565^20252+20252^29565 127321 Hans Havermann 03/2021 4855 fibonacci(609165)-3 127308 Jon Grantham 08/2023 4857 (F(5)^182099-F(4)^182099)/F(3) 127282 Wayne Halsdorf 08/2013 4856 (5^182099-3^182099)/2 127282 Kellen Shenton 05/2022 4858 (16*10^127259+197)/3 127260 Robert Price 04/2019 4859 (26*10^127240+61)/3 127241 Robert Price 10/2019 4860 (234483*27^88884-145)/26 127230 Curtis Bright 05/2015 4861 2^422515-114997 127190 Enzo Doria 06/2015 4862 5*10^127179-3 127180 Robert Price 07/2015 4863 31678^10343+10343^31678 127176 Hans Havermann 03/2021 4864 (44*10^127169-233)/9 127170 Robert Price 01/2019 4865 34947^4352+4352^34947 127162 Hans Havermann 03/2021 4866 6*10^127158+19 127159 Robert Price 11/2021 4867 30469^14902+14902^30469 127155 Hans Havermann 03/2021 4868 5*10^127153+77 127154 Robert Price 12/2018 4869 29941^17620+17620^29941 127130 Hans Havermann 02/2021 4870 31607^10516+10516^31607 127119 Hans Havermann 03/2021 4871 (19*10^127118-97)/3 127119 Robert Price 10/2021 4872 (29*10^127111+691)/9 127112 Robert Price 08/2021 4873 736^44335+44335^736 127104 Norbert Schneider 07/2019 4874 33040^7023+7023^33040 127090 Hans Havermann 03/2021 4875 (4*10^127081+167)/9 127081 Robert Price 03/2022 4876 29748^18661+18661^29748 127052 Hans Havermann 03/2021 4877 27905^28578-28578^27905 127049 Frank Doornink 03/2024 4878 -516776642557847117490*Bern(37960)/34256837217082767928421792453 127042 Thomas Ritschel 06/2017 4879 (78^67141-1)/77 127036 Paul Bourdelais 09/2017 4880 (14*10^127014-137)/3 127015 Robert Price 04/2021 4881 31436^10965+10965^31436 127002 Hans Havermann 03/2021 4882 28905^24758+24758^28905 127001 Hans Havermann 03/2021 4883 2^421860-113285 126993 Enzo Doria 07/2014 4884 (10^127030+7)/81234833/9230384921/6092460488946445358851 126991 Alfred Reich 07/2021 4885 (2^421827-7)/11 126982 Lelio R Paula 05/2015 4886 26268^28729-28729^26268 126966 Frank Doornink 03/2024 4887 11^121910-840 126957 Enzo Doria 12/2012 4888 (56*10^126935+187)/9 126936 Robert Price 10/2021 4889 28915^24538+24538^28915 126933 Hans Havermann 03/2021 4890 (29*10^126928-77)/3 126929 Robert Price 02/2020 4891 (259*10^126919-1)/3 126921 Robert Price 12/2020 4892 10^126919+204567 126920 Patrick De Geest 05/2021 4893 (2^421617+100280245065) 126920 Paul Bourdelais 05/2022 4894 10^126919-100001 126919 Robert Price 07/2020 4895 28340^28503+28503^28340 126907 Norbert Schneider 02/2021 4896 2^421534-3001935 126895 Paul Bourdelais 07/2023 4897 (71^68539+1)/72 126882 Paul Bourdelais 09/2017 4898 (5*10^126871-119)/3 126872 Robert Price 03/2018 4899 331^50339-10004 126846 Enzo Doria 07/2012 4900 2^421363-2790757 126843 Enzo Doria 03/2016 4901 (106*10^126839-1)/3 126841 Serge Batalov 12/2014 4902 37938^2203+2203^37938 126828 Hans Havermann 03/2021 4903 (13*10^126819+77)/9 126820 Robert Price 07/2022 4904 (7*2^421243+1)/39 126807 Lelio R Paula 05/2014 4906 (14*10^126784-83)/3 126785 Robert Price 12/2018 4905 2^421169-3001935 126785 Paul Bourdelais 07/2023 4907 2^421161-286183 126783 Enzo Doria 06/2015 4908 26733^28628-28628^26733 126738 Frank Doornink 03/2024 4909 (106*10^126726+17)/3 126728 Robert Price 04/2021 4910 30718^13347+13347^30718 126724 Hans Havermann 03/2021 4911 2^420939-113935 126716 Enzo Doria 10/2014 4912 11*23^93048+356 126708 Eric Chen 08/2023 4913 177^56363-2 126703 Lelio R Paula 10/2017 4914 2^420741-113659 126656 Enzo Doria 08/2014 4915 2^420694-21 126642 Lelio R Paula 05/2017 4916 (13*10^126638+437)/9 126639 Robert Price 04/2018 4917 (167*10^126637-17)/3 126639 Robert Price 03/2020 4918 4*10^126625+87 126626 Robert Price 08/2018 4919 (31*2^420556+1)/7 126601 Lelio R Paula 05/2014 4920 7*10^126600-99 126601 Robert Price 06/2019 4921 U(655247)/250330563881/206066063082749 126596 Serge Batalov 07/2024 4922 2^420424-59189 126561 Enzo Doria 10/2015 4923 28717^25534+25534^28717 126560 Hans Havermann 03/2021 4924 (86*10^126542+103)/9 126543 Robert Price 12/2021 4925 (19*10^126517-7)/3 126518 Robert Price 12/2023 4926 28922^23655+23655^28922 126503 Hans Havermann 03/2021 4927 2^420126+71893 126471 Enzo Doria 04/2016 4928 25982^28643-28643^25982 126450 Frank Doornink 03/2024 4929 (43*10^126441+47)/9 126442 Robert Price 12/2018 4930 8*10^126408+71 126409 Robert Price 05/2022 4931 2^419866+1877059 126393 Enzo Doria 07/2016 4932 29315^20484+20484^29315 126390 Hans Havermann 03/2021 4933 29433^19676+19676^29433 126384 Hans Havermann 03/2021 4934 F(604711) 126377 Henri Lifchitz 02/2005 4935 2^419757+72707 126360 Enzo Doria 04/2016 4936 2^419720-21569 126349 Enzo Doria 07/2013 4937 2^419637+29 126324 Henri Lifchitz 02/2006 4938 31004^11865+11865^31004 126319 Hans Havermann 03/2021 4939 2^419612+1876741 126316 Enzo Doria 07/2016 4940 2^419520+2793271 126289 Enzo Doria 03/2016 4941 (2^419447-5)/369 126264 Lelio R Paula 05/2014 4942 2^419328-1859939 126231 Enzo Doria 03/2016 4943 2^419282-1851507 126217 Enzo Doria 08/2015 4944 (133*10^126212+17)/3 126214 Robert Price 11/2021 4945 2^419251+1866143 126208 Enzo Doria 03/2016 4946 11^121185+2 126202 Robert Price 05/2014 4947 28203^28352+28352^28203 126175 Norbert Schneider 01/2021 4948 (23*2^419036-1)/1393 126141 Lelio R Paula 05/2014 4949 2^418851+23 126087 Robert Price 09/2015 4950 (2^418849-9)/2681 126083 Lelio R Paula 05/2014 4951 2^418829+167 126081 Lelio R Paula 01/2012 4952 31037^11530+11530^31037 126067 Hans Havermann 03/2021 4953 4*10^126064-69 126065 Robert Price 01/2022 4954 (31*2^418782-1)/75891 126063 Lelio R Paula 05/2014 4955 (19*2^418754-1)/15 126058 Lelio R Paula 05/2014 4956 (35*10^126048-323)/9 126049 Robert Price 10/2021 4957 33016^6551+6551^33016 126000 Hans Havermann 03/2021 4958 2^418548-111546435 125996 Paul Bourdelais 10/2021 4959 25134^28625-28625^25134 125958 Frank Doornink 12/2023 4960 34736^4227+4227^34736 125954 Hans Havermann 03/2021 4961 26197^28502-28502^26197 125930 Frank Doornink 03/2024 4962 2^418319-109501 125927 Enzo Doria 04/2014 4963 2^418316-112373 125926 Enzo Doria 06/2014 4964 40398^1309+1309^40398 125919 Hans Havermann 03/2021 4965 (8*10^125894-29)/3 125895 Robert Price 07/2018 4966 (26*10^125886-413)/9 125887 Robert Price 05/2018 4967 10^(2*62938+1)-7*10^62938-1 125877 Robert Price 07/2023 4968 55*10^125847+9 125849 Robert Price 03/2022 4969 4*10^125832+57 125833 Robert Price 05/2022 4970 2^417968+1869811 125821 Enzo Doria 06/2016 4971 2^417902+63 125802 Lelio R Paula 09/2015 4972 (10^125792-91)/9 125792 Serge Batalov 12/2014 4973 30438^13573+13573^30438 125791 Hans Havermann 03/2021 4974 32867^6714+6714^32867 125782 Hans Havermann 03/2021 4975 31155^10892+10892^31155 125777 Hans Havermann 03/2021 4976 (35*10^125754-593)/9 125755 Robert Price 07/2018 4977 30455^13464+13464^30455 125754 Hans Havermann 03/2021 4978 (32*10^125751-77)/9 125752 Robert Price 06/2018 4979 2^417704+77011 125742 Enzo Doria 05/2016 4980 29755^16816+16816^29755 125737 Hans Havermann 03/2021 4981 (22*10^125734+203)/9 125735 Robert Price 10/2021 4982 29918^15915+15915^29918 125710 Hans Havermann 03/2021 4983 (10^125706+149)/3 125706 Serge Batalov 12/2014 4984 28531^25368+25368^28531 125659 Hans Havermann 03/2021 4985 2^417419-115309 125656 Enzo Doria 07/2015 4986 (46*10^125642+593)/9 125643 Robert Price 04/2022 4987 2^417315+213953 125625 Enzo Doria 10/2023 4988 2^417300+77281 125620 Enzo Doria 05/2016 4989 30638^12537+12537^30638 125561 Hans Havermann 03/2021 4990 2^417095-1657 125559 Yves Minet 07/2014 4991 30162^14525+14525^30162 125538 Hans Havermann 03/2021 4992 (56*10^125535+583)/9 125536 Robert Price 08/2021 4993 (23*10^125517-179)/3 125518 Robert Price 06/2022 4994 9*10^125516+29 125517 Robert Price 03/2022 4995 (88*10^125492-637)/9 125493 Robert Price 11/2020 4996 28958^21525+21525^28958 125474 Hans Havermann 02/2021 4999 2^416773-25 125462 Lelio R Paula 09/2015 4997 (10^125482+7)/162685667/1639829194459 125462 Alfred Reich 07/2021 4998 26078^28409-28409^26078 125462 Frank Doornink 03/2024 5000 33889^5032+5032^33889 125449 Hans Havermann 03/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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